Methods of Risk Pooling in Business Logistics
and Their Application
Inauguraldissertation
zur Erlangung des akademischen Grades
„Doktor der Wirtschaftswissenschaften“
(Dr. rer. pol.)
eingereicht an der
Wirtschaftswissenschaftlichen Fakultät
der Europa-Universität Viadrina
in Frankfurt (Oder)
im September 2010
von
Gerald Oeser
Frankfurt (Oder)
“Uncertainty is the only certainty there is,
and knowing how to live with insecurity is the only security.”
John Allen Paulos,
Professor of Mathematics at Temple University in Philadelphia
To my brother,
who never failed to support me
Acknowledgements
First and foremost I would like to express my gratitude to my Ph.D. advisor Prof. Dr.
Dr. h.c. Knut Richter, Chair of General Business Administration, especially Industrial
Management, European University Viadrina Frankfurt (Oder), Germany for his extensive
mentoring. He also kindly gave me the opportunity of gaining experience in teaching graduate courses in addition to my research.
For willingly delivering his expert opinion on my thesis as the second referee I thank
Prof. Dr. Joachim Käschel, Professorship of Production and Industrial Management, Technical University Chemnitz, Germany very much.
I would also like to gratefully acknowledge the support of all employees of Prof. Richter's chair, especially Dr. Grigory Pishchulov: Among other things, he helped me carry out
the “Subadditivity Proof for the Order Quantity Function (5.1)” in Appendix E mathematically formally correctly.
Furthermore, I thank Prof. Dr. Dr. h.c. Werner Delfmann, Director of the Department of
Business Policy and Logistics, University of Cologne, Germany for the opportunity offered
and for showing me that the world cannot be explained by mathematics alone.
Moreover, I appreciate the diverse support of the following professors during my Master's and doctoral studies: Ravi M. Anupindi (University of Michigan), Ronald H. Ballou
(Case Western Reserve University), Gérard Cachon (University of Pennsylvania), Ian
Caddy (University of Western Sydney, Australia), Sunil Chopra (Northwestern University), Chandrasekhar Das (emeritus, University of Northern Iowa), David Dilts (Oregon
Health and Science University), Bruno Durand (University of Nantes, France), Philip T.
Evers (University of Maryland), Amit Eynan (University of Richmond), Dieter Feige
(emeritus, University of Nuremberg, Germany), Jaime Alonso Gomez (EGADE - Tec de
Monterrey, Mexico City and University of San Diego), Drummond Kahn (University of
Oregon), Peter Köchel (emeritus, Technical University Chemnitz, Germany), David H.
Maister (formerly Harvard Business School), Alan C. McKinnon (Heriot-Watt University,
UK), Esmail Mohebbi (University of West Florida), Steven Nahmias (Santa Clara University), Teofilo Ozuna, Jr. (The University of Texas-Pan American), David F. Pyke (University of San Diego), Pietro Romano (University of Udine, Italy), Wolfgang Schmid (European University Viadrina Frankfurt (Oder), Germany), Yossi Sheffi (Massachusetts Institute of Technology), Edward Silver (emeritus, University of Calgary, Canada), Jacky YukChow So (University of Macau, China), Jayashankar M. Swaminathan (University of
North Carolina), Christian Terwiesch (University of Pennsylvania), Ulrich Thonemann
(University of Cologne, Germany), Biao Yang (University of York, UK), and Walter Zinn
(The Ohio State University).
I express gratitude to the paper merchant wholesaler Papierco for the insight into its operations, the opportunity of optimizing its logistics, and the financial support.
I am also thankful to my friends: Without them writing this dissertation would have
been a lonesome experience.
Finally, I thank my father for constantly pushing and financially supporting me and
proofreading my thesis.
Geleitwort
Die vorgelegte Dissertation widmet sich dem großen Thema Risk Pooling in der BusinessLogistik. Die Aggregation von Risiken der Logistikprozesse ist ein derart universelles
Problem, so dass Autoren verschiedenster Wissenschafts- und Anwendungsgebiete dazu
ihre Positionen, Lösungsansätze und Modelle dargestellt haben. Bisher hatte noch niemand
den Mut aufgebracht, diese kaum überblickbare Menge an Literaturquellen zu sichten und
nach wissenschaftlichen Kriterien zu ordnen. Herr Oeser hat sich dieser Aufgabe gestellt
und hat sie mit Bravour gemeistert.
Bei aller Bedeutung dieser aufwendigen akademischen Aktivitäten darf jedoch nicht vergessen werden, dass Risk Pooling ein Problem der Praxis ist, und dass die entsprechenden
theoretischen Untersuchungen letztendlich der Praxis dienen sollen. Die Vielfältigkeit des
Problems kann dabei kaum durch ein relevantes Basismodell erfasst werden. Es ist das
Verdienst des Autors, mit der Entwicklung einer Grundkonzeption für ein Entscheidungsunterstützungssystem zur Auswahl der geeigneten Risk Pooling Strategien Unternehmen
und besonders Unternehmensberatungen ein Instrument in die Hand zu geben, mit dem
sich die vielfältigen Situationen der Unternehmen analysieren lassen. Er belässt es jedoch
nicht beim Entwurf der Konzeption, sondern demonstriert auch überzeugend dessen Anwendung anhand eines Unternehmens.
Es ließen sich viele weitere Vorzüge des hier veröffentlichten Werkes nennen. Es soll an
dieser Stelle jedoch dem Leser überlassen bleiben sich ein Urteil zu bilden. Herr Oeser
bietet dem Leser mit seiner Dissertation auf jeden Fall keine „leichte Kost“, denn der behandelte Gegenstand lässt eine oberflächliche Betrachtung nicht zu.
Wer sollte dieses Werk lesen? Wissenschaftler und Studenten aus den Gebieten Operations
Management, Logistik, Operations Research werden hier viel Neues und Interessantes,
auch viele Probleme für die weitere Forschung finden. Unternehmensberatungen werden
viele angeführte Lösungen zur Komplexitätsbewältigung in ihren Projekten anwenden
können. Ich bin überzeugt, dass die vorgelegte Dissertation neue Forschungen und Projekte
anregen wird. Das ist das Schönste, was sich ein Autor wohl wünschen kann.
Prof. Dr. Dr. h.c. Knut Richter
Table of Contents
List of Figures .................................................................................................................... X
List of Tables ..................................................................................................................... XI
List of Abbreviations, Signs, and Symbols ................................................................... XII
Abstract
................................................................................................................... XIV
1
Introduction ................................................................................................. 1
1.1 Problem: Growing Uncertainty in Business Logistics and
Need for a Tool to Choose Among Risk Pooling Countermeasures ............ 1 1.2 Objective ....................................................................................................... 3 1.3 Object and Method ........................................................................................ 3 1.4 Structure and Contents .................................................................................. 4 2 Risk Pooling in Business Logistics ............................................................. 6 2.1 Business Logistics Risk Pooling Research ................................................... 6 2.2 Placing Risk Pooling in the Supply Chain, Business Logistics,
and a Value Chain ......................................................................................... 8 2.3
Defining Risk Pooling ................................................................................. 11 2.4 Explaining Risk Pooling ............................................................................. 14 2.5 Characteristics of Risk Pooling ................................................................... 19 3 Methods of Risk Pooling ........................................................................... 24 3.1 Storage: Inventory Pooling ......................................................................... 27 3.2 Transportation ............................................................................................. 35 3.2.1 Virtual Pooling ............................................................................................ 35 3.2.2 Transshipments ........................................................................................... 35 3.3 Procurement ................................................................................................ 40 3.3.1 Centralized Ordering ................................................................................... 40 3.3.2 Order Splitting ............................................................................................ 41 3.4 Production ................................................................................................... 43 3.4.1 Component Commonality ........................................................................... 43 3.4.2 Postponement .............................................................................................. 45 3.4.3 Capacity Pooling ......................................................................................... 49 VII
Table of Contents
3.5 Sales and Distribution ................................................................................. 51 3.5.1 Product Pooling ........................................................................................... 51 3.5.2 Product Substitution .................................................................................... 52 4 Choosing Suitable Risk Pooling Methods ............................................... 53 4.1 Contingency Theory .................................................................................... 53 4.2 Conditions Favoring the Individual Risk Pooling Methods ....................... 54 4.3 The Risk Pooling Methods' Advantages, Disadvantages,
Performance, and Trade-Offs ...................................................................... 55 4.4 A Risk Pooling Decision Support Tool ...................................................... 56 5 Applying Risk Pooling at Papierco .......................................................... 74 5.1 Papierco ....................................................................................................... 74 5.2 Problems Papierco Faces ............................................................................ 75 5.2.1 Fierce Competition in German Paper Wholesale ........................................ 75 5.2.2 Supplier Lead Time Uncertainty ................................................................. 75 5.2.3 Customer Demand Uncertainty ................................................................... 76 5.2.4 Distribution Requirements Planning (DRP) ............................................... 80 5.2.5 Demand Forecasting Methods .................................................................... 82 5.3 Solving Papierco's Problems ....................................................................... 87 5.3.1 Determining Suitable Risk Pooling Methods for Papierco ......................... 87 5.3.2 Emergency Transshipments between Papierco's German Locations .......... 91 5.3.2.1 Optimizing Catchment Areas ...................................................................... 91 5.3.2.2 Increase in Transshipments and Its Causes ................................................. 94 5.3.2.3 Transshipments Are Worthwhile for Papierco ........................................... 96 5.3.3 Centralized Ordering ................................................................................. 101 5.3.3.1 Papierco's Current Order Policy ............................................................... 101 5.3.3.2 Stock-to-Demand Order Policy with Centralized Ordering and
Minimum Order and Saltus Quantities ..................................................... 105 5.3.3.3 Benefits of Centralized Ordering for Papierco ......................................... 107 5.3.4 Product Pooling ......................................................................................... 117 5.3.5 Inventory Pooling ...................................................................................... 118 5.3.6
Challenges in IT and Organization ........................................................... 121 5.4
Summary ................................................................................................... 123 6 Conclusion ............................................................................................... 126 VIII
Table of Contents
Appendix A: A Survey on Risk Pooling Knowledge and Application in
102 German Manufacturing and Trading Companies ........................ 134 1 Introduction ............................................................................................. 135 1.1 Motivation: Scarce Survey Research on Risk Pooling ............................. 135 1.2 Objective ................................................................................................... 140 2 The Survey ............................................................................................... 142 2.1 Research Design ........................................................................................ 142 2.2 Data Analysis and Findings ...................................................................... 147 2.2.1 Risk Pooling Knowledge and Utilization in
the German Sample Companies ................................................................ 147 2.2.2 Association between the Knowledge of
Different Risk Pooling Concepts .............................................................. 151 2.2.3 Association between Knowledge and Utilization of
Risk Pooling Concepts .............................................................................. 154 2.2.4 Association of the Utilization of Different Risk Pooling Concepts ........... 156 2.2.5 Risk Pooling Knowledge and Utilization in
the Responding Manufacturing and Trading Companies ......................... 161 2.2.6 Knowledge and Utilization of the Different Risk Pooling Concepts
in Small and Large Responding Companies ............................................. 164 3 Critical Appraisal .................................................................................... 166 4 Questionnaire .......................................................................................... 169 5 Answers .................................................................................................... 170 Appendix B: Proof of the Square Root Law for Regular, Safety, and
Total Stock ............................................................................................... 172 Appendix C: What Causes the Savings in Regular Stock through Centralization
Measured by the SRL? ........................................................................... 176 Appendix D: Tables ....................................................................................................... 178 Appendix E: Subadditivity Proof for the Order Quantity Function (5.1) ............... 202 Bibliography .................................................................................................................... 204 IX
List of Figures
Figure 2.1:
Number of Publications on Risk Pooling in Business Logistics .................. 7 Figure 2.2:
Placing Risk Pooling in Business Logistics .................................................. 9 Figure 2.3:
Important Value Activities Using Risk Pooling Methods .......................... 11 Figure 4.1:
Risk Pooling Decision Support Tool .......................................................... 56 Figure 5.1:
Total Fine Paper Sales in Tons per Month in Germany
(BVdDP 2010a: 8) ...................................................................................... 76 Figure 5.2:
Papierco's Total Fine Paper Sales to Customers in Germany
in Tons per Month ....................................................................................... 77 Figure 5.3:
Papierco's 2007 Warehouse Sales to Customers per Week
of Seven Standard Paper Products from the Hemmingen Warehouse ........ 78 Figure 5.4:
2007 Incoming Goods, Warehouse Sales, and Inventory at
Warehouse Hemmingen .............................................................................. 80 Figure 5.5:
2007 Incoming Goods, Warehouse Sales, and Inventory at
Warehouse Reinbek .................................................................................... 81 Figure 5.6:
Comparison of Current and Optimal Catchment Areas of Papierco's
Warehouses ................................................................................................. 93 Figure 5.7:
Inventory Turnover Curves for Papierco .................................................. 104 Figure 5.8a:
Product Purchase Planning at Papierco's Member Companies ................. 120 Figure 5.8b:
Product Purchase Planning at Papierco's Member Companies ................. 120 Figure 5.9:
Stockkeeping at Papierco's Warehouses in February 2008 ...................... 121 Figure A.1:
Risk Pooling Knowledge and Utilization in
the German Sample Companies ................................................................ 147 Figure A.2:
Risk Pooling Knowledge and Utilization in the
Sample Manufacturing and Trading Companies ...................................... 161 Figure A.3:
Knowledge and Utilization of the Different Risk Pooling Concepts in
Small and Large Responding Companies ................................................. 164 Figure A.4:
Questionnaire ............................................................................................ 169 X
List of Tables
Table 3.1:
Risk Pooling Methods' Building Blocks ..................................................... 26 Table 5.1:
The Extent of Transshipments at Papierco ................................................. 94 Table 5.2:
Effects of Centralized Ordering at Papierco ............................................. 109 Table A.1:
Comparing Respondents with the Total Population of
Manufacturing and Trading Companies in Germany ............................... 143 Table A.2:
Significant Correlations at the 5 % Level of
the Knowledge of Risk Pooling Concepts ................................................ 154 Table A.3:
Significant Correlations at the 5 % Level (except in the case Product
Substitution/Demand Reshape) between Knowledge and
Utilization of Risk Pooling Concepts ....................................................... 155 Table A.4:
Significant Correlations at the 5 % Level between the Utilization of
Risk Pooling Concepts .............................................................................. 160
Table A.5:
Survey Participants' Answers to the Questionnaire .................................. 171 Table D.1:
Fulfillment of the SRL's Assumptions by Eleven Surveyed Companies .. 178 Table D.2:
Comparison of Important Inventory Consolidation Effect,
Portfolio Effect, and Square Root Law Models ........................................ 179 Table D.3:
Conditions Favoring the Various Risk Pooling Methods ......................... 185 Table D.4
The Risk Pooling Methods' Advantages, Disadvantages,
Performance, and Trade-Offs .................................................................... 195 XI
List of Abbreviations, Signs, and Symbols
Common general, business, logistics, supply chain management (SCM), operations research (OR), mathematical, and statistical abbreviations, signs, and symbols apply1 and are
not listed here.
CC
component commonality
CE
consolidation effect
CO
centralized ordering
COE
centralized ordering effect
COV
coefficient of variation of demand
CP
capacity pooling
CS
cycle stock
Dipl.-Kfm.
Diplomkaufmann (MBA equivalent)
DP
demand pooling
DUR
demand uncertainty reduction
EFR
effective fill rate for the customer
ELT
emergency lateral transshipment
EOS
economies of scale
FR
item fill rate
IC
inventory holding cost
i. i. d.
independent and identically distributed
IP
inventory pooling
ITO
in terms of
LP
lead time pooling
LT
lead time
LTUR
lead time or lead time uncertainty reduction
n. e. c.
not elsewhere classified
NLT
endogenous lead times
OP
order policy
OS
order splitting
1
Cf. e. g. Soanes and Hawker (2008), Friedman (2007), Lowe (2002), Obal (2006), Silver et al. (1998) and
Slack (1999), Clapham and Nicholson (2009), and Dodge (2006).
XII
List of Abbreviations, Signs, and Symbols
PCE
portfolio cost effect
PE
portfolio effect
PM
postponement
PoD
point of (product) differentiation
PP
product pooling
PQE
portfolio quantity effect
PRE
proportional reduction of error
PS
product substitution
RMSE
root mean square error
RPDST
risk pooling decision support tool
RS
regular stock
SL
transshipment sending location
SLA
service level adjustment
sqrt
square root
SRL
square root law
SS
safety stock
TC
transportation cost
TS
transshipments
TSC
transshipment cost
VP
virtual pooling
vs.
versus, here: is traded off against
XLT
exogenous lead times
≈
is approximately equal to
≻
is preferred to
XIII
Abstract
Purpose/topicality: Demand and lead time uncertainty in business logistics increase, but can
be mitigated by risk pooling. Risk pooling can reduce costs for a given service level, which is
especially valuable in the current economic downturn. The extensive, but fragmented and inconsistent risk pooling literature has grown particularly in the last years. It mostly deals with
specific mathematical models and does not compare the various risk pooling methods in terms
of their suitability for specific conditions.
Approach: Therefore this treatise provides an integrated review of research on risk
pooling, notably on inventory pooling and the square root law, according to a value-chain
structure. It identifies ten major risk pooling methods and develops tools to compare and
choose between them for different economic conditions following a contingency approach.
These tools are applied to a German paper merchant wholesaler, which suffers from customer demand and supplier lead time uncertainty. Finally, a survey explores the knowledge
and usage of the various risk pooling concepts and their associations in 102 German manufacturing and trading companies. Triangulation (combining literature, example, modeling,
and survey research) enhances our investigation.
Originality/value: For the first time this research presents (1) a comprehensive and
concise definition of risk pooling distinguishing between variability, uncertainty, and risk,
(2) a classification, characterization, and juxtaposition of risk pooling methods in business
logistics on the basis of value activities and their uncertainty reduction abilities, (3) a decision support tool to choose between risk pooling methods based on a contingency approach, (4) an application of risk pooling methods at a German paper wholesaler, and (5) a
survey on the knowledge and utilization of risk pooling concepts and their associations in
102 German manufacturing and trading companies.
XIV
1
Introduction
1.1
Problem: Growing Uncertainty in Business Logistics and
Need for a Tool to Choose Among Risk Pooling
Countermeasures
Product variety has increased dramatically in almost every industry2 particularly due to increased customization3. Product life cycles have become shorter, demand fluctuations more
rapid, and products can be found and compared easily on the internet.4
This causes difficulties in forecasting for an increased number of products, demand and
lead time uncertainty, intensified pressure for product availability, and higher inventory
levels5 to provide the same service6. This trend is expected to continue and likely grow
worse.7
Supply chains8 are more susceptible to disturbances today because of their globalization, increased dependence on outsourcing and partnerships, single sourcing, little leeway
in the supply chain, and increasing global competition.9 Disruptions, such as production or
shipment delays, affect profitability (growth in operating income, sales, costs, assets, and
inventory).10
Risk pooling is “[o]ne of the most powerful tools used to address [demand and/or lead
time] variability in the supply chain”11 particularly in a period of economic downturn12, as
it allows to reduce costs and to increase competitiveness.
2
3
4
5
6
7
8
9
10
11
12
Cox and Alm (1998), Van Hoek (1998a: 95), Aviv und Federgruen (2001a), Ihde (2001: 36), Piontek
(2007: 86), Ganesh et al. (2008: 1124f.).
Ihde (2001: 36), Chopra and Meindl (2007: 305), Piontek (2007: 86).
Rabinovich and Evers (2003a: 226), Chopra and Meindl (2007: 305, 333).
Dubelaar et al. (2001: 96).
Ihde (2001: 36), Swaminathan (2001: 125ff.), Chopra and Meindl (2007: 305, 333), Rumyantsev and
Netessine (2007: 1)
Cecere and Keltz (2008).
“A supply chain consists of all parties involved, directly or indirectly, in fulfilling a customer request.
The supply chain includes not only the manufacturer and suppliers, but also transporters, warehouses, retailers, and even customers themselves” (Chopra and Meindl 2007: 3).
Dilts (2005: 21). These ideas of Professor David M. Dilts, Owen Graduate School of Management, Vanderbilt University, have not appeared in a formal publication yet. He granted us permission to cite them as
personal correspondence on July 23, 2008.
Hendricks and Singhal (2002, 2003, 2005a, 2005b, 2005c), Hoffman (2005).
Simchi-Levi et al. (2008: 48). We will differentiate between the often confused terms variability, uncertainty, and risk in section 2.3.
Cf. Hoffman (2008), Chain Drug Review (2009a), Hamstra (2009), Orgel (2009), Pinto (2009b), Ryan
(2009).
1
1 Introduction
Although “risk pooling is often central to many recent operational innovations and
strategies”13, an important concept in business logistics and supply chain management
(SCM)14, and was already described in logistics in 196715, it is mentioned in few German
text books16 mostly limited to the square root law (SRL). Most other publications also only
consider inventory pooling17 or a single other type18 of risk pooling19. Exceptions are Neale
et al. (2003: 44f., 50, 55), Fleischmann et al. (2004: 70, 93), Taylor (2004: 301ff.), Muckstadt (2005: 150ff.), Reiner (2005: 434), Anupindi et al. (2006), Heil (2006), Brandimarte
and Zotteri (2007: 30, 36, 38, 39, 57, 58, 70), Sheffi (2007), Simchi-Levi et al. (2008), Sobel (2008: 172), Van Mieghem (2008), Cachon and Terwiesch (2009), and Bidgoli (2010).
Our survey of 102 German manufacturing and trading companies of various sizes and
industries (see appendix A20) showed that the different risk pooling concepts are known
fairly well, but not widely applied despite their potential benefits. Choosing risk pooling
methods is difficult for companies, as the literature does not compare the various methods
in terms of their suitability for certain conditions holistically.21 Most of the work in risk
13
14
15
16
17
18
19
20
21
Cachon and Terwiesch (2009: 350).
Romano (2006: 320).
Flaks (1967: 266).
For example Pfohl (2004a: 115ff.), Tempelmeier (2006: 41f., 153f.), Bretzke (2008: 147, 152, 154).
For example Bramel and Simchi-Levi (1997: 219f.), Martinez et al. (2002: 14), Christopher and Peck
(2003: 132), Dekker et al. (2004: 32), Ghiani et al. (2004: 9), Daskin et al. (2005: 53f.), Li (2007: 210),
Taylor (2008: 13-3), Mathaisel (2009: 19), Shah (2009: 89f.), Wisner et al. (2009: 513).
A type is “a category of […] things having common characteristics” (Soanes and Hawker 2008). We
distinguish ten main types of risk pooling that have in common that they may reduce total demand and/or
lead time variability and thus uncertainty and risk by pooling individual demand and/or lead time variabilities. We call them methods (e. g. in the title of this treatise), whenever we focus on the ways of risk
pooling, as a method is “a way of doing something” (Soanes and Hawker 2008). If the focus is on choosing and implementing one or several risk pooling methods for a specific company under specific conditions, we refer to this as risk pooling strategy. A strategy is “a plan designed to achieve a particular longterm aim” (Soanes and Hawker 2008). In the case of risk pooling this plan can comprise one or more risk
pooling methods combined in order to reduce demand and/or lead time uncertainty. We use the term concept, if we aim at the “abstract idea” (Soanes and Hawker 2008) or would like to include the SRL, PE,
and inventory turnover curve, which are rather tools to measure the risk pooling effect on inventories than
risk pooling methods.
Pfohl (2004b: 126, 355), Enarsson (2006: 178).
For the sake of readability and content unity we placed the survey in the appendix.
However, Evers (1999) compares inventory centralization, transshipments, and order splitting. Swaminathan (2001) designs a framework for deciding between part and procurement standardization (component
commonality), process standardization (postponement), and product standardization (substitution) according to product and process modularity, Wanke and Saliby (2009: 690) one for choosing between inventory centralization (demand pooling) and regular transshipments (“serving […] demands from all centralized facilities” and enabling demand and lead time pooling). Benjaafar et al. (2004a, 2005) find in systems with endogenous supply lead times, multisourcing (Benjaafar et al. 2004a: 1441f., 1446) and capacity pooling (Benjaafar et al. 2005: 550, 563) perform better than inventory pooling, if utilization (arrival
rate divided by service rate) is high. Eynan and Fouque (2005) show that demand reshape is more efficient than component commonality.
2
1 Introduction
pooling is rather focused on one aspect and holistic treatments are rare.22 There is little
empirical and – to our knowledge – no survey research on the various methods of risk
pooling combined. Most publications develop mathematical models for a specific risk
pooling method under certain assumptions and (optimal inventory) policies that minimize
inventory for a given service level or maximize service level for a given inventory. They
do not explore whether this risk pooling method is the best for the given situation or
whether it can be combined with other ones.
1.2
Objective
Thus the objective of this treatise is to advance research on and aid practice in selecting and
applying risk pooling methods in business logistics. More specifically, the aims of this research
can be formulated as follows:
1.
Develop the first comprehensive and concise definition of risk pooling.
2.
Critically review and structure the research on risk pooling within a value-chain
framework according to this definition.
3.
Develop tools to compare and choose appropriate risk pooling methods and models for different economic conditions with a contingency approach.
4.
Apply these tools to a German paper merchant wholesaler, which faces customer
demand and supplier lead time uncertainty.
5.
Examine the knowledge and usage of the various risk pooling concepts and their
associations in 102 German trading and manufacturing companies by means of a
survey.
1.3
Object and Method
The research object (German: Erfahrungsgegenstand) is an empirical phenomenon (a part of
reality) that is to be described. The scientific object or selection principle (German: Erkenntnisgegenstand) is the perspective and specific question used to examine the research object.23
Our research object comprises business logistics in a company that experiences demand and/or lead time uncertainty. Our scientific object is risk pooling that can decrease
this uncertainty of the company, which is perceived as a collection of value activities (val22
23
Personal correspondence with Professor Christian Terwiesch, The Wharton School, University of Pennsylvania on July 2, 2008.
Schneider (1987: 34f.), Chmielewicz (1994: 19ff.), Söllner (2008: 5), Neus (2009: 2).
3
1 Introduction
ue chain approach). Business logistics plans, organizes, handles, and controls all material,
product, and information flows across these value activities24 in an efficient, effective, and
customer-oriented manner (logistics perspective). Our main specific research questions
are: What risk pooling methods are available? What economic conditions make the individual methods worthwhile? How can a company choose adequate risk pooling methods?
We derive the adequacy of the identified risk pooling methods from contingency factors
(contingency approach).
In order to enhance the quality of our research we use triangulation25 to gather various
types of information26 on risk pooling by literature, example, modeling, and survey research. This integrated approach also accounts for our holistic ambition and leads to results
not attainable by the individual research methods separately27. Weaknesses of some methods can be balanced by the strengths of others.28 Van Hoek (2001: 182f.) already proposed triangulation to improve research on postponement, one type of risk pooling. For
problems of triangulation, such as coping with conflicting results, epistemological problems, and the debatable higher validity of findings, please refer to e. g. Bryman (1992:
63f.), Denzin and Lincoln (2005: 912), Blaikie (1991: 122f.), and Fielding and Fielding
(1986: 33). A holistic approach may not be as profound as an atomistic one. However, as
noted before such a holistic approach is novel to risk pooling research.
1.4
Structure and Contents
This treatise is divided into six chapters and an appendix. After this introduction (chapter 1),
we outline previous risk pooling research in business logistics, identify ten main types of risk
pooling, and place them in the supply chain, business logistics, and a value chain. This results
in the five logistics value activities storage, transportation, procurement, production, and sales
and distribution, where risk pooling is important. Completing outlining our research framework, we define, explain, and characterize risk pooling in business logistics (chapter 2).
Chapter 3 defines, classifies, and characterizes the ten identified risk pooling methods
within the five logistics value activities and according to their uncertainty reduction abilities.
24
25
26
27
28
To Porter (2008: 75) inbound and outbound logistics are primary value activities themselves besides operations, marketing and sales, and service. We adopt a cross-functional view of logistics.
Denzin (1978: 291) defines triangulation as “the combination of methodologies in the study of the same
phenomenon”.
Graman and Magazine (2006: 1070).
Jick (1979: 603f.), Fielding and Fielding (1986: 33), Graman and Magazine (2006: 1070).
Blaikie (1991: 115).
4
1 Introduction
Research on inventory pooling is reviewed in more detail29, as it is the earliest and most
extensive and prominent one. In particular, we attempt to remedy inconsistencies regarding
the SRL, a tool to estimate the inventory savings from risk pooling by inventory pooling:
Under what assumptions can the SRL be applied to regular, safety, and total stock, as researchers do not agree on them? What causes the inventory savings measured by the SRL?
Are its results confirmed in practice? Is the SRL questioned justifiedly? After examining the
portfolio effect (PE), a generalization of the SRL, and the inventory turnover curve, we compare the various SRL and PE models in a synopsis (table D.2) based on their assumptions
and assign them to groups. This facilitates choosing an appropriate model to determine stock
savings from inventory pooling for specific conditions or adapt the existing models by adding or dropping assumptions.
Chapter 4 merges the results of our literature review in a synopsis about conditions
making the various risk pooling methods favorable, their advantages, disadvantages, and
basic trade-offs. Based on this synopsis and contingency theory, a Risk Pooling Decision
Support Tool is developed for choosing an appropriate risk pooling strategy for a specific
company and specific conditions.
This tool is applied to a German paper wholesaler in chapter 5 to choose suitable risk
pooling methods to cope with demand and lead time uncertainty. In this context we also
show that in contrast to Maister (1976: 132) and Evers (1995: 2, 14f.) centralization or centralized ordering can reduce cycle stocks, if the replacement principle or stock-to-demand
replenishment policy is followed in case minimum order and saltus quantities have to be
observed (section 5.3.3.2).
If risk pooling is shown to be beneficial in theory and in practice also for this German
paper wholesaler, to what extent are its different methods known, applied, and associated in
102 German manufacturing and trading companies? To answer this question we present a
survey in appendix A for the above reasons. Such a survey has not been conducted before
and is demanded by some authors30.
The conclusion (chapter 6) summarizes our findings and identifies avenues for further research.
29
30
Professor Walter Zinn, Fisher College of Business, The Ohio State University, believes this is sorely
needed (personal correspondence on July 4, 2008).
For example by Thomas and Tyworth (2006: 254f.) for order splitting and by Huang and Li (2008b: 19)
for postponement.
5
2
Risk Pooling in Business Logistics
This chapter outlines our research framework: It gives an overview of previous risk pooling
research (section 2.1), identifies ten main types of risk pooling and embeds them in the supply
chain, business logistics, and a value chain (section 2.2), which sets the structure for chapter 3,
defines risk pooling in business logistics (section 2.3), explains its mathematical and statistical
foundations (section 2.4) and examines five general features of risk pooling (section 2.5).
2.1
Business Logistics Risk Pooling Research
Risk pooling in business logistics is an active field of research with well over 600 publications so far. The number of publications in this area has steadily increased since its scarce beginnings in the 1960s, gained momentum especially in the 80s and 90s and reached its peak in
2003 as figure 2.1 shows. Perhaps driven by the economic downturn, research activity in 2009
was the highest after 2003. Most research focused on inventory pooling (centralization, the
square root law, portfolio effect, and inventory turnover curve), postponement and delayed
(product) differentiation, and transshipments and inventory sharing. Figure 2.1 is based on the
literature databases Business Source Complete, Business Source Premier, EconLit, and Regional Business News accessed via EBSCOhost® January 11, 2010.
After the concept borrowed from modern portfolio and insurance theory has been mainly applied to inventory centralization, meanwhile research focuses on other forms of risk
pooling, especially postponement and transshipments, and the coordination of risk pooling arrangements and cost and profit allocation through contracts31 and fair allocation
rules, schemes, or methods32 with game theory.
The academics dealing with risk pooling in business logistics are of different backgrounds (mathematics, operations research (OR), operations management (OM), management science, decision sciences, statistics, computer sciences, engineering, business
administration, management, economics, game theory, production, marketing, logistics/supply chain management, physical distribution, and transportation), orientation
(quantitative, analytical, modeling, simulation, empirical, and qualitative research), and
31
32
Dana and Spier (2001), Cheng et al. (2002), Cachon (2003), Wang et al. (2004), Bartholdi and
Kemahloğlu-Ziya (2005), Cachon and Lariviere (2005), Özen et al. (2008, 2010).
Gerchak and Gupta (1991), Robinson (1993), Hartman and Dror (1996), Anupindi et al. (2001), Lehrer
(2002), Granot and Sošić (2003), Ben-Zvi and Gerchak (2007), Dror and Hartman (2007), Wong et al.
(2007a), Dror et al. (2008). Robinson (1993), Raghunathan (2003), Kemahloğlu-Ziya (2004), Bartholdi
and Kemahloğlu-Ziya (2005), and Sošić (2006) consider allocations based on the Shapley (1953) value.
6
2 Risk Pooling in Business Logistics
prominence. Therefore they use inconsistent terms33, frameworks, and structures and
made our thorough literature review and definitions necessary. One might argue that due
to these differences this research must not be compared and only major research should be
cited. However, in contrast to previous research we would like to pursue a more holistic
approach to convey an integrated overview of business logistics risk pooling. Even less
prominent research can draw attention to important details and show directions for further
research. Some often cited risk pooling research has not been published in highly ranked
journals.34 Nevertheless most of the cited references are from the latter.
Most risk pooling research is quantitative and designs mathematical models of problems, develops solution methods (exact methods, algorithms, simulation methods, and heuristics), and determines solutions (optimal inventory control and risk pooling, e. g. transshipment, policies).
60
Inventory Pooling (150)
Postponement (105)
Transshipments (95)
50
Component Commonality (55)
Virtual Pooling (51)
Capacity Pooling (41)
Number of Publications
Product Substitution (40)
40
Order Splitting (37)
Centralized Ordering (27)
Product Pooling (21)
30
20
10
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
0
Year of Publication
Figure 2.1: Number of Publications on Risk Pooling in Business Logistics
33
34
Bender et al. (2004: 233) made similar observations for location theory.
For example Eppen and Schrage (1981).
7
2 Risk Pooling in Business Logistics
2.2
Placing Risk Pooling in the Supply Chain,
Business Logistics, and a Value Chain
Business logistics35 comprises the holistic, market-conform, and efficient planning, organization, handling, and control of all material, product, and information flows from the supplier to
the company, within the company, and from the company to the customer36 and back (reverse
logistics37).
As figure 2.2 shows, the efficient and effective material, product, and information flow
is impaired by inter alia demand and lead time uncertainty. Risk pooling methods can mitigate these uncertainties. They can be implemented at or between the various supply chain
members (suppliers, manufacturers, wholesalers, distribution centers, central warehouses,
delivery or regional warehouses, retailers, stores, and customers).
Thoroughly reviewing the literature referred to in section 2.1, we identified ten risk
pooling methods: capacity pooling, central ordering, component commonality, inventory pooling, order splitting, postponement, product pooling, product substitution,
transshipments, and virtual pooling. We will define and characterize them in detail in
chapter 3.
They can be implemented everywhere along the supply chain. Component commonality
rather concerns production. In general capacity and inventory pooling and postponement
may pool inventories or capacities of or for different locations. Component commonality,
postponement, product pooling, and product substitution may refer to products or their
components. Transshipments and virtual pooling deal with product, material, and information flows between supply chain members within an echelon or across echelons, and central ordering and order splitting with procurement between supply chain members.
In our opinion, all mentioned risk pooling methods but order splitting can reduce demand uncertainty, order splitting only lead time uncertainty, component commonality,
capacity pooling, inventory pooling, product pooling, and product substitution only de-
35
36
37
Business logistics (management) is difficult to distinguish from supply chain management (SCM). The
terms are often used synonymously, although logistics is majorly seen as a part of SCM and not vice versa as in earlier literature (Ballou 2004b: 4, 6f., Larson and Halldórsson 2004, CSCMP 2010). According
to Kotzab (2000) the German business logistics conception already comprised a holistic management
along the whole value creation chain before it adopted the English term SCM. Gabler's business enzyclopedia defines SCM as building and administrating integrated logistics chains (material and information
flows) from raw materials production via processing to end consumers (Alisch et al. 2004: 2870).
Wegner (1996: 8f.).
See e. g. Richter (1996a, 1996b, 1997), Richter and Dobos (1999, 2003a, 2003b), Dobos and Richter
(2000), Richter and Sombrutzki (2000), Richter and Weber (2001), Richter and Gobsch (2005), Gobsch
(2007).
8
2 Risk Pooling in Business Logistics
mand uncertainty. Transshipments and virtual pooling, postponement, and central ordering
may dampen both uncertainties. Concerning order splitting and component commonality
there are dissenting individual opinions, which we will elaborate on in section 4.4.
Various economic conditions have been found to favor the different risk pooling methods. We will focus on these favorable conditions in chapter 4. They flow into a Risk
Pooling Decision Support Tool that helps to determine suitable risk pooling methods for
specific conditions (section 4.4). This tool is applied to determine adequate risk pooling
methods for a German paper merchant wholesaler for coping with its demand and lead
time uncertainty in chapter 5.
Demand Uncertainty
Suppliers
Manufacturers
Distributors
Retailers
Customers
Lead Time Uncertainty
Economic
Conditions
Material, product, and information flow
Risk pooling methods
Figure 2.2: Placing Risk Pooling in Business Logistics
Supply chain member names based on Chopra and Meindl (2007: 5).
Logistics may be considered as a cross-organizational (figure 2.2) and at every member of the
above supply chain a cross-departmental coordination function across all divisions, especially
storage, transportation, procurement, production of goods and services (including R&D,
recycling, and remanufacturing), and sales and distribution (including order processing, recovery, return, and disposal)38 in the value chain in figure 2.3.
38
Delfmann (2000: 323f.), Ballou (2004b: 9ff., 27, 29), Kuhlang and Matyas (2005: 659f.), Grün et al.
(2009: 15, 305), Wannenwetsch (2009: 21f.).
9
2 Risk Pooling in Business Logistics
The value chain is a management concept that was developed by Porter (1985: 33ff.)
and describes a company as a collection of activities. These activities create value, use resources, and are linked in processes. In our value chain, the main value activities are procurement, production, and sales and distribution, which are supported by the value activities transportation and storage. Value activities are “technologically and economically distinct activities [… a company] performs to do business”39.
Inventory pooling (IP) mainly pertains to storage, virtual pooling (VP) via dropshipping and cross-filling and transshipments (TS) to transportation, centralized ordering
(CO) and order splitting (OS) to procurement, capacity pooling (CP), component commonality (CC), and (form) postponement (PM) to production, and product pooling (PP) and
product substitution (PS) to sales. However, VP, extending a location's inventories to other
locations' ones, is also related to storage and sales, transportation and sales or service capacities may be pooled, any logistics decision may be postponed, and PP and PS may be
applied in production as well. This not mutually exclusive and exhaustive classification is
reflected in figure 2.3 and the next chapter's structure. We structured our review according
to the value chain approach, because we focus on the impact of risk pooling on the five
mentioned logistics value activities.
Risk pooling helps a company to cope with demand and/or lead time uncertainty and
thus to carry out these value activities at a lower cost for a given service level, a higher
service level for a given cost, or a combination of both40. Thus it may increase expected
profit41 by reducing expected costs and/or increasing expected revenue.
It may allow a company to win a competitive advantage over its competitors by effectively combining Porter's (2008: 75) competition strategies of differentiation and cost leadership, e. g. in mass customization enabled by postponement42.
39
40
41
42
Porter (2008: 75)
Cf. Chopra and Meindl (2007: 336), Cachon and Terwiesch (2009: 325, 350).
Porter's (1985: 38) value chain considers margin instead of profit. “Margin is the difference between total
value and the collective cost of performing the value activities”.
For example Feitzinger and Lee (1997).
10
2 Risk Pooling in Business Logistics
Transportation
CP, PM, TS, VP
Procurement
CO, OS, PM
Production
CC, CP, PM, PP,
PS
Sales &
Distribution
CP, PM, PP,
PS, VP
Profit
Storage
IP, PM, VP
Figure 2.3: Important Value Activities Using Risk Pooling Methods
2.3 Defining Risk Pooling
The literature offers various definitions of and confusion about the terms variability, variance,
or volatility43, uncertainty44, and risk45. Lead time and demand uncertainty may arise from
lead time and demand variability or incomplete knowledge46. “Uncertainty is the inability to
determine the true state of affairs of a system”47. “Uncertainty caused by variability is a result
of inherent fluctuations or differences in the quantity of concern. More precisely, variability
occurs when the quantity of concern is not a specific value but rather a population of values”48.
Lead time and demand uncertainty may lead to economic risk49, the possibility50 of a negative
deviation from expected values or desired targets51. The corporate target is expected profit
(figure 2.3), the difference of expected revenue and expected cost.52 The possibility of a positive deviation from an expected value constitutes a chance.53
Despite the costs risk pooling entails54, it may reduce variability and thus uncertainty
and expected (ordering, inventory holding, stockout, and backorder) costs55 and/or increase
expected revenue (product availability, fill rate, service level)56 and thus expected profit57.
43
44
45
46
47
48
49
50
51
52
53
54
Hubbard (2009: 84f.). “Outside of finance, volatility may not necessarily entail risk—this excludes considering volatility alone as synonymous with risk” (Hubbard 2009: 91).
Knight (2005: 19ff.), Haimes (2009: 265ff.), Hubbard (2010: 49f.).
Wagner (1997: 51), Knight (2005: 19ff.), Hubbard (2009: 79ff., 2010: 49f.).
Cf. Haimes (2009: 265). For a detailed treatment of the confusion about the terms uncertainty and variability please refer to Haimes (2009: 265ff.).
Haimes (2009: 265).
Haimes (2009: 266).
Bowersox et al. (1986: 58), Delfmann (1999: 195), Pishchulov (2008: 17).
Wagner (1997: 51).
Cf. e. g. Wagner (1997: 51), Köhne (2007: 321).
Wagner (1997: 52).
Wagner (1997: 51).
Kim and Benjaafar (2002: 16), Cachon and Terwiesch (2009: 328).
11
2 Risk Pooling in Business Logistics
We define risk pooling in business logistics as consolidating individual variabilities
(measured with the standard deviation58) of demand and/or lead time in order to reduce the total variability59 they form and thus uncertainty and risk60 (the possibility
of not achieving business objectives61). The individual variabilities are consolidated by
aggregating62 demands63 (demand pooling64) and/or lead times65 (lead time pooling66).
Consolidating and aggregating mean “combining several different elements […] into a
whole”67.
As individual variabilities68 and not individual risks69 are pooled, the term risk pooling
is misleading. Nonetheless, we use it, because it is conventional.
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
Eppen (1979), Chen and Lin (1989), Tagaras (1989), Tagaras and Cohen (1992: 1080f.), Evers (1996:
114, 1997: 71f.), Cherikh (2000: 755), Eynan and Fouque (2003: 704), Kemahloğlu-Ziya (2004), Bartholdi and Kemahloğlu-Ziya (2005), Wong (2005), Jiang et al. (2006: 25), Thomas and Tyworth (2006:
253), Chopra and Meindl (2007: 324ff.), Pishchulov (2008: 8, 17f.), Schmitt et al. (2008a: 14, 20), Simchi-Levi et al. (2008: 48), Cachon and Terwiesch (2009: 325, 331, 344, 350).
Krishnan and Rao (1965), Tagaras (1989), Tagaras and Cohen (1992: 1080f.), Evers (1996: 111, 114,
1997: 71f., 1999: 122), Eynan (1999), Cherikh (2000: 755), Ballou and Burnetas (2000, 2003), Xu et al.
(2003), Ballou (2004b: 385-389), Wong (2005), Kroll (2006), Reyes and Meade (2006), Chopra and
Meindl (2007: 324ff.), Cachon and Terwiesch (2009: 325, 329, 344, 350).
Anupindi and Bassok (1999), Cherikh (2000: 755), Lin et al. (2001a), Eynan and Fouque (2003: 704, 707,
2005: 98), Kemahloğlu-Ziya (2004), Bartholdi and Kemahloğlu-Ziya (2005), Özen et al. (2005), Chopra
and Meindl (2007: 324ff.), Simchi-Levi et al. (2008: 234-238), Cachon and Terwiesch (2009: 331), Yang
and Schrage (2009: 837).
Sussams (1986: 8), Romano (2006: 320). “The standard deviation is the most commonly used and the
most important measure of variability” (Gravetter and Wallnau 2008: 109). Zinn et al. (1989: 2) and Chopra and Meindl (2007: 307) consider the standard deviation a measure of uncertainty. Cachon and Terwiesch (2009: 331f., 282f.) and Chopra and Meindl (2007: 307) use the derived coefficient of variation
(standard deviation divided by mean) as a measure for demand variability or uncertainty.
Pooling independent random variables does not change total variability measured with the variance. Of
course, one could argue that the measuring unit of the variance is squared and therefore difficult to interpret and that the standard deviation and not the variance is used to calculate safety stock. Pooling variabilities measured with the range may even increase total variability.
Cf. e. g. Chopra and Meindl (2007: 336).
Cf. e. g. Pishchulov (2008: 18).
Wagner (1997: 51).
Cf. e. g. Anupindi et al. (2006: 167), Chopra and Meindl (2007: 336).
Gerchak and Mossman (1992: 804), Swaminathan (2001: 131), Hillier (2002b: 570), Randall et al. (2002:
56), Gerchak and He (2003: 1027), Özer (2003: 269), Chopra and Sodhi (2004: 55, 60), Nahmias (2005:
334), Anupindi et al. (2006: 167, 187), Çömez et al. (2006), Romano (2006: 320), Chopra and Meindl
(2007: 177), Pishchulov (2008: 8, 18, 26), Simchi-Levi et al. (2008: 48, 196, 281, 348), Yu et al.
(2008: 1), Yang and Schrage (2009: 837), Bidgoli (2010: 209).
Evers (1997: 55, 57, 1999: 121f.), Benjaafar and Kim (2001), Benjaafar et al. (2004a: 1442, 2004b: 91),
Chopra and Sodhi (2004: 59ff.), Tomlin and Wang (2005: 37), Gürbüz et al. (2007: 302), Van Mieghem
(2007: 1270f.), Ganesh et al. (2008: 1134), Cachon and Terwiesch (2009: 332), Wanke and Saliby (2009:
690), Yang and Schrage (2009: 837).
Thomas and Tyworth (2006: 254).
Evers (1999: 121f.), Cachon and Terwiesch (2009: 336).
Soanes and Hawker (2008).
Gerchak and He (2003: 1028).
The business logistics risk pooling literature finds “the risk related to the uncertainty” of individual demands (Zinn 1990: 12), risk “over uncertainty in customer demand” (Anupindi and Bassok 1999: 187),
standard deviations (Zinn 1990: 13) or variances of individual demands (Zinn 1990: 16), risk “over demand uncertainty” (Weng 1999: 75) or risk “over random supply lead time” (Weng 1999: 82), “inventory
12
2 Risk Pooling in Business Logistics
Among others Hempel (1970: 654), Wacker (2004: 630), and the references they give
make requirements for a “good”70 definition. To our knowledge previous attempts to define risk pooling do not satisfy them. They merely describe its causes71, effects72, or aim73,
only target demand pooling74, and equate risk pooling with inventory pooling75 and the
square root law76. Moreover they do neither define nor differentiate between variability77,
uncertainty, and risk. The business logistics risk pooling literature states risk pooling reduces

variability78, “lead-time variability”79, lead time demand variability80, demand variability81, demand variation82, variation83, “demand variance”84, variance of delivery time85, “the variance of the retailers' net inventory processes”86, “the mean and
variance of cycle stock”87,

uncertainty88, demand uncertainty89, “the uncertainty the firm faces”90, “the effect
of uncertainty”91,
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
risks” (Van Hoek 2001: 174, Pishchulov 2008: 27), “inventory risk” (Kemahlioğlu-Ziya 2004: 76), “forecast risk” (Chopra and Sodhi 2004: 58, 60), risk (Schwarz 1989: 830, 832, McGavin et al. 1993: 1093,
Chopra and Sodhi 2004: 58, 60f., Simchi-Levi et al. 2008: 357, Yang and Schrage 2009: 837), risks (Aviv
and Federgruen 2001a: 514, Gerchak and He 2003: 1027), “risk over the outside-supplier leadtime”
(Schwarz 1989: 828, McGavin et al. 1993: 1093), “lead-time risk” (Thomas and Tyworth 2006: 245f.,
2007: 169), “lead-time uncertainty” (Evers 1997: 70, Thomas and Tyworth 2006: 245), “lead-time fluctuations” (Evers 1997: 70), “demand uncertainty” (Evers 1997: 70), uncertainty (Evers 1994: 51, Rabinovich and Evers 2003a: 206), or “quantity and timing uncertainty” (Collier 1982: 1303) is or are pooled.
“A ‘good’ [formal conceptual] definition […] is a concise, clear verbal expression of a unique concept
that can be used for strict empirical testing” (Wacker 2004: 631). Hempel (1970: 654) requires inclusivity, exclusivity, differentiability, clarity, communicability, consistency, and parsimony.
Nahmias (2005: 334), Anupindi et al. (2006: 168), Romano (2006: 320), Simchi-Levi et al. (2008: 48),
Wisner et al. (2009: 513), Bidgoli (2010: 209).
Gerchak and He (2003: 1027), Özer (2003: 269), Romano (2006: 320), Simchi-Levi et al. (2008: 48),
Cachon and Terwiesch (2009: 325, 350), Bidgoli (2010: 209).
Chopra and Meindl (2007: 212), Cachon and Terwiesch (2009: 321).
Flaks (1967: 266), Gerchak and Mossman (1992: 804), Gerchak and He (2003: 1027), Özer (2003: 269),
Nahmias (2005: 334), Anupindi et al. (2006: 187), Chopra and Meindl (2007: 212).
Anupindi et al. (2006: 168).
Wisner et al. (2009: 513).
Tallon (1993: 192, 199f.) equates variability with uncertainty.
Eynan and Fouque (2005: 91), Anupindi et al. (2006: 167).
Thomas and Tyworth (2007: 171).
Benjaafar and Kim (2001).
Flaks (1967: 266), Zinn (1990: 11), Randall et al. (2002: 56), Eynan and Fouque (2003: 705, 2005: 91),
Romano (2006: 320), Thomas and Tyworth (2006: 255, 2007: 188), Chopra and Meindl (2007: 212),
Pishchulov (2008: 18), Simchi-Levi et al. (2008: 48), Cachon and Terwiesch (2009: 325, 331), Wisner et
al. (2009: 513), Bidgoli (2010: 209).
Eynan and Fouque (2005: 91), Nahmias (2005: 334).
Evers (1999: 133).
Kemahlioğlu-Ziya (2004: 71).
Masters (1980: 71), Ihde (2001: 33).
Schwarz (1989: 830).
Thomas and Tyworth (2006: 247f.)
Pishchulov (2008: 22), Simchi-Levi et al. (2008: 281).
Eynan and Fouque (2003: 714), Pishchulov (2008: 17).
13
2 Risk Pooling in Business Logistics

“the risk associated to the variability”92, the “impact of individual risks”93, “risks
associated with forecasting errors and inventory mismanagement”94, and “inventory
risk”95.
Risk pooling is described “to hedge uncertainty so that the firm is in a better position to mitigate the consequence of uncertainty”96, “enables one to avoid […] uncertainty”97, or “removes
some of the uncertainty involved in planning stock levels”98.
It is also referred to as “statistical economies of scale”99, “portfolio efficiencies”100,
“Pooling Efficiency trough Aggregation” or “Principle of Aggregation”101, and “IMPACT
OF AGGREGATION ON SAFETY INVENTORY”102.
Risk pooling is also considered a form of operational hedging. “Hedging is the action
of a decision maker to mitigate a particular risk exposure. Operational hedging is risk mitigation using operational instruments”103, e. g. pure diversification or demand pooling104.
For more on operational hedging please refer to Boyabatli and Toktay (2004) and Van
Mieghem (2008: 313-350).
2.4
Explaining Risk Pooling
Risk pooling can be shown e. g. for inventory or location pooling: Let a single product be
stocked at n separate locations. Demand for this product is a normal random variable105 xi with
known mean µi and standard deviation106 σi for each location i = 1, …, n. The standard devia90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
Cachon and Terwiesch (2009: 321).
Özer (2003: 269).
Risk pooling “is applied to portfolio theory in finance here [sic!] the risk associated to the variability in
the return from individual stocks is diluted when an investor keeps a portfolio of stocks“ (Zinn 1990: 12).
Dilts (2005: 23).
Yang and Schrage (2009: 837).
Chopra and Sodhi (2004: 59).
Cachon and Terwiesch (2009: 321).
Pishchulov (2008: 26) remarks this for risk pooling through delayed differentiation.
Jackson and Muckstadt (1989: 2).
Eppen (1979: 498), Eppen and Schrage (1981: 52), Evers (1994: 51), Özer (2003: 269), Rabinovich and
Evers (2003a: 206).
Eppen and Schrage (1981: 52).
Anupindi et al. (2006: 187, 189).
Chopra and Meindl (2007: 318).
Van Mieghem (2007: 1270).
Van Mieghem (2007: 1270f.).
A random variable is a variable that takes its values (realizations) with certain probabilities respectively
whose values are assigned to certain probability densities (Alisch et al. 2004: 3454).
If (the empirical distribution of) demand is forecast (Thonemann 2005: 255f.), σi is the standard deviation
of the distribution of the forecast error in formula (2.1) for calculating safety stock (Caron and Marchet
1996: 239, Pfohl 2004a: 114, Thonemann 2005: 255f., Chopra and Meindl 2007: 306). An estimate of
expected demand (forecast value) is ordered to satisfy the expected value of demand and safety stock is
14
2 Risk Pooling in Business Logistics
tion σi is a measure of dispersion of individual values of the random variable xi around the
mean µi for every entity i and therefore a measure of xi's variability107.
If each location just satisfies its own demand, location i needs to hold an amount of
safety stock that allows it to hedge against the demand uncertainty associated with xi. Let
the optimal safety stock at location i in accordance with the newsboy model108 be
(2.1)
,
where z is the safety factor that corresponds to a certain target service level. Therefore,
the total safety stock across all locations is
∑
.
(2.2)
If all inventory holding is centralized at one location, this location needs to serve the total demand
∑
.
(2.3)
The individual demands are aggregated across all locations. Safety stock in the centralized system is
(2.4)
,
where
∑
2∑
109
∑
(2.5)
is the standard deviation of x and ρij is the correlation coefficient of the value of the random
variable for locations i and j. It can be formally shown that the aggregated variability (standard
deviation of total demand σa) is less than or equal to the sum of the individual variabilities
107
108
109
built up as protection against the forecast error, which is at least as high as the demand uncertainty or
standard deviation of demand (personal correspondence with Professor Ulrich W. Thonemann, University
of Cologne, in 2008), and not against uncertainty in demand (Thonemann 2005: 255f.). A high safety
stock is needed, if the (standard deviation of the) forecast error is high. The size of demand fluctuations is
irrelevant (Thonemann 2005: 257). If the distribution of demand is known, σi is the standard deviation of
demand (Zinn et al. 1989: 4) and safety stock is held to hedge against uncertainty in demand. The higher
the uncertainty in demand, the higher is the safety stock. The standard deviation of demand is zero and no
safety stock is needed, if there is no demand uncertainty (Thonemann 2005: 238) and no lead time uncertainty either. Nonetheless, some companies forecast demand, but wrongly use the standard deviation of
demand instead of the standard deviation of the forecast error in calculating safety stock (Korovessi and
Linninger 2006: 489f.).
Gravetter and Wallnau (2008: 109).
See e. g. Thonemann (2005: 220), Cachon and Terwiesch (2009: 235).
Cf. Mood et al. (1974: 178), Zinn et al. (1989: 5), Jorion (2009: 43). This expression is also written
∑
2∑
∑
(Eppen 1979: 500) or
∑
2∑
∑
(cf.
Weisstein 2010). “The double summation sign ∑ ∑ indicates that all possible combinations of i and j
should be included in calculating the total value” (Moyer et al. 1992: 222), where j is larger than i.
15
2 Risk Pooling in Business Logistics
(sum of standard deviations of demand at the n locations σ) because of the subadditivity property of the square root of non-negative real numbers110:
∑
∑
2∑
∑
.
(2.6)
Therefore the safety stock in the centralized system is less than or equal to the one in the
decentralized one
∑
∑
2∑
∑
.
(2.7)
Inequality (2.6) is a special case of the known Minkowski inequality for p = 2. It is always correct, if the variances exist, therefore also for the Poisson and Binomial distribution.111
Hence, the standard deviation of the aggregate demand is lower than or equal to the sum
of the standard deviations of the individual demands. Consequently, inventory pooling or
centralization at a single location can reduce the amount of safety stock necessary to ensure a given service level. The reduction in safety stock depends on the correlations between xi, i = 1, …, n. Inventory pooling does not always reduce safety stock due to the
less-than-or-equal sign.
Yet, the sum of the individual variabilities (standard deviations) only equals the total
aggregated variability (the square root of the sum of the individual variances plus two
times the covariance of the random variable's value for two entities i and j) in two cases:
(1)
The random variables xi are perfectly positively correlated (the coefficient of
correlation ρij equals 1,
2∑
∑
i, j):
∑
∑
∑
112
(2.8)
∑
(2)
∑
1
∑
∑
.
Random variables xi cannot mutually balance their fluctuations, if at least
n-1 σi equal zero: If n-1 σi equal zero, (2.6) becomes
(2.9)
for this single non-zero σi. If all σi are zero, (2.6) becomes
110
111
112
Gaukler (2007).
Minkowski (1896), Abramowitz and Stegun (1972: 11), Bauer (1974: 72), Gradshteyn and Ryzhik (2007:
1061).
Cf. Moyer et al. (1992: 222). This expression is also written
∑
∑
∑
,
(cf.
Jorion 2009: 43).
16
2 Risk Pooling in Business Logistics
0
(2.10)
.
Apart from this, for independent (the correlation coefficient ρij is equal to 0,
i, j) nor-
mally distributed random variables risk pooling leads to variability reduction:
∑
∑
.
(2.11)
The highest possible variability reduction is achieved, if there are negative correlations which make the second term under the square root equal to minus the first term113 in
(2.6).
Some authors114 give the impression that risk pooling always reduces total variability or
enables to reduce inventory, although this must not be the case as shown above.
Likewise industry and academia often assume that inventory pooling, a type of risk
pooling, always is beneficial, i. e. it either reduces costs or increases profits, and that the
value of inventory pooling increases with increasing variability of demand.115
Kemahlioğlu-Ziya (2004: 40) states this was only always correct for normally distributed
demand such as in Eppen (1979) or Eppen and Schrage (1981). She neglects though that
this is not correct for perfectly positively correlated demands and if at least n-1 σi equal
zero.
Furthermore, for uncertain demand and certain conditions more willingness to substitute
may not lead to higher expected profits or “lower optimal total inventory”116 for full117 and
partial substitution or risk pooling118.
113
114
115
116
117
118
Cf. Eppen (1979: 500).
Tallon (1993: 186) imprecisely remarks, “Mathematically, the square root of the sum of the variances is
less than the sum of the individual standard deviations”. Likewise, Anupindi et al. (2006: 191) inaccurately state “the inventory benefits” from physical centralization “result from the statistical principle
called the principle of aggregation, which states that the standard deviation of the sum of random variables is less than the sum of the individual standard deviations”. Gaukler (2007) uses the less-than-orequal sign, but inconsistently says the standard deviation of the aggregate demand was lower than (not
lower than or equal to) the sum of the standard deviations of the individual demands. Although Gaukler
(2007) states his remarks were not intended to be a rigorous derivation of this concept, they should be
consistent. “It is well known that the pooled demand has a lower standard deviation than the sum of standard deviations of individual demands. Thus, the safety stock as well as inventory holding and shortage
costs are lower when products are more substitutable” (Ganesh et al. 2008: 1134). “Inventory pooling
represents a strategy of consolidating inventories and aggregating stochastic demands, enabling reductions in inventory holding and shortage costs” (Pishchulov 2008: 8). “Risk pooling suggests that demand
variability is reduced if one aggregates demand across locations” (Romano 2006: 320, Simchi-Levi et al.
2008: 48). “The aggregation of demand stemming from risk pooling leads to reduction in demand variability, and thus a decrease in safety stock and average inventory” (Simchi-Levi et al. 2008: 50). “Centralizing inventory reduces both safety stock and average inventory in the system” (Simchi-Levi et al. 2008:
51). Finally, inventory pooling does not automatically reduce inventory, but it may allow to reduce the
inventory necessary to provide a given service level.
Kemahlioğlu-Ziya (2004: 40).
Yang and Schrage (2009: 837).
Baker et al. (1986), Pasternack and Drezner (1991), Gerchak and Mossman (1992).
McGillivary and Silver (1978), Parlar and Goyal (1984), Anupindi and Bassok (1999), Ernst and Kouvelis (1999), Rajaram and Tang (2001), Netessine and Rudi (2003).
17
2 Risk Pooling in Business Logistics
Yang and Schrage (2009) show this “inventory anomaly” (after demand substitution or
risk pooling the company ought to hold more stock rather than less) for full substitution
with any right skewed demand distribution119 if the shortage is somewhat higher than the
holding cost per unit, for partial substitution with exponential, Normal, Poisson, and uniform demands even if they are negatively correlated, as well as for more than one period,
with backlogging, lost sales, more than two products, and with setup costs. The inventory
anomaly is increasing as the underage is close to the overage cost per unit and as the correlation between demands decreases.120 The relative difference of the shortage to holding
cost for which the anomaly arises increases with increasing right skewedness. A company
will not face the inventory anomaly, if it uses a shortage penalty, but minimizes inventory
carrying costs subject to a fixed target service level. However, it may not seize the chance
to increase sales and profits, if it augments demand pooling without raising inventory. The
likelihood of the inventory anomaly is higher with short lead times and lower with less
frequent but larger orders, e. g. with high setup costs.121
Inventory pooling may reduce costs and increase profits for the supply chain party holding inventory122, but may reduce the total supply chain profits. In a two-echelon supply
chain, where the upper echelon (the supplier) carries inventory, the lower echelon (the retailers), whose revenues depend only on sales, may lose profits due to pooling.123 The supplier and the retailers are likely to benefit from risk pooling inventory, if the stockout penalty cost is high.124
The normal random variable xi in our derivation of risk pooling can also be the demands
for i unique components, product versions, substitute products, customized products, or
(replenishment) lead times to i locations. They are aggregated to the demand for a common
component in component commonality125, universal product in product pooling, all substitutes in product substitution or demand reshape, the undifferentiated generic product in
postponement or delayed product differentiation, or to an aggregated lead time across all
locations, suppliers, or deliveries in lead time pooling (emergency transshipments and order splitting). The aggregated demand and/or lead time x may fluctuate less, as the stochas119
120
121
122
123
124
125
“Actual demand distributions tend to be right skewed” (Yang and Schrage 2009: 847).
Yang and Schrage (2003: 1).
Yang and Schrage (2009: 847).
Kemahloğlu-Ziya (2004), Bartholdi and Kemahloğlu-Ziya (2005).
Anupindi and Bassok (1999).
Dai et al. (2008: 411).
Dogramaci (1979: 130) shows that “the standard deviation of demand for the common component (σc)
would be less than or equal to” the sum of “the standard deviation[s] of lead time demand” of the components it replaces.
18
2 Risk Pooling in Business Logistics
tic fluctuations (σi) of the individual demands and/or lead times usually balance each other
to a certain extent (equation 2.6).
Risk pooling by demand pooling in transshipments, virtual pooling, centralized ordering, and capacity pooling can be derived in the same manner as shown for inventory pooling: Demands are pooled across locations.
2.5
Characteristics of Risk Pooling
We now turn to describing five important characteristics common to most risk pooling methods: (1) increasing returns, but (2) diminishing marginal returns with increasing application
as well as increasing benefit with (3) increasing demand variability, (4) decreasing demand
correlation, and (5) decreasing concentration of uncertainty.
(1) The benefit of or return on risk pooling is variability reduction and thus enabled inventory reduction for a given service level or increase in service level for a given inventory. The risk pooling return generally (in the following cases) increases with increasing
application or the number of participants:
It augments with the number of

participating stock-keeping locations in inventory pooling126, time and logistics
postponement127, transshipments128, and cross-filling129,

(substitutable) products and degree of substitution in product substitution, demand
reshape130, and resource flexibility131,

products in the product line132 or products being postponed133 in manufacturing
postponement,

products sharing components (increasing commonality) in component commonality134, as well as
126
127
128
129
130
131
132
133
134
Lin et al. (2001a), Heil (2006: 170), Netessine and Rudi (2006), Milner and Kouvelis (2007), Cachon and
Terwiesch (2009: 282f.).
Zinn and Bowersox (1988: 133), Heil (2006: 170).
Jönsson and Silver (1987a: 224), Robinson (1990), Diks and de Kok (1996: 378), Tagaras (1999), Evers
(2001: 313), Herer et al. (2002), Tagaras and Vlachos (2002), Dong and Rudi (2004), Burton and Banerjee (2005), Hu et al. (2005), Heil (2006: 170).
Ballou and Burnetas (2000, 2003), Ballou (2004b: 385-389).
Eynan and Fouque (2003, 2005), Ganesh et al. (2008: 1124).
Tomlin and Wang (2005: 51).
Zinn (1990: 14), Swaminathan and Tayur (1998).
Graman and Magazine (2006: 1075).
Collier (1982: 1303), Srinivasan et al. (1992: 26), Grotzinger et al. (1993: 532f.), Eynan and Fouque
(2005), Chew et al. (2006: 247).
19
2 Risk Pooling in Business Logistics

retailers in pooling over the outside-supplier lead time or centralized ordering135
and risk pooling by drop-shipping or virtual pooling136.
(2) However, the marginal benefit of risk pooling commonly decreases with each additional increase in risk pooling or participant. There appear to be diminishing marginal
returns to risk pooling137, e. g. to cross-filling138 and transshipments with increasing number of locations transshipping139 or increasingly even allocation of demand across locations140, to virtual pooling by drop-shipping with increasing number of retailers141, to component commonality142, postponement143, product substitution144, capacity pooling, and
location pooling145.
The marginal benefit of location pooling decreases with increasing number of pooled
locations146, so that the main benefit is gained by consolidating a few locations and it might
not be necessary to pool all locations147. The same applies to transshipments.148
Capacity pooling with a little bit of flexibility149 as long as it is designed with long
chains150 almost has the same benefit as full flexibility. Companies can benefit from any
135
136
137
138
139
140
141
142
143
144
145
146
147
148
Jackson and Muckstadt (1989: 14), Kumar and Schwarz (1995), Gürbüz et al. (2007).
Netessine and Rudi (2006: 845).
Similarly, in corporate finance we can observe diminishing marginal risk reduction with increasing number of securities: At first diversification reduces portfolio risk (standard deviation or volatility) rapidly,
then more slowly with increasing number of randomly chosen stocks (Statman 1987: 353, 355). In recent
years stocks have become individually more volatile but are increasingly less than perfectly correlated.
Therefore an investor needs to hold more stocks to capture the majority of benefits from diversification
than before (Campbell et al. 2001: 40).
Ballou and Burnetas (2000, 2003), Ballou (2004b: 385-389). Based on Ballou's (2003b: 81) numerical
example, we devise the general formula for the effective fill rate EFR for the customer in dependence of
the for all locations equal item fill rate FR (0
1) and the number n of locations that cross-fill as
. The first derivative of EFR with respect to n shows that the more locations cross1
1
⁄
· ln 1
0. However, the incremental infill the higher is the EFR:
1
⁄
crease in EFR diminishes with increasing number of locations taking part in cross-filling:
· ln 1
· ln 1
0.
1
Evers (1997: 70).
Evers (1996: 128).
Netessine and Rudi (2006: 852).
Chopra and Meindl (2007: 327f.) find by a numerical example that “the marginal benefit [… marginal
reduction in safety stock] decreases with increasing commonality” for independent and normally distributed end-product demand, but formulate this result as if generally valid. Bagchi and Gutierrez (1992)
show by two numerical examples (817) that “increasing component commonality results in increasing
marginal returns when the criteria are aggregate service level and aggregate stock requirement” (815) for
two end-products that face independent, identically exponentially, geometrically, or Poisson distributed
demands and share up to three components (815, 817f., 824). They do not give an intuitive explanation
(829).
Zinn (1990: 14), Graman and Magazine (2006: 1075, 1080).
Eynan and Fouque (2003: 707, 2005: 96).
Cachon and Terwiesch (2009: 323, 349).
Cachon and Terwiesch (2009: 323, 349).
Cachon and Terwiesch (2009: 323f.).
Tagaras (1989), Evers (1997: 71f.), Ballou and Burnetas (2000, 2003), Ballou (2004b: 385-389), Kranenburg and Van Houtum (2009).
20
2 Risk Pooling in Business Logistics
amount of risk pooling as long as they implement it appropriately151 and demand is not
perfectly positively correlated. Graman and Magazine (2006: 1075) similarly observe pertaining to postponement “that it is only necessary to postpone a portion of a product to
realize most of the benefits of such a strategy”. “The mathematical inventory model shows
that almost all of the positive benefits of postponement (such as lower inventories) can be
achieved with a partial (low-capacity) postponement scenario”152.
Cachon and Terwiesch (2009: 324) show diminishing marginal returns of location pooling with increasing mean for independent Poisson demands.153 This must not necessarily
hold for other distributions such as the normal one.154
(3) The (demand) risk pooling effect decreases with increasing demand correlation155
and any Magnitude (relative sizes of the standard deviations of demand), and increases
149
150
151
152
153
Flexibility means that a plant is capable of producing more than one product. With no flexibility each
plant can only produce one product; with total flexibility every plant can produce every product (as in
manufacturing postponement). Graphically lines called links indicate which plant is capable of producing
which product. Flexibility allows production shifts to high selling products to avoid lost sales (Cachon
and Terwiesch 2009: 344f.).
“A chain is a group of plants and [… products] that are connected via links” (Cachon and Terwiesch
2009: 346).
Cachon and Terwiesch (2009: 349).
Graman and Magazine (2006: 1080).
“[T]he standard deviation of a Poisson distribution equals the square root of its mean. Therefore, Coeffi √
[…].
cient of variation of a Poisson distribution
√
As the mean of a Poisson distribution increases, its coefficient of variation decreases, that is, the Poisson
distribution becomes less variable. Less variable demand leads to less inventory for any given service
level. Hence, combining locations with Poisson demand reduces the required inventory investment because a higher demand rate implies less variable demand. However, because the coefficient of variation
decreases with the square root of the mean, it decreases at a decreasing rate. In other words, each incremental increase in the mean has a proportionally smaller impact on the coefficient of variation, and hence
on the expected inventory investment” (Cachon and Terwiesch 2006: 324). This can also be derived for⁄
mally: The first derivative of the coefficient of variation
√ ⁄ with respect to the mean λ
154
is smaller than zero, the second one larger than zero:
0,
0.
⁄
⁄
For the normal distribution it depends on how the coefficient of variation changes with respect to the
mean. With the Poisson distribution it decreases as the mean increases, but this is not necessarily the case
with the normal distribution. However, we find that there are at least diminishing marginal returns to
pooling of normally distributed independent demands with the same standard deviation and mean. For
normally distributed independent demand the coefficient of variation of pooled demand is
∑
∑
. If the standard deviation and mean is the same at each pooled location i, this expression simpli√
fies to
√
. The first and second derivative of COV with respect to the number n of
pooled locations shows that as n increases COV decreases at a decreasing rate:
⁄
155
⁄
0,
0.
Eppen (1979), Zinn et al. (1989: 12), Inderfurth (1991: 109, 111), Netessine and Rudi (2003: 329), Alfaro
and Corbett (2003), Corbett and Rajaram (2004, 2006), Heil (2006: 170), Chopra and Meindl (2007: 319),
Cachon and Terwiesch (2009: 349). In serial or divergent multi-stage base-stock production/distribution
systems the lower the demand correlation, the further upstream safety stocks should be held and vice versa and the lower the worth of safety stocks because of product-dependent risk diversification (risk pool21
2 Risk Pooling in Business Logistics
with decreasing correlation and Magnitude156. Likewise the value of lead time risk pooling
(order splitting157 and transshipments) increases with decreasing correlation of replenishment lead times.
Therefore, many “companies attempt to reduce inventory and manufacturing costs by
manipulating correlated demand sources, or inducing demand patterns that balance each
other in an average sense”158, i. e. by risk pooling, while maintaining sales.159
The bullwhip effect160 can be reduced by risk pooling (effects)161, production smoothing, and seasonality162, so that it may be overestimated163.
Evers and Beier (1993) and Evers (1995) debatably show that there are no further savings in safety stock after a first consolidation because of the arising perfectly positive correlation.
Tyagi and Das (1999: 211) show that if demands are correlated and one appropriately
takes advantage of their characteristics, a partial may be more cost-efficient than complete
pooling of customers.
On the other hand, Xu and Evers (2003) claim that partial can never outperform complete pooling only based on demand correlation. Examples suggesting that one should prefer partial to complete aggregation were based on inconsistent correlation matrices.
(4) The benefits of risk pooling generally increase with a structured (“a common linear
transformation”164) increase in demand variability165, if lead times are exogenous (for inventory pooling, product consolidation, and delayed differentiation166). Gerchak and He
156
157
158
159
160
161
162
163
164
165
166
ing) (Inderfurth 1991: 109, 111). Nonetheless, the total safety stock size may increase with decreasing
correlation due to the impact of time-dependent risk diversification on carrying safety stocks at the still
more costly final stage level because of long replenishment lead times (Inderfurth 1991: 111).
Zinn et al. (1989: 3, 12), cf. Tallon (1993: 201), Tyagi and Das (1998: 201), Wanke (2009: 122).
Minner (2003: 273), Thomas and Tyworth (2006: 254, 2007: 188).
Burer and Dror (2006: 1).
Gerchak and Gupta (1991), Ruusunen et al. (1991), Hartman and Dror (2003: 243f.), Tyagi and Das
(1999).
The bullwhip effect describes that demand (order) variabilities are amplified as they move upstream the
supply chain (Lee et al. 1997a: 93, 1997b: 546, 2004: 1875, Sucky 2009: 311). It is caused by demand
forecast updating or demand signaling, order batching, price fluctuation, as well as rationing and shortage
gaming (Lee et al. 1997a: 95, 1997b: 546, 2004: 1883) and can be counteracted by avoiding multiple demand forecast updates, breaking order batches, stabilizing prices, and eliminating gaming in shortage situations (Lee et al. 1997a: 98ff., 1997b: 555ff., 2004: 1883ff.).
Hartman and Dror (2003: 244), Lee et al. (2004: 1882), Cachon et al. (2007: 475), Chen and Lee (2009:
781), Sucky (2009: 311).
Cachon et al. (2007).
Cachon et al. (2007), Sucky (2009).
Gerchak and He (2003: 1027).
Kemahlioğlu-Ziya (2004: 22), Zinn et al. (1989), Alfaro and Corbett (2003), Eppen (1979).
Benjaafar and Kim (2001: 19f.), Benjaafar et al. (2004b: 90f., 2005).
22
2 Risk Pooling in Business Logistics
(2003) provide a newsvendor counterexample with convex ordering where increased variability of two individual demands reduces the benefits of risk pooling.
If supply lead times are endogenous in multi-item finite capacity production-inventory
systems, both higher demand variability167 and capacity utilization (arrival rate divided by
service rate)168 or asymmetric backordering or holding costs make risk (inventory) pooling169 less valuable170.
(5) Assuming a multivariate normal distribution and uncorrelated demands, the value of
pooling is lower when uncertainty is more concentrated, i. e. the less uniform or more
dispersed the values of the standard deviations of the demands are.171 Correspondingly,
“the PE will be larger when variances are of similar rather than highly varying magnitude”172.
167
168
169
170
171
172
Benjaafar and Kim (2001: 19), Kim and Benjaafar (2002: 15), Benjaafar et al. (2004a: 1446).
Benjaafar and Kim (2001: 19), Kim and Benjaafar (2002: 15), Benjaafar et al. (2004a: 1438, 2004b: 71,
2005: 550).
“While the relative benefit of inventory pooling tends to diminish with utilization, the relative benefit of
capacity pooling tends to increase with utilization” (Benjaafar et al. 2005: 550).
Kim and Benjaafar (2002: 15).
Alfaro and Corbett (2003: 24).
Tyagi and Das (1998: 201), cf. Zinn et al. (1989).
23
3
Methods of Risk Pooling
After clarifying the prerequisites in the previous chapter, we will now enumerate the ten identified risk pooling methods and their synonyms, present a classification according to their ability
to pool demands and/or lead times, and define, classify, and characterize them correspondingly
within the structure of the aforementioned five logistics value activities.
First, under the heading storage we deal with inventory pooling and centralization, the
SRL, PE, and inventory turnover curve, as this area shows the earliest and most extensive
research in risk pooling (cf. figure 2.1) and requires a review173. The various SRL and PE
models are compared in a synopsis (table D.2) based on their assumptions. This facilitates
choosing an appropriate model to determine stock savings from inventory pooling for specific conditions or adapt the existing models by adding or dropping assumptions and relates our centralized ordering considerations in section 5.3.3.2 to these models.
Afterwards, virtual pooling, which is related to inventory pooling, and transshipments
are examined (transportation). Upon considering risk pooling in these two original (traditional) logistics duties that refer to the transfer of objects (above all of goods)174, we survey
it in the derivative logistics areas175 procurement (centralized ordering and order splitting),
production (component commonality, postponement, and capacity pooling), and sales and
distribution (product pooling and substitution) downstream the value chain.
Perhaps since risk pooling and centralization of inventories (distribution or warehouse
networks) are closely related, the terms inventory pooling176 or just pooling177 are often
used interchangeably and ambiguously for risk pooling (methods), although inventory
pooling literally merely refers to the consolidation or centralization of inventory, is a
type178 or manifestation179 of risk pooling, and takes advantage of the possible benefits of
risk pooling.
173
174
175
176
177
178
179
Personal correspondence with Professor Walter Zinn, Fisher College of Business, The Ohio State University on July 4, 2008.
Delfmann (2000: 323).
Delfmann (2000: 323).
Benjaafar and Kim (2001: 13), Kemahlioğlu-Ziya (2004: 11), Gaur and Ravindran (2006: 482), Pishchulov (2008: iii, 23f., 26, 28ff., 133), Simchi-Levi et al. (2008: 239).
Evers (1999: 121), Benjaafar and Kim (2001: 13), Alfaro and Corbett (2003: 12), Kemahlioğlu-Ziya
(2004: 11), Pishchulov (2008: iv, vi, vii, 8, 17f.).
“A finite set of outlets with randomly fluctuating demands bands together to reduce costs by buying,
storing and distributing their inventory jointly. This is termed inventory centralization and is a type of risk
pooling” (Burer and Dror 2006: 1). Cachon and Terwiesch (2009: 321).
Gerchak and He (2003: 1027).
24
3 Methods of Risk Pooling
After a thorough literature review we conclude that apart from
(1)
inventory pooling180, location pooling181, or (physical) inventory or warehouse centralization182 (SRL, PE, selective stock keeping, inventory turnover
curve),
risk pooling in business logistics can also be achieved by
(2)
virtual pooling183, virtual inventory or inventories184, “electronic inventory”185, virtual centralization186, virtual warehouse187 or warehousing188, “virtually aggregating inventories”189, or information centralization190,
(3)
transshipments (stock sharing between inventory locations)191 or “location
substitution”192,
(4)
centralized ordering193, “consolidated distribution”194, “risk pooling over the
outside-supplier lead time”195, or ”warehouse risk-pooling”196,
(5)
order splitting or multiple suppliers197,
(6)
component commonality198, component sharing199, part standardization200, or
procurement standardization201,
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
Benjaafar and Kim (2001: 13), Alfaro and Corbett (2003: 13), Anupindi et al. (2006: 189, 273), Heil
(2006), Yang and Schrage (2009: 837). Cf. also references in section 1.1.
Cachon and Terwiesch (2009: 321ff.).
Eppen (1979), Zinn (1990: 12), Benjaafar and Kim (2001: 13), Martinez et al. (2002: 14), Ghiani et al.
(2004: 9), Reiner (2005: 434), Anupindi et al. (2006: 187-194), Sheffi (2006: 117f., 2007), Brandimarte
and Zotteri (2007: 57f.), Chopra and Meindl (2007: 336), Pishchulov (2008: iii, 17, 133).
Cachon and Terwiesch (2009: 321, 350, 469), Mahar et al. (2009: 561).
Snyder (1995), Christopher (1998: 135), Hutchings (1999), Caddy and Helou (2000: 1715), Planning &
Reporting (2001), Randall et al. (2002: 56), Sawyers (2003), Ballou (2004b: 335, 385-389), Kroll (2006).
Christopher (1998: 135).
Anupindi et al. (2006: 194f., 314, 335).
Electrical Wholesaling (1997), Faloon (1999), Franse (1999), Duvall (2000), Purchasing (2000), AFSAC
(2001), Gourmet Retailer (2002).
Verkoeijen and deHaas (1998).
Chopra and Meindl (2007: 336).
Chopra and Meindl (2007: 321f.).
Benjaafar and Kim (2001: 13), Taylor (2004: 301ff.), Diruf (2005, 2007), Nonås and Jörnsten (2005:
521), Muckstadt (2005: 150ff.), Heil (2006), Sheffi (2006: 248, 2007), Yang and Schrage (2009: 837).
Yang and Schrage (2009: 838).
Diruf (2005, 2007), Nonås and Jörnsten (2005: 521), Heil (2006).
Cachon and Terwiesch (2009: 336ff.).
Schwarz (1989: 828), Pishchulov (2008: iii, 133).
Schwarz (1989: 828).
Sheffi (2007: 99f., 215-222).
Alfaro and Corbett (2003: 15), Neale et al. (2003), Reiner (2005: 434), Anupindi et al. (2006: 192, 194,
273), Sheffi (2006, 2007: 184-186), Brandimarte and Zotteri (2007: 30, 36, 38f.), Chopra and Meindl
(2007: 326ff.), Yang and Schrage (2009: 837), Bidgoli (2010: 21).
Benjaafar and Kim (2001: 13).
Zinn (1990: 12), Swaminathan (2001: 132), Simchi-Levi et al. (2008: 345ff.).
Swaminathan (2001: 132), Simchi-Levi et al. (2008: 345ff.).
25
3 Methods of Risk Pooling
postponement, delayed (product) differentiation,202 process standardiza-
(7)
tion203, or “modularization strategies”204,
(8)
capacity pooling and flexible manufacturing205,
(9)
product pooling206, stock keeping unit (SKU) rationalization207, universal or
generic design208, or product standardization209, as well as
product substitution210, “item substitution”211, interchangeability212, “de-
(10)
mand reshape”213, or “product commonalities”214.
Risk Pooling Methods
Building Blocks
IP
VP
TS
CO
OS
CC
PM
CP
PP
PS
DP
1
1
1
1
0
1
1
1
1
1
LP
0
0
1
0
1
0
0
0
0
0
Table 3.1: Risk Pooling Methods' Building Blocks
As highlighted in our definition in section 2.3, risk pooling (methods) may take advantage of
demand pooling (DP) and/or lead time pooling (LP). DP aggregates stochastic demands, so
that higher-than-average demands may balance lower-than-average ones.215 LP balances higher-than-average and lower-than-average lead times: A late-arriving order may be compensated
by an early-arriving one216, so that safety stock can be reduced, inventory availability in202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
Benjaafar and Kim (2001: 13), Alfaro and Corbett (2003: 12), Neale et al. (2003), Fleischmann et al.
(2004: 93), Taylor (2004: 301ff.), Sheffi (2004: 95f., 100, 2006: 297, 2007), Hwarng et al. (2005: 2841,
2842), Reiner (2005: 434), Anupindi et al. (2006: 167, 169, 193), Enarsson (2006: 178), Heil (2006),
Brandimarte and Zotteri (2007: 39, 70), Chopra and Meindl (2007: 328f.), Pishchulov (2008: iii, 27, 133),
Sobel (2008: 172), Cachon and Terwiesch (2009: 341ff.), Yang and Schrage (2009: 837). Many authors
consider postponement and delayed (product) differentiation synonyms (e. g. Lee and Tang 1997, Johnson and Anderson 2000, Aviv and Federgruen 2001a: 512, 2001b: 578, Swaminathan and Lee 2003, Matthews and Syed 2004, Anupindi et al. 2006: 193, Caux et al. 2006: 3244, Anand and Girotra 2007, Li et
al. 2007, Simchi-Levi et al. 2008: 190, 346, Graman and Sanders 2009, LeBlanc et al. 2009). At least
form postponement can be equated with delayed (product) differentiation and therefore the latter be considered a subform of postponement. For a distinction of these terms, which is not relevant for our further
considerations, please refer to Pishchulov (2008: 24-29).
Swaminathan (2001: 132), Simchi-Levi et al. (2008: 345ff.).
Reiner (2005: 434).
Anupindi et al. (2006: 224), Graves (2008: 36), Cachon and Terwiesch (2009: 344ff.).
Cachon and Terwiesch (2009: 321, 330ff.).
Alfaro and Corbett (2003: 12), Neale et al. (2003), Sheffi (2006: 119, 2007), Sobel (2008: 172).
Pishchulov (2008: 17), Cachon and Terwiesch (2009: 330).
Swaminathan (2001: 132), Simchi-Levi et al. (2008: 345ff.).
Anupindi et al. (2006: 192), Chopra and Meindl (2007: 324ff.), Yang and Schrage (2009: 837).
Benjaafar and Kim (2001: 13).
Sheffi (2006: 210, 2007).
Eynan and Fouque (2003, 2005).
Reiner (2005: 434).
Evers (1997: 55), Chen and Chen (2003).
Evers (1999: 122).
26
3 Methods of Risk Pooling
creased, or both217. Transshipments pool both lead times and demands, order splitting only the
former.218
Cachon and Terwiesch (2009: 336) consider consolidated distribution and delayed differentiation types of LP: Lead times between the supplier and the retail stores in the directdelivery model are combined to a single lead time between the supplier and the distribution
center (DC) in the consolidated-distribution model.219 Actually (forecast) demands are
pooled over or during the outside-supplier lead time220. Thus it is likely that higher-thanaverage and lower-than-average demands balance each other and inventory can be reduced
for a given service level (DP).
All risk pooling building blocks can reduce variability and thus inventory221 for a given
service level, increase the service level for a given inventory, or a combination of both222.
Table 3.1 can result in a classification according to the notation DP/LP that indicates
which risk pooling properties the risk pooling method of concern relies upon. A 1 indicates
that the respective property applies, a 0 the contrary. IP would be classified as a 1/0 – risk
pooling method.
3.1
Storage: Inventory Pooling
Inventory pooling is the combination of inventories and satisfying various demands from it in
order to reduce inventory holding and shortage costs through risk pooling.223 It is also called
vendor pooling224, product consolidation225, demand pooling226, pooling227, distributor integration228, location pooling229, or inventory centralization230. It can e. g. be achieved by inventory231 or warehouse (system) centralization232 or selective stock keeping respectively specializa-
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
Evers (1997: 71, 1999: 122).
Evers (1997, 1999: 121).
Cachon and Terwiesch (2009: 339).
Eppen and Schrage (1981), Schwarz (1989), Schoenmeyr (2005: 4), Gürbüz et al. (2007: 293).
Cf. Romano (2006: 320), Simchi-Levi et al. (2008: 48), Cachon and Terwiesch (2009: 325, 350), Bidgoli
(2010: 209).
Cf. Chopra and Meindl (2007: 336), Cachon and Terwiesch (2009: 325, 350).
Benjaafar and Kim (2001: 13), Kim and Benjaafar (2002: 12), Gerchak and He (2003: 1027), Benjaafar et
al. (2005), Anupindi et al. (2006: 191), Pishchulov (2008: 8, 17), Cachon and Terwiesch (2009: 322).
Monezka and Carter (1976: 207).
Benjaafar et al. (2004b: 73).
Benjaafar et al. (2004a: 1442, 2004b: 91).
Kemahloğlu-Ziya (2004), Bartholdi and Kemahloğlu-Ziya (2005), Benjaafar et al. (2005).
Simchi-Levi et al. (2008: 261, 263).
Cachon and Terwiesch (2009: 322).
Monezka and Carter (1976: 207).
Benjaafar et al. (2004a: 1438).
Eppen (1979), Benjaafar and Kim (2001: 13), Taylor (2004: 304f.), Reiner (2005: 434), Heil (2006).
27
3 Methods of Risk Pooling
tion233. The latter strives to reduce inventory carrying cost treating products differently without
reducing the service level substantially. For example, products with a low turnover might be
stocked only at few locations due to cost considerations.234
Inventory pooling is e. g. considered in location and allocation decisions235, satisfying
both on-line and store demand236, speculative online exchanges237, airline revenue management238, for spare parts of airlines239 and of U.S. manufacturing companies240, and for
Saturn241, General Motors242, Intel243, and Airbus244.
Inventory pooling is a 1/0 – risk pooling method: Inventories are consolidated and stochastic demands aggregated, as they are satisfied from the consolidated inventory245. Thus
demand variabilities may balance each other (demand pooling). The lead times to the separate inventories are pooled to the lead time to the consolidated stock according to Cachon
and Terwiesch's (2009: 336, 339) notion of lead time pooling, but this actually is demand
pooling during the replenishment lead time. Inventory pooling does not pool lead times, so
that their variabilities may balance each other according to Evers (1997: 69ff., 1999: 121)
and Wanke and Saliby (2009: 678f.).
Inventory centralization can reduce expected costs in a cost minimization model246 or
increase profits and service level247 in a profit maximization model248 or in incentivecompatible laboratory experiments in behavioral operations management (OM)249, even if
233
Anupindi et al. (2006: 191f.), Chopra and Meindl (2007: 322ff.)
Pfohl (2004a: 122f.).
235
Nozick and Turnquist (2001), Teo et al. (2001), Shen et al. (2003), Miranda and Garrido (2004), Hall
(2004), Croxton and Zinn (2005), Klijn and Slikker (2005), Shu et al. (2005), Snyder et al. (2007), Vidyarthi et al. (2007), Naseraldin and Herer (2008), Ozsen et al. (2008), Taaffe et al. (2008), Lee and Jeong
(2009).
236
Bendoly (2004), Bendoly et al. (2007: 426).
237
Milner and Kouvelis (2007).
238
“Airline revenue management involves dynamically controlling the availability and prices of many different classes of tickets to maximize revenues” (Zhang and Cooper 2005: 415).
239
Hearn (2007), Burchell (2009), Cattrysse et al. (2009).
240
Carter and Monczka (1978).
241
Treece (1996).
242
Kisiel (2000).
243
Johnson (2005).
244
Aviation Week & Space Technology (2006).
245
Pishchulov (2008: 8, 17).
246
For example Eppen (1979), Chen and Lin (1989).
247
Eynan (1999).
248
For example Cherikh (2000), Lin et al. (2001a).
249
Ho et al. (2009).
234
28
3 Methods of Risk Pooling
locations differ in profitability (selling price and stockout costs)250, because “of risk pooling over uncertainty in customer demand”251 and economies of scale252 and scope253.
Centralization (decreasing the number of warehouses) generally reduces inbound transportation costs from the supplier to the warehouses because of a higher utilization of transportation means (economies of density254), possibly the distances between the production
facility and the central warehouse(s)255, and the unit costs256 in the warehouse system due
to higher utilization (economies of scale). The systemwide total throughput is distributed
over a smaller number of warehouses and thus the average throughput per warehouse increases.257 The warehouse costs per item (unit costs for space, product handling, and personnel) decrease through economies of scale.258 The fixed costs per order and per unit
holding costs usually diminish with centralization.259 Fixed warehouse costs, especially
personnel costs, are distributed over a larger warehouse throughput so that the unit costs
decrease with increasing utilization260 and the return on rationalization investments in more
productive low-cost methods increases (economies of scale)261. Variable warehouse costs,
particularly handling costs, diminish by mechanization or automation.262 However, increasing mechanization or automation reduces flexibility263.
250
251
252
253
254
255
256
257
258
259
260
261
262
263
Eynan (1999: 38ff.) considers a central warehouse for a single product that supplies retailers from different markets, which differ in product prices and stockout costs, according to the first come, first served
principle. Surprisingly the centralized system usually performs better than the decentralized one: Considering the whole system, possible cannibalization effects of low-price-market demands at the expense of
high-price-market ones are overcompensated.
Anupindi and Bassok (1999: 187), cf. Teo et al. (2001), Lim et al. (2002: 668), Snyder and Shen (2006),
Schmitt et al. (2008a, 2008b), Ho et al. (2009).
Lim et al. (2002: 668), Rabinovich and Evers (2003a). Economies of scale are decreasing unit costs with
increasing output (Adam 1979: 950, Gutenberg 1983, Busse von Colbe and Laßmann 1986: 197, Monopolkommision 1986: 231, Chandler 1990: 17, Bohr 1996: 375, Samuelson and Nordhaus 1998, Alisch et
al. 2004: 771).
Rabinovich and Evers (2003a). Economies of scope arise as cost synergy effects, if the combined production of goods is cheaper than the separate one (Alisch et al. 2004: 771). In the literature among others the
portfolio effect is given as an economic reasoning for them: Diversification in different projects reduces
the total investment risk. Fritsch et al. (2001: 96) observe this effect with research and development in a
multi-product company, Bohr (1996: 382f.) with the general use of financial means.
Economies of density are cost advantages due to increasing utilization in a transportation system (Harris
1977, Caves et al. 1984: 472).
Fawcett et al. (1992: 37), Pfohl (1994: 141), Delfmann (1999: 193).
Unit costs are the costs that are defined by the distribution of total costs to the output to be produced
(Kistner and Steven 2002: 88).
Vahrenkamp (2000: 32).
Williams (1975), McKinnon (1989: 104).
Maister (1976: 132), McKinnon (1989: 102f.), Lim et al. (2002: 668).
Schulte (1999: 377), Vahrenkamp (2000: 34).
Paraschis (1989: 16), Pfohl (1994: 142), Vahrenkamp (2000: 34), Ihde (2001: 316).
Beuthe and Kreutzberger (2001: 249).
Stein (2000: 486), Ackerman and Brewer (2001: 231).
29
3 Methods of Risk Pooling
Centralization can lead to economies of massed reserves, if it is used to lower systemwide safety stock through risk pooling and thus unit holding costs.264 The latter are further
reduced by less inventory loss and thus lower risk costs in the centralized system.265 Economies of massed reserves are cost savings due to centralized reserve holding with increasing firm size.266 Among others Bowersox et al. (1986: 283ff.), Fawcett et al. (1992: 5),
Pfohl (1994: 141), and Delfmann (1999: 193) argue that in spite of constant basic inventory and increasing in transit inventory total inventory is lowered by reducing safety stock in
the centralized system. Higher utilization of inbound transportation means with centralization decreases the number of stock placements and removals.267 Therefore setups are reduced and larger loading and unloading equipment can be used saving time in the transportation system. Reducing idle time leads to a higher utilization in time and therefore to
economies of density using larger means of transportation.268
On the other hand, in a centralized logistics system outbound transportation costs may
be higher because of lower utilization269 and longer distances from the central warehouse(s) to customers270 and thus perhaps the service level might be lower271. Centralization may entail diseconomies of scale mostly in organization.272 With increasing size there
are no gains from rationalization anymore, but increasing transaction and coordination
costs and thus increasing warehouse unit costs in big warehouse systems.273
Das and Tyagi (1997) develop an optimization model for determining the optimal degree of centralization as a tradeoff between inventory and transportation costs.
Inventory centralization games optimize and allocate the savings from a centralized
inventory, so that the participants' cooperation is maintained.274
264
265
266
267
268
269
270
271
272
273
274
Bowersox et al. (1986: 286), Paraschis (1989: 16), Vahrenkamp (2000: 34f.), Ihde (1976: 39f., 2001:
316).
Vahrenkamp (2000: 32).
Scherer and Ross (1990: 100).
Schulte (1999: 377).
Pfohl (1994: 142), Vahrenkamp (2000: 35).
In the medium term smaller transportation vehicles might be used to increase utilization (Fawcett et al.
1992: 5, Delfmann 1999: 193, Vahrenkamp 2000: 31).
Delfmann (1999: 193), Ballou (2004b: 573f.).
Schulte (1999: 377), Vahrenkamp (2000: 31), Lee and Jeong (2009: 1169), Wanke (2009: 122).
Chandler (1990: 25), Scherer and Ross (1990: 103f.), Bohr (1996: 385f.).
Pfohl (1994: 143), Delfmann (1999: 194).
Hartman et al. (2000), Anupindi et al. (2001), Slikker et al. (2001, 2005), Müller et al. (2002: 118f.),
Granot and Sošić (2003), Hartman and Dror (2005: 93), Özen and Sošić (2006), Ben-Zvi and Gerchak
(2007), Chen and Zhang (2007, 2009), Drechsel and Kimms (2007), Dror et al. (2008), Özen et al.
(2008), Chen (2009), Zhang (2009).
30
3 Methods of Risk Pooling
The risk pooling effect on (safety) stock levels evoked by inventory pooling or centralization can be quantified with the square root law (SRL), portfolio effect (PE), and inventory turnover curve.
Maister's (1976) SRL states that the total system wide stock of n decentralized warehouses is equal to that of a single centralized one multiplied with the square root of the
number of warehouses n. There is some confusion about which part of inventory275 it can
be applied to and about its underlying assumptions276.
Nevertheless, it applies to regular stock277, if an economic order quantity (EOQ) order
policy is followed, the fixed cost per order and the per unit stock holding cost, demand at
every location, and total system demand is the same both before and after centralization.278
It holds for safety stock, if demands at the decentralized locations are uncorrelated279, the
variability (standard deviation) of demand at each decentralized location280, the safety factor (safety stock multiple)281 and average lead time are the same at all locations both before
and after consolidation, average total system demand remains the same after consolidation282, no transshipments occur283, lead times and demands are independent and identically distributed random variables and independent of each other284, the variances of lead time
are zero285, and the safety-factor (kσ) approach is used to set safety stock for all facilities
both before and after consolidation286. It applies to total inventory, the sum of regular and
safety stock287, if the aforementioned assumptions of the SRL as applied to regular and
safety stock hold collectively. A formal proof is given in appendix B.
The savings in regular stock measured by the SRL stem from the assumption of constant
275
276
277
278
279
280
281
282
283
284
285
286
287
Heskett et al. (1974: 462), Ballou (2004b: 380). Professor emeritus Ronald H. Ballou, Weatherhead
School of Management, Case Western Reserve University, agreed with us in a personal correspondence
on May 15, 2007.
Sussams (1986: 9), Bowersox et al. (2002: 469), Coyle et al. (2003: 259f.), Ballou (2004b: 380), Chopra
and Meindl (2007: 320).
Regular or cycle stock is the inventory “necessary to meet the average demand during the time between
successive replenishments. The amount of cycle stock is highly dependent on production lot sizes, economical shipment quantities, storage space limitations, replenishment lead times, price quantity discount
schedules, and inventory carrying costs” (Ballou 2004b: 331), and “affected by inventory policy” (Ballou
2004b: 379).
Maister (1976: 125, 127, 131).
Maister (1976: 132).
Maister (1976: 130).
Maister (1976: 132).
Evers and Beier (1993: 110), Evers (1995: 4).
Zinn et al. (1989: 2), Evers and Beier (1993: 110), Evers (1995: 4).
Evers and Beier (1993: 110), Evers (1995: 4).
Zinn et al. (1989: 2), Evers and Beier (1993: 110), Evers (1995: 4).
Maister (1976: 129).
Ballou (2004b: 380). Total inventory might also include pipeline, speculative, and obsolete stock (Ballou
2004b: 330f.), which is neglected here.
31
3 Methods of Risk Pooling
fixed costs per order, holding costs, and total demand for all locations before and after centralization. Thus, if an EOQ policy is followed, the total order fixed cost usually is lower because
of less orders and the inventory holding cost is lower due to a smaller total EOQ in the centralized than in the decentralized system. For the proof please refer to appendix C. This is called
“EOQ cost effect” by Schwarz (1981: 147) and “order quantity effect” by Evers (1995: 5).
Savings in safety stock stem from the subadditivity of the square root (the square root of
the sum of the individual demand variances of the decentralized locations is usually less than
the sum of the standard deviations of demand of the decentralized locations), i. e. from balancing demand variabilities (demand risk pooling). Schwarz (1981: 147), Zinn et al. (1989:
3), and Evers (1995: 5) identify this as the portfolio effect.
Total cost savings from centralizing safety stock are probably larger than the ones from
cycle stock centralization288, because centralized cycle stocks have to be transported to the
customer eventually, so that extra transportation costs are probably high. Centralized safety
stocks only have to be transported to the customer in the less frequent case of a stockout, so
that additional expenses for premium transportation are relatively small. If both cycle and
safety stocks are centralized some warehouses might be closed and fixed costs saved.289
Although some researchers290 claim the SRL estimated real savings well, in 13291
of 14292 practical cases we reviewed it overestimated actual inventory savings often sig288
289
290
291
Maister (1976: 134), Evers (1995: 17).
Maister (1976: 134), Evers (1995: 17).
Pfohl (1994: 141). Sussams (1986: 10) gives an example where a company's savings in safety stock (calculated with the standard deviation of demand of the decentralized and centralized depots) from reducing
the number of depots from five to one would only be 2.76 % higher than the ones predicted by the SRL,
although the variability (standard deviation) of demand at the decentralized depots is not the same, demands are not uncorrelated as the correlation coefficients we calculated show, but all locations use the
same safety stock multiple (two times the standard deviation of demand). The SRL assuming uncorrelated
demands coincidentally predicts similar savings to the ones calculated on the basis of the actual standard
deviations in this case. Here the correlations of sales between the different depots balance each other
when demands are consolidated, so that Zinn et al.'s (1989: 3) portfolio effect (percent reduction of safety
stock due to centralization of correlated demands) of 57.25 % resembles the savings of the SRL of
55.27 %. However, as Zinn et al. (1989: 6, 10) show this need not be the case at all. Note that Sussams
(1986: 10) compares two theoretical savings calculated with the SRL and on the basis of calculated standard deviations and not the theoretical savings estimated by the SRL with the actual savings realized by
the company and his table contains mistakes. He concludes that the SRL “has been tested against 24 different situations, and in all cases there was close agreement between the theoretical and the practical results. It was concluded that, subject to the reservations concerning the normality of the demand pattern,
the square root law may be used with confidence to estimate differences in buffer stock requirements for
different configurations of depots”. However, it is not clear whether the savings theoretically predicted
with the SRL were compared to actually realized or calculated savings and whether the assumptions of
the SRL as applied to safety stock were fulfilled in the practical cases. Therefore Sussams' (1986: 10)
conclusion is not intersubjectively verifiable.
Newson (1978), Voorhees and Sharp (1978: 75f.). Ballou (1981: 148ff.) shows for several real companies
from different industries that the inventory savings predicted by the SRL are higher than the actual savings. This might be caused by joint ordering (to benefit from volume buying and shipping, which increases inventory levels), forward buying, diversion from the EOQ pull policy for some products, use of
32
3 Methods of Risk Pooling
nificantly. This means its assumptions are not fulfilled293 in these cases or there were other
inventory-294 or service-related changes. It is difficult to isolate the effect of inventory centralization.295 The SRL shows the inventory necessary for a given service level in dependence of the number of stocking locations, if its underlying assumptions are fulfilled. This
does not mean that reducing the number of warehouses automatically reduces inventory.
None of the aforementioned sources states whether the assumptions to the SRL were
fulfilled. Therefore actually no statements can be made about the accuracy of the SRL's
results. However, it seems that the SRL “tends to over-predict”296 actual inventory savings,
as its assumptions are not fulfilled: In a survey that we conducted in the winter of 2008
none of the eleven participating companies from different countries and industries fulfilled
all assumptions of the SRL when applied to safety stock (table D.1). They fulfilled at least
two (respondents 1, 4, and 5) and at the most seven (respondent 10) of these eleven assumptions. Only one company (respondent 3) fulfilled all five assumptions necessary for
applying the SRL to regular stock. Two companies (respondents 4 and 11) did not fulfill
any of the assumptions of the SRL when applied to regular stock. Evers (1995: 17) already
remarked that the SRL is “based on numerous limiting assumptions which collectively are
not likely to be found in practice”, although Coyle et al. (2003: 259) call them “reasonable”.
292
293
294
295
296
push distribution (where production considerations are more important than inventory replenishment
ones) or a stock-to-demand order policy (relates inventory levels directly to demand), multiple product
types with different service policies in the aggregated product group, no equal product service levels and
costs, and poor inventory management. According to Ashford (1997: 20), Nike Europe intended to reduce
its footwear storage locations from 20 to 2 and was predicted by the consultancy Touche Ross to save
11 % of inventory costs (calculated by us with the given data) instead of 68 % as predicted by the SRL.
Nike planned to reduce its apparel storage locations from 20 to 1 with predicted savings of 12 % (calculated by us) as opposed to 78 %. Close-outs were estimated to decrease by 33 % for footwear and 50 %
for apparel. It is not stated how the inventory savings were predicted and whether they were actually realized. McKinnon (1997: 81), Watson and Morton (2000), Hammel et al. (2002). McKinnon (2003: 24)
considers two companies. Lovell et al. (2005), Progress Software Corporation (2007), clearpepper supply
chain consulting & education (2009). We interviewed the Supply Chain Manager of a U.S. wireless telecommunication device production company with 6,000 employees. This manufacturer reduced the number of warehouses from 80 to 15 and thus reduced regular stock by 50, safety stock by 75, and total average inventory by 50 %. The SRL predicts inventory savings of 56.70 % and thus estimates the savings in
regular and total stock fairly well in this case. Table D.1 shows which assumptions of the SRL this respondent 10 fulfilled.
A U.S. chemical company went from 100 to 89 warehouses. Inventory costs (including order processing
and warehousing costs) were reduced (projected by DISPLAN and later verified from accounting records)
by 76 % (compared to 6 % predicted by the SRL). These savings resulted not only from closing 11 warehouses, but also from reallocating demand among the remaining warehouses while maintaining the company's high level of customer service (Ballou 1979: 68).
Cf. Ballou (1981: 148ff.).
Ballou (1979: 68), McKinnon (1997: 81).
McKinnon (1997: 81).
McKinnon (1997: 81).
33
3 Methods of Risk Pooling
Researchers questioning Maister's (1976) SRL challenge its assumptions illogically297, do
make other assumptions and therefore arrive at different results298, or give no clear reason299.
Nonetheless, the other SRL- and PE-models compared in table D.2 might be applied
as their assumptions are fulfilled.
Eppen (1979) showed for the assumptions listed in table D.2 that the expected total system inventory holding and penalty costs increase with the square root of the number of
warehouses.300 His research was extended to Poisson demand301, any (non-negative) demand distributions with concave holding and penalty cost functions302, and to include costs
for the transportation of goods between locations with overage and underage in the centralized system303.
Zinn et al.'s (1989) portfolio effect (PE) is a generalization of the SRL and shows the
reduction in aggregate safety stock by centralizing several warehouses' inventories in one
warehouse in percent for the assumptions listed in table D.2. The PE was used to estimate
the effect of postponement on safety stock304 and extended to include holding, transportation, facility investment, and procurement costs305, multiple consolidation points306, variable lead times307, both safety and cycle stocks (“consolidation effect”) as well as various
assumptions308, the effect of non-emergency309 and emergency transshipments310, and unequal demand variances and possibly unequal capacities of centralized locations311.
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
Durand (2007).
Das (1978), Evers and Beier (1993), Evers (1995).
Durand and Paché (2006).
Kemahlioğlu-Ziya (2004: 9) wrongly states that Eppen (1979) “is the first to model and analyze the
benefits of inventory centralization”.
Stulman (1987).
Chen and Lin (1989).
Chang and Lin (1991). They are extended by Chang et al. (1996), who consider delay supply product
cost.
Zinn (1990).
Mahmoud (1992: 203ff.).
Evers and Beier (1993).
Tallon (1993).
Evers (1995).
Evers (1996). In nonemergency transshipments a certain proportion of demand is always filled from other
locations' inventory (Evers 1996: 129). The PE model of Evers and Beier (1993) can be utilized to determine the percentage reduction in safety stocks from nonemergency transshipments without considering
the effect on cycle stocks and transportation costs (Evers 1996: 111).
Evers (1997). The PE model of Evers (1996) underestimates the benefits of an emergency transshipment
policy, as it does not adequately consider the number of locations, lead times, and desired fill rates (Evers
1997: 68ff.).
Tyagi and Das (1998: 197). Savings in aggregate safety stocks are maximal, if every centralized location
delivers the same portion of each decentralized location's demand. Centralization can be beneficial, even
if customers have unequal demand variances and more centralized locations are established than there are
customer ones (Tyagi and Das 1998: 201f.).
34
3 Methods of Risk Pooling
The inventory turnover curve shows average inventory in dependence of the inventory
throughput for a specific company. It can be constructed from a company's stock status
reports and be used to estimate the average inventory (not only safety stock as with the PE)
for any (planned) warehouse throughput (shipments from the warehouse or sales) without
the limitations of the SRL. Thus one can assess the effect of centralization, decentralization
(changing the number and/or size of warehouses), or combining warehouses on average
inventory as well as the performance of inventory management and control policies for a
specific company.312
3.2
Transportation
3.2.1
Virtual Pooling
Virtual pooling extends a company's warehouse or warehouses beyond its or their physical
inventory to the inventory of other own or other companies' locations313 by means of information and communication technologies (ICT)314, drop-shipping315, and cross-filling316.
“[D]emand across [these locations] is pooled, which smoothes demand fluctuations”317. Therefore inventory availability is improved for a given “inventory investment” or maintained with
less inventory.318 If virtual pooling entails cross-filling, it may pool lead times. However, this
corresponds to transshipments and is considered in the next section. Therefore virtual pooling
is a 1/0 – risk pooling method.
3.2.2
Transshipments
Lateral transshipments are monitored company internal or external product shipments on the
same level or echelon of the value or supply chain, e. g. among retailers.319 They are also
called intra-echelon transshipments320, stock transfer321, lateral (re)supply322, inventory sharing323, stock redistribution324, virtual pooling325, or information pooling326.
312
313
314
315
316
317
318
319
320
321
Ballou (1981, 2000, 2004a, 2004b: 381f., 2005).
Caddy and Helou (2000: 1715), Planning & Reporting (2001), Kroll (2006).
Memon (1997), Christopher (1998: 135), Planning & Reporting (2001), SDM (2001), Frontline Solutions
Europe (2002), Electrical Wholesaling (2003), Mason et al. (2003), Fung et al. (2005), Kroll (2006), Cioletti (2007), Cachon and Terwiesch (2009: 350, 469).
Planning & Reporting (2001), Randall et al. (2002, 2006), Netessine and Rudi (2006).
Ballou (2004b: 335, 385-389).
Randall et al. (2002: 56).
Cachon and Terwiesch (2009: 350).
Lee (1987), Çömez et al. (2006), Herer et al. (2006: 185), Simchi-Levi et al. (2008: 239), Yang and
Schrage (2009: 838).
Burton and Banerjee (2005), Chiou (2008: 439).
Archibald et al. (1997).
35
3 Methods of Risk Pooling
Emergency or reactive327 lateral transshipments (ELT) transfer products from a location with a surplus to a location that faces a stockout328. Yang and Schrage (2009: 838)
regard ELT as “location substitution”.
Preventive or proactive329 lateral transshipments are conducted, if a retailer anticipates
a stockout before demands are realized330. Lee et al. (2007) combine emergency and preventive lateral transshipments in their transshipment policy “service level adjustment”
(SLA).
In virtual lateral transshipments a capacitated manufacturing plant designates arriving
demands to be served by another, more remote one. This can help capacitated plants to
work together to better deal with random demands and save costs. In contrast to the source
plant of real lateral transshipments the one of the virtual lateral transshipment may have
negative inventory levels throughout the transshipment process.331
All of the above lateral transshipments must not be confused with cross-docking (reloading of goods at transfer points or hubs)332 or shipping goods from a warehouse to a
demand-satisfying location333, which is also called transshipments sometimes.
If locations from the same echelon cannot transship inventory to prevent a stockout, an
upper-level supplier can fill the demand via a cross-level, inter-echelon, or vertical
transshipment334. This might resemble virtual pooling carried out by drop-shipping335.
Emergency transshipments pool both demands across locations or retailers336 (by permitting alternative locations to satisfy customer demands) and lead times (by providing
the whole system with the possibility of partial stock replenishments) and allow a company
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
Sherbrooke (1992), Yanagi and Sasaki (1992).
Anupindi et al. (2001), Grahovac and Chakravarty (2001), Zhao et al. (2005), Herer et al. (2006), Sošić
(2006), Chiou (2008: 427), Kutanoglu (2008).
Das (1975), Jönsson and Silver (1987a, 1987b), Bertrand and Bookbinder (1998), Tagaras and Vlachos
(2002), Hu et al. (2005).
Çömez et al. (2006).
Herer et al. (2006: 185), Özdemir et al. (2006a).
Herer et al. (2006: 185f.).
Lee (1987), Çömez et al. (2006), Herer et al. (2006: 185), Yang and Schrage (2009: 838).
Herer et al. (2006: 185f.).
Tagaras (1999), Lee et al. (2007). Preventive lateral transshipments are not useful in two-location periodic
review inventory systems with nonzero replenishment lead times and uncertain future material requirements and availability (Tagaras and Cohen 1992).
Yang and Qin (2007).
Campbell (1993), Hoppe and Tardos (2000), Petering and Murty (2009).
Köchel (2007).
Chiou (2008: 427, 439, 443).
Netessine and Rudi (2006).
Tagaras (1989), Tagaras and Cohen (1992), Evers (1997, 1999), Hong-Minh et al. (2000), Çömez et al.
(2006), Wanke and Saliby (2009), Yang and Schrage (2009: 837).
36
3 Methods of Risk Pooling
to remain close to customers337. They enable a company to exploit risk pooling338 or statistical economies of scale339, i. e. “advantages that result from the pooling of uncertainty”340.
As a result (safety) stock341 and (inventory holding, shortage, backorder, or total system) costs342 can be reduced for a given service level, which leads to leanness343, customer service level (fill rates, product availability, or delivery time) can be improved
without raising inventory levels344, which enables agility or flexibility345, or a combination of both (increasing service while decreasing inventory levels)346, which is called “leagility”347. Transshipments may decrease lost sales, the rejection rate of returns348, and replenishment lead times349 and improve revenues350 and performance351.
In a static stochastic demand system, transshipments balance stock levels at different locations through emergency stock transfers from one location with overage to another one
with underage. In a dynamic deterministic demand system, transshipments may save fixed
and variable replenishment costs352, if e. g. one location makes a larger replenishment order to transship some of it to other locations353 (cf. section 3.3.1 on centralized ordering).
Inventory consolidations do not pool lead times, may close stock keeping installations near markets354, restructure the logistics network fundamentally, which is difficult to
change or undo at least in the short term355, and increase order cycle times and/or transpor337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
Evers (1997, 1999), Wanke and Saliby (2009).
Tagaras and Vlachos (2002), Tagaras (1999), Dong and Rudi (2002, 2004), Çömez et al. (2006), Zhao
and Atkins (2009: 667).
Evers (1997, 1999).
Evers (1994: 51).
Jönsson and Silver (1987a: 224), Tagaras (1989), Diks and de Kok (1996: 378), Evers (1996), Mercer and
Tao (1996), Evers (1997: 71f.), Köchel (1998a: 190), Evers (1999), Kukreja et al. (2001), Herer et al.
(2002), Minner et al. (2003), Minner and Silver (2005).
Das (1975), Lee (1987), Robinson (1990), Evers (1996: 114), Köchel (1998a: 190), Alfredsson and Verrijdt (1999), Evers (2001: 313), Grahovac and Chakravarty (2001), Kukreja et al. (2001), Herer et al.
(2002), Tagaras and Vlachos (2002), Daskin (2003), Minner et al. (2003), Kukreja and Schmidt (2005),
Minner and Silver (2005), Wong (2005), Çömez et al. (2006), Yang and Qin (2007), Chiou (2008: 428),
Kutanoglu and Mahajan (2009: 728).
Herer et al. (2002).
Krishnan and Rao (1965), Tagaras (1989), Chang and Lin (1991), Sherbrooke (1992), Evers (1996, 1997:
71f., 1999), Hong-Minh et al. (2000), Herer et al. (2002), Minner et al. (2003), Xu et al. (2003), Minner
and Silver (2005), Zhao et al. (2005), Chiou (2008: 427), Kutanoglu (2008: 356).
Herer et al. (2002), Zhao et al. (2008).
Evers (1997), Needham and Evers (1998), Evers (1999), Minner et al. (2003), Minner and Silver (2005),
Zhao et al. (2008: 400).
Herer et al. (2002).
Ching et al. (2003).
Herer et al. (2002).
Reyes and Meade (2006).
Wong (2005), Wong et al. (2007b: 1045), Chiou (2008: 429).
Herer and Rashit (1999: 525), Herer and Tzur (2003: 419).
Herer and Tzur (2003: 419).
Evers (1999: 122).
Domschke and Drexl (1996: 1), Klose and Stähly (2000: 434), Klose (2001: 3).
37
3 Methods of Risk Pooling
tation costs to customers356. The stockout probability for a given system inventory level is
lower in a decentralized system with emergency transshipments than in a centralized
one.357 Therefore these two systems are not generally equal as in Chang and Lin (1991)
with no replenishment times and no transshipment transportation costs.358
Transshipments are similar to order splitting359, but orders from facilities employing
transshipments are not necessarily placed at the same time, while split orders are360 and
order splitting only pools lead times361.
Transshipments may decrease customer service (increase the number of receipts per order and/or order cycle times) and increase transportation or rebalancing362, transaction
(shipment documentation, receiving, handling and administration) costs363, the sending
location's cost of reordering the transshipped product from the supplier and its probability
of a stockout364, and daily average inventories365, and require willingness to share stock366.
Not all supply chain members may benefit from transshipments: they can increase
overall or retailer inventories and harm the distributor or individual retailers in a supply
chain, in which a manufacturer supplies integrated or autonomous retailers with a one-forone inventory policy via a central depot.367
Dong and Rudi (2002, 2004) find that if the wholesale price is endogenous, a single
manufacturer benefits from its retailers' transshipments, the more, the larger the risk pooling effect. The identical (except in their normal demands) retailers in many situations are
worse off under transshipment due to a higher wholesale price, especially if the risk pooling effect is large. Zhang (2005) extends Dong and Rudi's (2004) results under normal demand to general demand distributions.
Shao et al. (2009) also conclude that a manufacturer and the decentralized retailers via
which he sells may be hurt by transshipments. If the manufacturer controls the transshipment price, he prefers selling through decentralized retailers. If the latter control the trans-
356
357
358
359
360
361
362
363
364
365
366
367
Evers (1999: 122).
Evers (1997: 69ff., 1999: 121).
Evers (1997: 69ff.).
Sculli and Wu (1981), Hayya et al. (1987), Sculli and Shum (1990).
Evers (1997: 75).
Evers (1999: 122, 132).
Jönsson and Silver (1987a: 224), Diks and de Kok (1996: 378), Evers (1997: 56), Evers (1999: 122),
Burton and Banerjee (2005: 169).
Evers (1999: 122, 2001: 312f.).
Evers (2001: 312f.).
Reyes and Meade (2006).
Evers (1999: 122).
Grahovac and Chakravarty (2001).
38
3 Methods of Risk Pooling
shipment price, they realize higher profits than a chain store and the manufacturer may
prefer selling via a chain store.
Most research deals with transshipments of goods or commodities between warehouses,
retailers, or production locations. Cohen et al. (1980) consider transfers of patients between
hospitals and capacity decisions. Lue (2006) introduces transshipments to chemical manufacturing systems with continuous material flows to maintain non-stop operations, since it
is costly to shut down and restart the production process.
Transshipments affect the ordering policy and should be considered in it.368 The majority of publications model transshipments and determine (optimal) replenishment order and
transshipment369, ordering370, stocking, or inventory control371, stocking or inventory control and transshipment372, production and transshipment373, and transshipment374 policies,
rules, heuristics, or algorithms under different assumptions.
Similarly to the inventory centralization games in section 3.1, Anupindi et al. (2001),
Granot and Sošić (2003), Sošić (2006), and Zhao et al. (2005) study the conditions (profit
allocations) that make retailers jointly share their residual supply/demand with the other
retailers in a manner that maximizes the additional profit in inventory sharing games.
Small incentives for transshipments can achieve the benefits of a full-inventory sharing
policy.375
Köchel (1998a) provides a survey on multi-location inventory models with lateral
transshipments, foremost on research conducted at the Technical University Chemnitz,
Germany concerning the coordination of ordering decisions of all locations. Chiou (2008)
and Paterson et al. (2009) present more general reviews of transshipment problems in
supply chain systems and inventory models with lateral transshipments.
In summary, transshipments are a 1/1 – risk pooling method.
368
369
370
371
372
373
374
375
Robinson (1990), Hu et al. (2005), Kukreja and Schmidt (2005).
For example Köchel (1975, 1977, 1982, 1988), Tagaras (1989), Arnold and Köchel (1996), Arnold et al.
(1997), Köchel (1998b), Herer and Rashit (1999), Bhaumik and Kataria (2006).
For example Robinson (1990), Tagaras and Vlachos (2002), Hu et al. (2005), Herer et al. (2006), Olsson
(2009).
For example Das (1975), Lee (1987), Tagaras and Cohen (1992), Kukreja et al. (2001), Jung et al. (2003),
Kukreja and Schmidt (2005), Wong (2005), Wong et al. (2005a, 2005b, 2007b), Gong and Yucesan
(2006), Lue (2006), Yang and Qin (2007), Kranenburg and Van Houtum (2009).
Diks and de Kok (1996), Archibald et al. (1997), Hu et al. (2008).
Zhao et al. (2008).
Tagaras (1999), Evers (2001), Axsäter (2003a), Minner et al. (2003), Burton and Banerjee (2005: 169),
Minner and Silver (2005), Wee and Dada (2005), Çömez et al. (2006), Zhao et al. (2006), Archibald
(2007), Lee et al. (2007), Archibald et al. (2009).
Zhao et al. (2005).
39
3 Methods of Risk Pooling
3.3
Procurement
3.3.1
Centralized Ordering
Centralized ordering376 places joint orders for several locations and later allocates the orders
(perhaps by a depot) to the requisitioners or distribution points in consolidated distribution
according to current demand information.377 This is also called pooling risk over (the) outsidesupplier lead time(s)378, “lead time pooling […] achieved by consolidated distribution”379,
“coordinated replenishment”380, “central ordering”381, or “centralized purchasing”382.
The allocation decision is postponed and stochastic demands can be treated in an aggregate form until it is made. This reduces uncertainty and system stock “because of a portfolio
effect over the lead time from the supplier”383, “portfolio efficiencies”384, or “statistical
economies of scale”385. As explained at the beginning of this chapter, centralized ordering
does not entail lead time pooling, so that lower-than-average supplier lead times may not
balance higher-than-average ones. Consequently, centralized ordering is a 1/0 – risk pooling
method.
Compared to independent and individual or local386 ordering centralized ordering can lead
to economies of scale, i. e. it can take advantage of quantity discounts (“joint ordering effect”387) and save ordering388 and shipping costs389. It can make more frequent shipments
economical in comparison to direct delivery from the suppliers and thus reduce inventory
even further or increase the service level390.
If a warehouse, depot, or distribution center (DC) is introduced to allocate the stock391,
DC operating and extra transportation costs from the DC to the requisitioners or retailers are
incurred.392 A unit must travel a longer distance from the supplier to the retailer. However,
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
Eppen and Schrage (1981: 51), Erkip et al. (1990: 381), Ganeshan et al. (2007: 341), Gürbüz et al. (2007:
293).
Eppen and Schrage (1981), Cachon and Terwiesch (2009: 336-341).
Eppen and Schrage (1981), Schwarz (1989: 828), Schoenmeyr (2005: 4).
Cachon and Terwiesch (2009: 336).
Gürbüz et al. (2007: 293).
Ganeshan et al. (2007: 341).
Anupindi et al. (2006: 149f.).
Eppen and Schrage (1981: 67).
Eppen and Schrage (1981: 52).
Eppen (1979: 498), Eppen and Schrage (1981: 52).
Ganeshan et al. (2007: 341).
Eppen and Schrage (1981: 67).
Hu et al. (1997, 2005: 34), Gürbüz et al. (2007: 293).
Gürbüz et al. (2007: 293), Cachon and Terwiesch (2009: 341).
Cachon and Terwiesch (2009: 341).
Eppen and Schrage (1981), Schwarz (1989: 828), Cachon and Terwiesch (2009: 336ff.).
McGavin et al. (1993: 1094), Cachon and Terwiesch (2009: 341).
40
3 Methods of Risk Pooling
the holding cost for each unit of inventory at the DC is probably lower than at the retail
stores.393
The value of risk pooling through holding inventory at the warehouse, depot, or DC (“depot effect”394) and using this inventory “between system replenishments to ‘rebalance’ retailer inventories which have become ‘unbalanced’ due to variations in individual retailer demands” (between replenishment risk pooling)395 can be substantial396 (cf. inventory pooling).
Schwarz et al. (1985) and Badinelli and Schwarz (1988) find it is not significant, perhaps
because the model of Deuermeyer and Schwarz (1981) that they use does not allow the
warehouse to balance retailer inventory levels, if system stocks are low397.
3.3.2
Order Splitting
Order splitting is simultaneously partitioning a replenishment order into multiple orders with
multiple suppliers398 or into multiple deliveries (scheduled-release)399. The single order and
thus its lead time are split into multiple orders or deliveries and their lead times, so that the
variabilities of these lead times may balance each other400. Thus safety stock needed for a given service level (inventory availability, expected number of backorders or shortage cost) can be
reduced, service level increased for a given safety stock level, or both.401 It can also reduce
cycle stock due to successive deliveries of smaller split orders.402 Consequently, order splitting
only pools lead times, not demands403 and constitutes a 0/1 – risk pooling method.
Disadvantages of order splitting might include no “quantity and transportation discounts” because of smaller orders, a higher “administrative effort”, which electronic data
interchange might mitigate, and no “long-term partnership with a single supplier”, but multiple “suppliers may ensure competitive pricing and other favorable terms”.404
Thomas and Tyworth (2006: 246f., 2007: 170f.) critically review the literature on order
splitting: On the one hand, the literature assesses the effect of order splitting on the distri-
393
394
395
396
397
398
399
400
401
402
403
404
Cachon and Terwiesch (2009: 341).
Eppen and Schrage (1981: 67).
McGavin et al. (1993: 1093), cf. Schwarz (1989: 830).
Jackson and Muckstadt (1984a, 1984b, 1989), Jönsson and Silver (1987a, 1987b), Jackson (1988),
McGavin et al. (1993: 1104).
McGavin et al. (1993: 1093).
Evers (1999: 123), Thomas and Tyworth (2006: 245), Qi (2007).
Hill (1996), Chiang (2001), Mishra and Tadikamalla (2006), Thomas and Tyworth (2007: 188).
Evers (1999: 122).
Evers (1997: 71), Evers (1999: 123), Thomas and Tyworth (2006: 245f.).
Thomas and Tyworth (2006: 245).
Evers (1999: 123f.).
Evers (1999: 123).
41
3 Methods of Risk Pooling
bution of effective lead times405 and safety stock carrying and shortage costs with statistics.406 On the other hand, it compares the average total cost (inventory holding, ordering,
shortage, and purchase cost) of order splitting with the one of not order splitting407 and
finds that it reduces cycle stock408. Order splitting and the just-in-time inventory strategy
are analyzed by Pan and Liao (1989), Ramasesh (1990), Hong and Hayya (1992), Hong et
al. (1992), Kelle and Miller (2001), and Ryu and Lee (2003). Simultaneously splitting an
order among suppliers does not decrease the sum of in-transit and cycle stock, but only
total safety stock in the system409 and increases ordering410 and shipping costs411. Most
researchers neglect transportation economies of scale, the size of transportation costs compared to inventory costs, in-transit inventory412, the probability of lead time correlation413,
order dependent supply lead times and unit purchasing prices, and the derived disadvantages and advantages of order splitting414.
Options other than simultaneously splitting replenishment orders among several suppliers might be more promising:415 Delivering an order in sequential shipments can reduce
demand and production variability because of advance demand and delivery information.416 Orders can also be split between a fast, reliable and a cheaper, less reliable mode or
supplier in order to take advantage of cost-performance differences in transportation modes417 or between capacitated suppliers418. Lead time variability and freight rates could be
405
406
407
408
409
410
411
412
413
414
415
416
417
418
“The effective lead time in this case will be that of the minimum of the set of random variables
representing the lead time of each supplier” (Sculli and Wu 1981: 1003).
Sculli and Wu (1981), Hayya et al. (1987), Kelle and Silver (1990a, 1990b), Sculli and Shum (1990), Pan
et al. (1991), Ramasesh (1991), Fong (1992), Fong and Ord (1993), Guo and Ganeshan (1995), Fong and
Gempeshaw (1996), Fong et al. (2000), Geetha and Achary (2000), Kelle and Miller (2001), Mishra and
Tadikamalla (2006).
Ramasesh (1990), Ramasesh et al. (1991), Hong and Hayya (1992), Lau and Zhao (1993), Ramasesh et
al. (1993), Chiang and Benton (1994), Lau and Lau (1994), Lau and Zhao (1994), Gupta and Kini (1995),
Chiang and Chiang (1996), Mohebbi and Posner (1998), Ganeshan et al. (1999), Sedarage et al. (1999),
Tyworth and Ruiz-Torres (2000), Chiang (2001), Ghodsypour and O'Brien (2001), Ryu and Lee (2003).
Moinzadeh and Nahmias (1988), Pan and Liao (1989), Ramasesh (1990), Sculli and Shum (1990), Pan et
al. (1991), Ramasesh et al. (1991), Hong and Hayya (1992), Hong et al. (1992), Zhou and Lau (1992),
Lau and Zhao (1993), Ramasesh et al. (1993), Chiang and Benton (1994), Lau and Zhao (1994), Gupta
and Kini (1995), Chiang and Chiang (1996), Hill (1996), Ganeshan et al. (1999), Chiang (2001), Ghodsypour and O'Brien (2001), Ryu and Lee (2003).
Thomas and Tyworth (2006: 254).
Sajadieh and Eshghi (2009).
Thomas and Tyworth (2006: 246).
Thomas and Tyworth (2006: 254, 2007: 188).
Minner (2003: 273), Thomas and Tyworth (2006: 254, 2007: 188).
Sajadieh and Eshghi (2009: 3272).
Thomas and Tyworth (2006: 255).
Hill (1996), Janssen et al. (2000), Minner (2003: 276), Thomas and Tyworth (2006: 255).
Ganeshan et al. (1999), Minner (2003).
Qi (2007).
42
3 Methods of Risk Pooling
reduced by stable, periodic, long-term transportation commitments.419 Using emergency
transshipments instead of order splitting to reduce variation is attractive in many situations,
not only because order splitting is contrary to current theory and practice of vendor relations and lean production.420
3.4
Production
3.4.1
Component Commonality
Component commonality or part standardization421 designs products that share parts or components422. These common components can be used for several products.423
Component commonality is a 1/0 – risk pooling method: Demand for the individual
components is aggregated (pooled424) to the demand for the (fewer) generic common component(s).425
This may426 reduce the variability of demand (quantity and timing uncertainty) and the
required (safety) stock for any constant service level427, increase the service level for a
given inventory, or lead to a combination of both, inventory reduction and service increase428 due to risk pooling429. Furthermore, component commonality can lower setup,
ordering, inventory holding430, manufacturing431, logistics432, and part costs433 due to econ419
420
421
422
423
424
425
426
427
428
429
430
Thomas and Hackman (2003), Henig et al. (1997).
Evers (1999: 133).
Wacker and Treleven (1986: 219), Swaminathan (2001: 129), Simchi-Levi et al. (2008: 345).
Srinivasan et al. (1992), Jönsson et al. (1993), Meyer and Lehnerd (1997), Ma et al. (2002), Mirchandani
and Mishra (2002), Kim and Chhajed (2001), Labro (2004), Van Mieghem (2004), Ashayeri and Selen
(2005), Chew et al. (2006), Humair and Willems (2006). Swaminathan (2001: 131) and Simchi-Levi et al.
(2008: 348) also consider commonality in procurement standardization, which exploits commonality in
part and equipment purchasing. Demand can be pooled across a large variety of end products, if they are
produced on similar machines and/or use common components. Procurement standardization is most effective, if the product is nonmodular and the process modular.
Grotzinger et al. (1993: 524).
Yang and Schrage (2009: 837).
Dogramaci (1979: 129), Guerrero (1985: 409), Vakharia et al. (1996: 15), Kreng and Lee (2004), Labro
(2004: 363), Kulkarni et al. (2005: 247), Graman and Magazine (2006: 1074), Bidgoli (2010: 21).
Component commonality does not always reduce inventory in a dynamic inventory system with lead
times under some common allocation rules (Song and Zhao 2009: 493).
Roque (1977), Collier (1981: 95, 1982: 1303), McClain et al. (1984), Baker et al. (1986), Gerchak and
Henig (1986, 1989), Wacker and Treleven (1986: 219), Gerchak et al. (1988).
Bagchi and Gutierrez (1992: 824f., 829), Srinivasan et al. (1992), Grotzinger et al. (1993: 525f.),
McDermott and Stock (1994: 65), Eynan (1996), Eynan and Rosenblatt (1996), Thonemann and Brandeau (2000), Hillier (2002a, 2002b), Thomas et al. (2003), Labro (2004: 363), Mohebbi and Choobineh
(2005: 481), Chopra and Meindl (2007: 326ff.).
Srinivasan et al. (1992: 26f.), Grotzinger et al. (1993: 524), Swaminathan (2001: 129), Labro (2004: 363),
Chew et al. (2006), Simchi-Levi et al. (2008: 345).
Dogramaci (1979: 129), Collier (1981: 95, 1982: 1303), Guerrero (1985: 402), Thonemann and Brandeau
(2000), Swaminathan (2001: 129, 131), Hillier (2002b: 570), Ma et al. (2002: 524), Mirchandani and
Mishra (2002), Mohebbi and Choobineh (2005: 473), Simchi-Levi et al. (2008: 345, 348).
43
3 Methods of Risk Pooling
omies of scale434 or order pooling435, as well as product design costs436 and design and
manufacturing time437. The order-pooling benefit may be more important than the riskpooling one.438 Component commonality increases the survival probability of start-up
companies439 and possibly revenue440.
Total stock of product-specific components may increase though441 depending on the
used service-level measure442. Although component commonality may reduce the average
work load, it may increase workload variability and work-in-process inventory variability.443
Excessive part commonality can reduce product differentiation, so that less expensive
customization options might cannibalize sales of more expensive parts.444 While customer
valuation for the high-value product and the chargeable price may be reduced, the ones for
the low-value one may be increased by using commonality in vertical product line extensions.445
Sometimes, it is necessary to redesign products and/or processes to achieve commonality.446 This may result in a smaller and more economical set of components though.447 The
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
Collier (1981: 95), Hayes and Wheelwright (1984: 229-274), Walleigh (1989), Kim and Chhajed (2001:
219).
Kim and Chhajed (2001: 219).
Collier (1982: 1303).
Collier (1982: 1303), Kim and Chhajed (2001: 219), Swaminathan (2001: 129, 131), Simchi-Levi et al.
(2008: 345, 348).
Hillier (2002b: 570).
Desai et al. (2001).
Maskell (1991: 184f.), Berry et al. (1992), McDermott and Stock (1994: 65), Sheu and Wacker (1997),
Mirchandani and Mishra (2002).
Hillier (2002b: 570).
Thomas et al. (2003).
Component commonality allows to produce more of a higher-margin product instead of a low-margin
one, if demand exceeds capacity. Therefore it may be optimal even for perfectly positively correlated demands (no risk-pooling benefit), if products have sufficiently different margins (“revenue-maximization
option”) (Van Mieghem 2004: 422).
Baker et al. (1986), Gerchak and Henig (1986: 157), Gerchak et al. (1988), Gerchak and Henig (1989:
61), Van Mieghem (2004: 423).
Gerchak et al. (1988).
Guerrero (1985: 409), Vakharia et al. (1996: 3), Ma et al. (2002).
Ulrich and Ellison (1999), Kim and Chhajed (2000, 2001: 219), Desai et al. (2001), Krishnan and Gupta
(2001), Ramdas and Sawhney (2001), Simpson et al. (2001), Swaminathan (2001: 131), Heese and Swaminathan (2006), Simchi-Levi et al. (2008: 348).
Kim and Chhajed (2001: 219).
Bagchi and Gutierrez (1992: 817), Swaminathan (2001: 129), Ma et al. (2002: 536), Simchi-Levi et al.
(2008: 345).
Whybark (1989).
44
3 Methods of Risk Pooling
common component may be more expensive than the unique components it replaces.448
Still component commonality may reduce total cost.449
Using commonality as backup safety stock, if unique parts are not available, is better
than no commonality or pure commonality, where only common parts are used.450 Pure
commonality is not optimal unless it is free or there are high fixed product and process
redesign or complexity costs for procuring and handling two inputs.451
A component-mismatch problem due to demand uncertainty for end products may
arise.452 The equal-fractile allocation policy453 that allocates the components so that all
products have an equal probability of being out of stock at the end of the period can help to
reduce the required safety stock for a given target service level. However, it may keep
amply available components at the component level for the product with the highest demand variability (“worst-case product”), although they may be employed to manufacture
other end products. This can be avoided by modifying the policy accordingly.454
Although some publications assert that cost decreases with commonality in general,
there are contradictory claims on the effect of commonality on various cost elements and
commonality's impact on total cost cannot be determined in general yet.455
Wazed et al. (2008) review the literature on component commonality. For a review of
advantages and disadvantages of component commonality in manufacturing and degree of
commonality indices in designing new or assessing existing product families please refer to
Wazed et al. (2009). Boysen and Scholl (2009) develop a general solution framework for
component-commonality problems.
3.4.2
Postponement
Postponement in general means delaying a decision in production, logistics, or distribution in
order to be able to use more accurate information because of a shorter forecast period and an
aggregate forecast456, especially in industries with high demand uncertainty,457 and commit448
449
450
451
452
453
454
455
456
Hillier (2002a, 2002b), Van Mieghem (2004: 419), Zhou and Grubbström (2004), Mohebbi and Choobineh (2005: 473).
Van Mieghem (2004: 419), Hillier (2002a, 2002b).
Hillier (2002a).
Van Mieghem (2004: 423).
Baker (1985), Chew et al. (2006: 240).
Cf. Eppen and Schrage (1981), Bollapragada et al. (1998).
Chew et al. (2006: 239f., 248).
Labro (2004: 358, 366).
Aggregate forecasts usually are more accurate than disaggregate ones (Lawrence and Zanakis 1984: 25,
Neumann 1996: 9f., Swaminathan 2001: 126f., Sheffi 2004: 93f., Alicke 2005: 44, Nahmias 2005: 55,
Anupindi et al. 2006: 168, 187, Donnellan et al. 2006: x, Chopra and Meindl 2007: 188f., Simchi-Levi et
al. 2008: 190, 194, 345, Shah 2009: 166, Bretzke 2010: 77f., Schnuckel 2010: 152) because of statistical
45
3 Methods of Risk Pooling
ting resources rather to demand than to a forecast458. The opposite strategy of holding finished
goods at locations close to customers in anticipation of sales is called speculation.459
Postponement strategies can be applied to form, time, and place.460 This can include
product development461, purchasing462, order(ing)463, fulfillment assignment464, production465, manufacturing466, assembly467, packaging468, labeling469, delivery470, and pricing
postponement471. Form postponement delays product finalization or differentiation until
after customer orders have been received.472 Time postponement delays the forward
movement of stock.473 Rabinovich and Evers (2003b: 36, 41f.) consider emergency transshipments and inventory centralization forms of time postponement. Place postponement
keeps inventories in centralized locations until customer orders are received.474 Logistics or
geographic postponement combines time and place postponement.475 It delays the transportation to individual market areas.476 Pull postponement moves the decoupling point477 up-
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
balancing effects, statistical economies of scale, or risk pooling (Bretzke 2010: 77f.). For further explanations please refer to e. g. Neumann (1996: 9f.), Sheffi (2004: 93), Alicke (2005: 44), Nahmias (2005: 55),
Donnellan et al. (2006: x), Simchi-Levi et al. (2008: 60), and Schnuckel (2010: 152).
Pfohl (1994: 143), Swaminathan and Tayur (1998), Swaminathan (2001: 129f.), Sheffi (2004: 95f., 100),
Anupindi et al. (2006: 192f.), Chopra and Meindl (2007: 362), García-Dastugue and Lambert (2007:
57f.), Piontek (2007: 86f.), Simchi-Levi et al. (2008: 346), LeBlanc et al. (2009: 19).
Bucklin (1965), Van Hoek (2001: 161).
Bucklin (1965).
Van Hoek et al. (1998: 33).
Yang et al. (2004: 1052), Piontek (2007: 86).
Yang et al. (2004: 1052).
Granot and Yin (2008), Chen and Lee (2009), Li et al. (2009).
Allowing online sales to accumulate and postponing assigning them to fulfillment sites can reduce holding, backorder, and transportation costs (Mahar et al. 2009: 561).
Yang et al. (2004: 1052), Anupindi and Jiang (2008: 1876).
Zinn and Bowersox (1988), Huang and Lo (2003).
Zinn and Bowersox (1988).
Zinn and Bowersox (1988), Howard (1994), Graman and Magazine (1998), Cholette (2009), Graman
(2010).
Zinn and Bowersox (1988), Cholette (2009).
Anupindi and Jiang (2008: 1876).
Van Mieghem and Dada (1999), Boone et al. (2007: 597), Granot and Yin (2008).
Bowersox and Closs (1996), Lee (1998), Van Hoek (2001: 167), Rabinovich and Evers (2003b: 33), Li et
al. (2007: 31), Harrison and Skipworth (2008), Wong et al. (2009).
Zinn and Bowersox (1988), Bowersox and Closs (1996), Van Hoek et al. (1998: 33), Rabinovich and
Evers (2003b: 33), Nair (2005: 449).
Bowersox and Closs (1996), Van Hoek et al. (1998: 33), Rabinovich and Evers (2003b: 33), Nair (2005:
449).
Pfohl (1994: 145), Bowersox and Closs (1996: 473), Lee (1998), Van Hoek (1998a), Van Hoek et al.
(1998: 33), Özer and Xiong (2008).
Pfohl (1994: 145).
Up to the decoupling point, order-penetration-point, variant determination point, freeze point (Piontek
2007: 86f.), or point of (product) differentiation (PoD) (Lee 1996, Lee and Tang 1997, Meyr 2003) standardized products are made to stock customer-anonymously based on sales forecasts (push strategy). After an order has been received, the standardized products are transformed into various variants customerindividually (make-to-order pull strategy) (Piontek 2007: 86f., Harrison and Skipworth 2008).
46
3 Methods of Risk Pooling
stream to assemble to order478. Waller et al. (2000: 138) consider upstream postponement,
e. g. delaying ordering of raw materials, and downstream postponement, e. g. distribution
or place postponement.
Postponement allows to ship a single common generic product longer down the supply
chain and change it to individual products (differentiate it) more responsively according to
more recent demand information later.479 On the preceding levels of the supply chain the
demands for the individual products are aggregated to the demand for the generic product (demand pooling480), which fluctuates less, since the stochastic fluctuations of the individual demands balance each other to a certain extent because of the risk pooling effect.481
Postponement constitutes a 1/0 – risk pooling method.
Furthermore, inventories of the common intermediate product can function as a common buffer.482 A learning effect may arise, if forecasts can be improved on the basis of
observed sales data.483 Thus the total inventory holding costs and stockouts can be reduced
and customer service level484 and profits increased485 by better matching supply and demand486.
Besides this risk and cost reduction, postponement can lead to economies of scale, synergistic effects, delayed increase in costs in the value chain and thus decreased capital
commitment, and higher flexibility or leagility.487 However, it is usually necessary to redesign488 the product specifically for delayed differentiation and to modify the order of manufacturing steps (resequence or operations reversal)489. This may decrease production volume variability though.490 Time-based postponement at the company level can increase
478
479
480
481
482
483
484
485
486
487
488
489
490
Lee (1998).
Lee (1996), Aviv and Federgruen (2001b: 579).
Yang and Schrage (2009: 837).
Lee and Tang (1997: 52), Aviv and Federgruen (2001a: 514, 2001b: 579), Alfaro and Corbett (2003: 12,
15), Piontek (2007: 87), Dominguez and Lashkari (2004: 2113), Anupindi et al. (2006: 192f.), Caux et al.
(2006), Jiang et al. (2006), Cholette (2009).
Weng (1999), Aviv and Federgruen (2001b: 579).
Aviv and Federgruen (2001b: 579).
Lee (1996), Lee and Tang (1997), Jiang et al. (2006), Davila and Wouters (2007), Li et al. (2008, 2009),
LeBlanc et al. (2009: 19), Mahar and Wright (2009), Wong et al. (2009).
Jiang et al. (2006), Chopra and Meindl (2007: 364), Cholette (2009).
Chopra and Meindl (2007: 364).
Aviv and Federgruen (2001b: 579), Herer et al. (2002), Piontek (2007: 86f.).
Swaminathan (2001: 129f.), Kim and Benjaafar (2002: 12), Yang et al. (2005b: 994), Davila and Wouters
(2007: 2245), Shao and Ji (2008), Simchi-Levi et al. (2008: 346).
Lee and Tang (1997: 40, 1998), Kapuscinski and Tayur (1999), Jain and Paul (2001), Swaminathan
(2001: 129f.), Shao and Ji (2008), Simchi-Levi et al. (2008: 346).
Jain and Paul (2001).
47
3 Methods of Risk Pooling
supply chain inventory, as other members of the supply chain may be forced to use more
speculation, i. e. hold more inventories.491
Postponement reduces risk associated with order mix and order quantity, but may increase stockouts or lost sales due to longer lead, delivery, or order cycle times.492 Speculation provides a high availability and flexibility because of short lead times and few stockouts.493 Decreasing (increasing) speculation and increasing (decreasing) postponement
increases (decreases) transportation costs and decreases (increases) inventory holding
costs.494
Postponement and speculation can be combined installing an intermediary stage between the suppliers and the buyers close to the buyers and holding uncommitted, anticipatory inventory of the suppliers ready to be shipped on request495 or “postponing only the
uncertain part of the demand and producing the predictable part at a lower cost without
postponement” in “tailored postponement”496. “The combined principle of postponementspeculation”497 may lower both inventory risk by centralization and order fulfillment times
and lost sales.498 Internet retailers, for instance, depend more on both inventory location
speculation (in-stock inventory) and postponement (drop-shipping) to fulfill their orders as
their market share and product popularity increase.499
As products are only delivered after a customer order is received, in general postponement leads to a centralized logistics system.500 Speculation rather has a decentralizing
effect on the logistics system501 and finished products inventory is stored as close as possible to customers. At the same time speculative processes lead to consolidated flows of
goods because of higher order quantities.502 Consolidated flows of goods support the tendency towards centralized logistics systems.503 These opposite movements are no contra-
491
492
493
494
495
496
497
498
499
500
501
502
503
García-Dastugue and Lambert (2007).
Zinn and Bowersox (1988: 126), Van Hoek (2001: 161), Rabinovich and Evers (2003b: 35), Yang et al.
(2005b: 994), Graman and Magazine (2006: 1078), Pishchulov (2008: 13).
Bucklin (1965: 27), Delfmann (1999: 195).
Bucklin (1965: 27), Zinn and Bowersox (1988: 126), Graman and Magazine (1998), Delfmann (1999:
195), Van Hoek (2001: 161).
Bucklin (1965: 31).
Chopra and Meindl (2007: 366).
Bucklin (1965: 28).
Bucklin (1965: 31), Pishchulov (2008: 27).
Bailey and Rabinovich (2005).
Shapiro and Heskett (1985: 53), Zinn and Bowersox (1988: 126), Pfohl (1994: 145), Pagh and Cooper
(1998: 14), Van Hoek (1998a: 95), Van Hoek et al. (1999b: 506), Nair (2005: 458).
Shapiro and Heskett (1985: 53), Klaas (2002: 154).
Pagh and Cooper (1998: 14), Delfmann (1999: 195), Klaas (2002: 157).
Pfohl et al. (1992: 95), Kloster (2002: 122).
48
3 Methods of Risk Pooling
diction, but rather proof of the complex interdependencies between process and structure
variables in logistics systems.504
In practice there is a trend towards customer order oriented logistics systems505 or postponement as a logical consequence to centralization506, increasing uncertainty in buyer
markets, increasing product variety, individualization of demands, and regional expansion
of supply in a globalized economy507.
Postponement is analyzed by Eppen and Schrage (1981) in the steel industry, Heskett
and Signorelli (1984) at Benetton, Fisher and Raman (1996) at Sport Obermeyer, Feitzinger and Lee (1997) at HewlettPackard, Magretta (1998), Van Hoek (1998b), and Kumar
and Craig (2007) at Dell, Inc., Van Hoek (1998b) with the SMART car, Battezzati and
Magnani (2000) for industrial and fast moving consumer goods in Italy, Brown et al.
(2000) at a semiconductor firm, Chiou et al. (2002) in the Taiwanese IT industry, Huang
and Lo (2003) in the Taiwanese desktop personal computer industry, Dominguez and
Lashkari (2004) at a major household appliance manufacturer in Mexico, Caux et al.
(2006) in the aluminum-conversion industry, Davila and Wouters (2007) at a disk drive
manufacturer, Cholette (2009) in wine distribution, ElMaraghy and Mahmoudi (2009) in
the optimal location of nodes of a global automobile wiper supply chain considering currency exchange rates and the optimal modular product structure, Kumar et al. (2009) at 3M
Company, Kumar and Wilson (2009) in off-shored manufacturing, and Wong et al. (2009)
in terms of the optimal differentiation point positioning and stocking levels.
Van Hoek (2001) reviews the literature on postponement dating back to 1965 and puts
it in a systematic framework. Boone et al. (2007) review postponement literature published
from 1999 to 2006 and conclude research should be extended to non-manufacturing postponement, investigate the slow rate of postponement adoption among practitioners, and
continue assessing the relationship between postponement and uncertainty.
3.4.3
Capacity Pooling
Capacity pooling is the consolidation of production508, service509, transportation510, or inventory capacities of several facilities.511 Without pooling every facility fulfills demand just with its
504
505
506
507
508
509
510
Klaas (2002: 157f.).
Van Hoek et al. (1999b: 506).
Van Hoek (1998a: 95).
Ihde (2001: 36).
Plambeck and Taylor (2003), Iyer and Jain (2004), Jain (2007), Simchi-Levi et al. (2008: 281).
Cachon and Terwiesch (2009: 149ff., 325, 349, 467).
Masters (1980: 71), Evers (1994), Ihde (2001: 33), Chen and Chen (2003), Chen and Ren (2007).
49
3 Methods of Risk Pooling
own capacity. With pooling demand is aggregated and fulfilled by a single (perhaps virtually)
joint facility.512 If demand is stochastic, a higher service level can be attained with the same
capacity or the same service level can be offered with less capacity.513 It is also advantageous,
if there are economies of scale in obtaining capacity or satisfying demand.514 Capacity pooling
may pool supplier lead times, if the capacities receive separate deliveries from the suppliers
and provide the whole system with the possibility of partial stock replenishments515. However,
this is considered under stock sharing (transshipments). Consequently, capacity pooling is regarded as a 1/0 – risk pooling method.
It is predominantly associated with combining manufacturing capacity516 and thus creating manufacturing flexibility517. We adopt this view in the following and subsume pooling
of inventory capacity under inventory pooling. Manufacturing flexibility means that a plant
is capable of producing more than one product. With no flexibility each plant can only
produce one product, with total flexibility every plant can produce every product (as in
manufacturing postponement). Flexibility allows production shifts to high selling products
to avoid lost sales.518
Capacity pooling can increase effective capacity to serve more demand, which leads to
higher expected sales, profits, and capacity utilization519 or lower manufacturing flow
time.520 Aggregating demands which were served by individual capacities before and are
now served with pooled capacity can reduce demand variability and thus the demandcapacity mismatch cost. However, installing flexibility is expensive521. If demands are of
different variability, pooling production capacities may increase inventory costs for the
low-demand-variability facility522 or total cost523.
511
512
513
514
515
516
517
518
519
520
521
522
523
Anupindi et al. (2006: 223), Yu et al. (2008: 1), Cachon and Terwiesch (2009: 463).
Yu et al. (2008: 1).
Anupindi et al. (2006: 224), Yu et al. (2008: 1).
Yu et al. (2008: 1).
Cf. Evers (1997, 1999), Wanke and Saliby (2009).
Plambeck and Taylor (2003), Iyer and Jain (2004), Jain (2007), Simchi-Levi et al. (2008: 281).
Upton (1994, 1995), Jordan and Graves (1995), Weng (1998), Pringle (2003), Chopra and Sodhi (2004:
59), Goyal et al. (2006), Van Mieghem (2007), Mayne et al. (2008), Cachon and Terwiesch (2009: 344351).
Cachon and Terwiesch (2009: 344f.).
Pooling server capacity in a queuing system does not affect utilization, as demand is never lost, but might
have to wait longer than desired. The amount of demand fulfilled is independent of the capacity structure
(Cachon and Terwiesch 2009: 346).
Weng (1998: 587), Chen and Chen (2003), Plambeck and Taylor (2003), Chen and Ren (2007), Van
Mieghem (2007: 1251), Cachon and Terwiesch (2009: 344).
Cachon and Terwiesch (2009: 151, 348).
Iyer and Jain (2004).
Jain (2007).
50
3 Methods of Risk Pooling
3.5
Sales and Distribution
3.5.1
Product Pooling
Product pooling is the unification of several product designs to a single generic or “universal
design”524 or reducing the number of products or stock-keeping units (“SKU rationalization”525) thereby serving demands that were served by their own product variant before with
fewer products.526
The demands for the different products are aggregated to the demand for the universal
design or the reduced number of SKUs, which fluctuates less thanks to risk pooling. Thus
product pooling can reduce demand variability, improve matching of supply and demand,
reduce the demand-supply mismatch cost527, and increase sales and profit or lower inventory for a given target service level.528 Thus, product pooling constitutes a 1/0 – risk pooling
method.
However, a universal design might not provide the desired functionality to consumers
and therefore might not achieve the same total demand as a set of focused designs. It does
not permit price discrimination and may be more expensive than focused designs, because
the components or quality of components of the universal design targeted to many different
uses might not be necessary to some consumers. There might be economies of scale in
production and procurement of a single universal component relative to small quantities of
several components and lower labor costs though.529 The risk pooling benefits of selling a
universal product may compensate its higher cost.530
Product pooling is closely related to postponement, where the differentiation of a universal product to individual ones is delayed531, standardization, and component commonality. It may prohibit risk pooling benefits from product substitution.
524
525
526
527
528
529
530
531
Cachon and Terwiesch (2009: 330).
Jabbonsky (1994), Lahey (1997), Kulpa (2001), Pamplin (2002), Alfaro and Corbett (2003: 12), Neale et
al. (2003), HTT (2005), Sheffi (2006: 119, 2007), Covino (2008), Harper (2008), Sobel (2008: 172),
Chain Drug Review (2009a, 2009b), Hamstra (2009), MMR (2009), Orgel (2009), Pinto (2009a, 2009b),
Ryan (2009), Thayer (2009).
Alfaro and Corbett (2003: 12), Cachon and Terwiesch (2009: 330-336, 467).
The demand-supply mismatch cost is the cost of left over inventory (overage cost) and the opportunity
cost of lost sales (underage cost) (Cachon and Terwiesch 2009: 257-263, 433f.).
Cachon and Terwiesch (2009: 331), Hamstra (2009), Ryan (2009), Thayer (2009: 23).
Cachon and Terwiesch (2009: 335), Hamstra (2009), Ryan (2009), Thayer (2009: 23).
Cattani (2000).
Alfaro and Corbett (2003: 25).
51
3 Methods of Risk Pooling
3.5.2
Product Substitution
In product substitution one tries to make customers buy another alternative product, because
the original customer wish is out of stock532 or although it is available (“demand reshape”533).
In manufacturer-driven substitution the manufacturer or supplier makes the decision to
substitute. Typically the manufacturer or supplier substitutes a higher-value or functionality
product, component, or service for a lower-value or functionality one that is not available
(downward substitution).534 Axsäter (2003b: 438) compares this to unidirectional transshipments, where transshipments are only allowed in one direction, perhaps because warehouses
differ in their shortage costs. Swaminathan (2001: 130) and Simchi-Levi et al. (2008: 348) relate
substitution to product standardization: With risk pooling through product standardization a
large variety of products may be offered, but only a few kept in inventory. If a product not kept
in stock is ordered, either the product is made or procured or the order filled by downward substitution.
In customer-driven substitution, a customer makes the decision to substitute, because his
original wish is not available.535
If only one of two products is a substitute for the other one, this is called one-way substitution. In two-way substitution either product substitutes for the other one.536
Substitution allows the manufacturer or retailer to aggregate demand across substitutable
components or products537 (demand pooling538). Demand reshape increases the demand mean
and variability of one product while reducing them for the other product. Substitution and demand reshape reduce total demand variance539 (“demand-pooling effect of substitution”540) and
thus allow to reduce the safety stock for a given customer service level (product availability, fill
rate, or average backlogged demand)541, increase service level without increasing inventory, or a
combination of both542 or increase total profit and raise the customer service level simultaneously by risk pooling543. Product substitution is a 1/0 – risk pooling method.
532
533
534
535
536
537
538
539
540
541
542
543
Swaminathan (2001: 130), Chopra and Meindl (2007: 324ff.), Simchi-Levi et al. (2008: 348).
Eynan and Fouque (2003, 2005).
Gerchak et al. (1996), Hsu and Bassok (1999), Bassok et al. (1999), Swaminathan (2001: 130), Chopra
and Meindl (2007: 324), Simchi-Levi et al. (2008: 348).
Netessine and Rudi (2003), Chopra and Meindl (2007: 324).
Chopra and Meindl (2007: 325).
Chopra and Meindl (2007: 324ff.).
Yang and Schrage (2009: 837).
Eynan and Fouque (2003, 2005).
Ganesh et al. (2008: 1124).
Chopra and Meindl (2007: 326).
Liu and Lee (2007).
Weng (1999), Swaminathan (2001: 130), Eynan and Fouque (2003), Simchi-Levi et al. (2008: 348).
52
4
Choosing Suitable Risk Pooling Methods
Findings from our thorough literature review are now merged in a synoptic comparison about
conditions favoring the ten identified risk pooling methods, their advantages, disadvantages,
and basic trade-offs. Based on this synopsis a decision support tool is developed for choosing
appropriate risk pooling methods for a specific situation. Therefore a situational approach is
used.
4.1
Contingency Theory
We adopt a situational approach similar to contingency theory. It claims that there is no “one
best way” as e. g. in Weberian bureaucracy544 to manage a company or make decisions.545 It
depends (is contingent) on internal and external conditions (contingency factors).546 “The best
way to organize depends on the nature of the environment to which the organization must relate”547.
Contingency theory is mainly criticized for its positivist548, deterministic, unidirectional,
linear relationships and reduction of complex situations to a limited number of contingency
factors.549
Different from the usual contingency approach we not only use quantitative, empirical550, but mainly qualitative analysis based on reviewed quantitative analyses, which Donaldson (1999) rejects. Kieser and Kubicek (1992: 220ff.), on the other hand, propose to
use empirical correlations not as causalities, but for further interpretations, hypotheses, and
empirical analyses. Höhne (2009: 89) and the references she gives support that contingency factors are based on both empirical analyses and plausibility assumptions.
We cannot confirm that there is “[o]ne best way for each given situation”551 as our contingency factors are not exhaustive and mutually exclusive and thus several risk pooling
methods may be adequate. However, Donaldson (1996: 118ff.) remarks there are as many
544
545
546
547
548
549
550
551
Weber (1980: 124ff., 551ff.).
Scherer and Beyer (1998: 333f.).
Drazin and van de Ven (1985), Miller and Friesen (1980: 268), Scherer and Beyer (1998: 334).
Scott (1981: 114).
Positivism is “a system recognizing only that which can be scientifically verified or logically proved”
(Soanes and Hawker 2008).
Miller and Friesen (1978: 921), Miller (1981: 2f.), Meyer (1993: 1176), Staehle (1994: 49f., 54), Schreyögg (1995: 159ff., 217f., 219), Frese (1992: 193), Scherer and Beyer (1998: 334ff.), Klaas (2002: 99f.),
Höhne (2009: 92f.).
Scherer and Beyer (1998: 334), Höhne (2009: 89, 91, 94).
Scherer and Beyer (1998: 334).
53
4 Choosing Suitable Risk Pooling Methods
combinations of environment, strategy, and structure (“fits”) as there are different environmental situations. Thus, for every situation (combination of contingency factors) there
may be one best risk pooling strategy, i. e. combination and implementation of risk pooling
methods.
Starbuck (1981, 1982: 3), Frese (2000: 488f.), and Schreyögg (2008: 54) consider the
contingency approach obsolete. Others, however, deem it important552, popular, often used,
and useful553, as it is open and flexible554, allows to be combined with other approaches to
advance research555, to make action and design recommendations556, to systematize contingency factors557, and to conduct a practice-oriented analysis558. Therefore it seems adequate for our research.
4.2
Conditions Favoring the Individual Risk Pooling Methods
Table D.3 is based on our thorough literature review and shows which conditions render which
risk pooling methods favorable. The favorable conditions are demand-, lead-time-, transportation-, service-level-, order-policy-, storage-, product-, process-, company-, and competitionrelated. The risk pooling methods (columns) are arranged according to the previous chapter's
structure.
Further research is needed to complete this table and confirm the favorable conditions
for the different risk pooling methods, especially for product pooling, central ordering,
(particularly non-manufacturing) capacity pooling, virtual pooling, and product substitution/demand reshape. We could only speculate and hypothesize about which risk pooling
methods the stated favorable conditions also apply to. Therefore, we only check marked
them for methods where there is confirmation in the literature and the table is not exhaustive. References and explanations are given in footnotes.
552
553
554
555
556
557
558
Pugh (1981), Donaldson (2001), Daft (2009: 26).
For example in management (Hiddemann 2007: 16, Schröder 2008: 68, Müller-Nedebock 2009: 22,
Sommerrock 2009: 88, 93f., Segal-Horn and Faulkner 2010: 157f.), organization (Dzimbiri 2009: 86,
Güttler 2009: 73f., Höhne 2009: 83, 91, 93f., March 2009: 25, Nobre et al. 2009: 31), finance (Pfeifer
2010: 253), information systems (Andres and Zmud 2001, Sugumaran and Arogyaswamy 2003, Khazanchi 2005), supply management (Staudinger 2007), business logistics and SCM (Hult et al. 2007, Huang et
al. 2008, Doch 2009: 39ff.), and supply chain risk management (Wagner and Bode 2008) research. The literature database Business Source Complete accessed via EBSCOhost® showed 1,139 results for the
search term “contingency theory” on June 18, 2010.
Staudinger (2007: 41), Güttler (2009: 73f.).
Sommerrock (2009: 144), Güttler (2009: 73f.).
Hiddemann (2007: 16), Schröder (2008: 69), Doch (2009: 39ff.), Pfeifer (2010: 262).
Doch (2009: 41).
Staudinger (2007: 41), Sommerrock (2009: 94).
54
4 Choosing Suitable Risk Pooling Methods
4.3
The Risk Pooling Methods' Advantages, Disadvantages,
Performance, and Trade-Offs
Table D.4 presents the considered risk pooling methods' possible advantages, disadvantages,
and basic trade-offs in choosing or rejecting them and compares their performance vis-à-vis
other ones.
In summary, the risk pooling methods may, on the one hand, reduce demand and/or lead
time variability, (safety) stock, lead time, as well as procurement, production, transportation, personnel, and warehouse cost and increase service level (product availability and
fill-rate), utilization, sales, profit, and competitiveness.
On the other hand, they may increase R&D, redesign, component, product, procurement, production, transportation, transaction, and warehousing cost, as well as cycle stock
and cycle time, and decrease customer service, sales, profit, and product functionality. We
only check marked the respective risk pooling method's most important effects that are
confirmed in the studied literature. References are given in footnotes. Explanations are
only given where essential, as we already dealt with the individual risk pooling methods in
detail earlier. These three choices maintain the readability of the table.
Tables D.3 and D.4 can be used to choose suitable risk pooling methods for a specific
company under specific conditions. Scoring methods could be applied or the risk pooling
method with the highest net present value or profit (advantages minus disadvantages expressed in monetary units) could be chosen. However, the following decision support tool
condenses the most definite distinguishing factors and helps to make a first decision on
possible risk pooling methods elegantly, before carrying out a more thorough cost-benefit
analysis.
55
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4 Choosing Suitable Risk Pooling Methods
A Risk Pooling Decision Support Tool
Figure 4.1: Risk Pooling Decision Support Tool
56
4 Choosing Suitable Risk Pooling Methods
The Risk Pooling Decision Support Tool (RPDST) depicted by a flow chart in figure 4.1 helps
in choosing a risk pooling strategy to cope with demand and/or lead time uncertainty (1), if
it cannot be reduced more efficiently by other means559.
To facilitate the reader's orientation we introduced numbers in round brackets in this
explanation and the flow chart. We will guide you through the flow chart step by step and
critically revisit it at the end.
(2) If product variety is important, inventory pooling (IP)560, capacity pooling
(CP)561, component commonality (CC)562, postponement (PM)563, product substitution
(PS)564, transshipments (TS)565, virtual pooling (VP)566, centralized ordering (CO), and
order splitting (OS) are a possibility. IP, CP, TS, VP, CO, and OS may also be applied, if
product variety is not important. The first four methods might make more sense, if product
variety is important. CC, PM, and PS are not expedient without product variety.
If product variety is not important, product pooling (PP), IP, CP, TS, VP, CO, and
OS are considered. PP is only meaningful, if product variety is not important. The other
methods may also be applied, if product variety is important.
(3) If product variety is important and the stockout penalty cost high compared to inventory carrying cost (savings), PS567, TS568, VP, CP, CC, PM569, CO570, and OS571 may be
559
560
561
562
563
564
565
566
567
568
In addition to risk pooling it may be reduced by e. g. adding inventory or capacity, having redundant
suppliers, which resembles order splitting, increasing responsiveness (Chopra and Sodhi 2004: 55, 60)
(quick response (Heil 2006)), flexibility, and capability (Chopra and Sodhi 2004: 55, 60), and improving
forecasting (Heil 2006). In LeBlanc et al.'s (2009: 29) model, for instance, PM is favorable unless the
forecast is completely accurate.
Pfohl (1994: 142), Schulte (1999: 378), Weng (1999: 80), Vahrenkamp (2000: 221), Alfaro and Corbett
(2003: 28).
Jordan and Graves (1995: 577), Cachon and Terwiesch (2009: 344).
Srinivasan et al. (1992: 27), Swaminathan (2001: 131), Simchi-Levi et al. (2008: 348), Song and Zhao
(2009: 493).
Zinn (1990: 14), Lee and Tang (1997: 52), Pagh and Cooper (1998: 24), Swaminathan and Tayur (1998),
Van Hoek (1998b, 2001: 161, 173), Van Hoek et al. (1998), Aviv and Federgruen (2001a: 514), Ihde
(2001: 36), Matthews and Syed (2004: 34), Graman and Magazine (2006: 1072), Chopra and Meindl
(2007: 363f.), Cachon and Terwiesch (2009: 342, 363). “The potential benefits of postponement in the
presence of product variety are reduced inventory levels and/or improved service levels” (Graman and
Magazine 2006: 1072). “In general, delayed differentiation is an ideal strategy when […] Customers demand many versions, that is, variety is important” (Cachon and Terwiesch 2009: 342).
Weng (1999: 80), Swaminathan (2001: 130), Eynan and Fouque (2003), Simchi-Levi et al. (2008: 348).
Grahovac and Chakravarty (2001), Wong (2005), Simchi-Levi et al. (2008: 231).
Guglielmo (1999), Randall et al. (2002: 56f., 2006: 567), Kroll (2006).
Liu and Lee (2007: 1, 41). Only the risk pooling effect is considered, the financial aspect of different
product margins neglected.
TS reduce demand and lead time variability by pooling demand and lead times, decrease stockouts, and
thus are sensible, if stockout costs are high (Evers 1997, Needham and Evers 1998, Evers 1999: 133,
2001: 313, Jung et al. 2003, Hu et al. 2005, Wee and Dada 2005: 1519, 1529, Zhao et al. 2005: 545, Lue
2006, Chiou 2008: 428). However, in Jung et al. (2003) the savings from lateral TS decrease with increasing shortage cost from a certain value upwards.
57
4 Choosing Suitable Risk Pooling Methods
applied. PS (costs of persuading a customer to buy a substitute in case of a stockout and
possible customer dissatisfaction because he did not obtain the desired product572), TS
(transshipping costs), VP (drop-shipping or cross-filling costs), CP (large costs to have
flexibility), and CC (common component costs) may only be worthwhile, if stockout costs
are high. PS573, PM574, CO575, and OS576 may also be considered, if the stockout penalty
cost is low. IP is suitable, if the stockout cost is low compared to the inventory (carrying
cost) savings from combining inventories, as it increases the distance between the inventory and the buyer and thus delivery time and therefore might increase stockouts577. As noted
earlier in section 2.4 and table D.3, Dai et al. (2008: 407, 410f.) show when IP by a supplier for two retailers may increase the supplier's and retailers' total profits. We consider IP
for low stockout costs only, as the decision for or against inventory pooling vis-à-vis the
other risk pooling methods is considered.
(4) If (2) is answered in the affirmative, (3) with “High”, and the supplier lead time is
highly variable/uncertain or long, TS578, VP, PM579, CO, and OS580 are considered. TS
569
570
571
572
573
574
575
576
577
578
PM may increase flexibility and responsiveness to customer demand (Zinn and Bowersox 1988: 133,
Herer et al. 2002, Davila and Wouters 2007), increase customer service, decrease stockout costs, and thus
may be sensible, if stockout costs are high.
Eppen and Schrage (1981: 51), Schoenmeyr (2005: 5). CO may increase responsiveness to customer
demand, if the allocation of the central order to the delivery warehouses, retailers, or stores can be postponed and made more responsively according to more recent demand information (Cachon and Terwiesch
2009: 341), decrease stockout costs, and thus may be sensible, if stockout costs are high.
OS can reduce lead time (variability) through lead time pooling and increase inventory availability.
Therefore it can be reasonable, if stockout costs are high (Evers 1999: 122, 132).
Swaminathan (2001: 131).
PS may be worthwhile in case of low stockout costs, if the sold substitute's profit margin is higher than
that of the original product wish. Besides, even if the original customer wish is available, PS or demand
reshape lowers the total variability of demand and thus inventory costs (Eynan and Fouque 2003, 2005).
Besides the risk and stockout cost reduction, PM can lead to economies of scale, synergistic effects, delayed increase in costs in the value chain and thus decreased capital commitment, and higher flexibility
(Lee and Tang 1997: 52, Van Hoek 2001: 162, Aviv and Federgruen 2001b: 579, Herer et al. 2002, Kim
and Benjaafar 2002: 16, Ma et al. 2002: 534, Graman and Magazine 2006: 1078, Piontek 2007: 86f.).
Therefore it may be worthwhile, even if stockout costs are not particularly high.
PM (Zinn and Bowersox 1988: 125f., Van Hoek 2001: 161, Rabinovich and Evers 2003b: 35, Yang et al.
2005b: 994, Graman and Magazine 2006: 1078, Pishchulov 2008: 13, Mahar and Wright 2009: 3061) and
CO (McGavin et al. 1993: 1094, Cachon and Terwiesch 2009: 341) may lead to a longer delivery time
(from the supplier to the retailer) and more stockouts, and therefore stockout costs should be low. Bucklin
(1965: 27) remarks that speculation, the opposite strategy to postponement, “limits the loss of consumer
goodwill due to stockouts”. CO may also increase stockouts, if it decreases local knowledge (Ganeshan et
al. 2007: 341).
Although OS may reduce lead time variability, the split orders are delivered sequentially and thus may
lead to more stockouts than a single order or delivery and stockout costs should be low (Chiang 2001: 73,
cf. Chiang and Chiang 1996).
McKinnon (1989: 104), Fawcett et al. (1992: 36ff.), Schulte (1999: 80, 377), Vahrenkamp (2000: 31f.),
Bowersox et al. (1986: 278f.), Evers (1999: 122f.), Ballou (2004b: 573f.), Schmitt et al. (2008a: 14), Cachon and Terwiesch (2009: 336).
Evers (1999: 132), Herer et al. (2002), Hu et al. (2005), Wanke and Saliby (2009). However, Evers
(1996) finds the percentage reduction in safety stocks obtained by using non-emergency transshipments
decreases with increasing coefficient of variation of lead time (lead time variability) and average lead
58
4 Choosing Suitable Risk Pooling Methods
and VP by cross-filling may pool demands and lead times, i. e. reduce demand and lead
time variability.581 Long order cycles582 and inflexible production processes583 favor TS.
Long supplier/production lead times support CO.584 For CO the lead time before the distribution center (DC) should be longer than the one after it.585 PM and CO may also reduce
lead time (variability/uncertainty): “Postponement permits firms to be more responsive and
other advantages that are often mentioned are risk-pooling and lead-time uncertainty reduction”586. If, for instance, in CO or consolidated distribution product differentiation is
delayed (PM) in the DC, total lead time may be reduced587. Since larger common orders
for multiple locations make more frequent shipments economically possible between the
suppliers and the DC and the DC and the retailers588, consolidated distribution might decrease lead time (uncertainty) despite the additional lead time from the DC to the various
retailers. If there is no DC and the retailers merely place joint orders with the suppliers
which are then allocated according to more recent demand information to the retailers just
before the delivery means leave the suppliers, there is no additional lead time between the
DC and the retailers. The retailers' higher demand power through CO and closer collaboration between the retailers and the suppliers might further reduce average lead times and
lead time fluctuations. OS only pools lead times589 and is only worthwhile, if lead time
579
580
581
582
583
584
585
586
587
588
589
time at each market (Evers 1996: 126ff.). It increases at a decreasing rate as the proportion of demand at
market i retained at facility i approaches the point where demand at i is spread evenly among all locations
(Evers 1996: 128). By spreading the demands, and therefore the variability, more evenly across locations,
the opportunity to smooth demand fluctuations increases at a decreasing rate (Evers 1996: 128).
Transhipments may be seen as a type of time postponement (Rabinovich and Evers 2003b).
Kelle and Silver (1990a, 1990b), Pan et al. (1991: 4), Evers (1997, 1999: 122, 132), Kelle and Miller
(2001), Thomas and Tyworth (2006, 2007: 178, 188). According to Thomas and Tyworth (2007: 188),
sequentially releasing a split order according to more recent demand information may reduce demand variability. Chiang and Chiang (1996) and Chiang (2001: 67, 73), however, recommend “splitting an order
into multiple deliveries“ for low demand variability or service level only. The number of stockout possibilities is proportional to the number of deliveries. Thus OS increases stockouts, the more, the more variable demand is. Kelle and Miller (2001: 407) find dual sourcing may decrease stockouts, if there is no
“single, reliable supplier [… and] the variability of the lead-time demand is considerable”, but is only
suitable, if lead time uncertainty cannot be reduced. According to Evers (1999: 123) and Wanke and Saliby (2009: 679) splitting a replenishment order into multiple orders only pools lead times, not demand.
Consequently, we recommend OS only for high lead time variability and its lead time pooling, but not its
debatable demand variability reduction effect.
Evers (1997, 1999: 121), Zhao et al. (2008).
Jönsson and Silver (1987a: 224).
Grahovac and Chakravarty (2001: 580).
Eppen and Schrage (1981: 51), Schoenmeyr (2005: 5).
Cachon and Terwiesch (2009: 341), cf. Kumar and Schwarz (1995).
Caux et al. (2006: 3243).
Dilts (2005: 43). Personal correspondence with Professor David M. Dilts on July 7, 2009.
Cachon and Terwiesch (2009: 341).
Evers (1999: 122, 132).
59
4 Choosing Suitable Risk Pooling Methods
variability590 and unit values are (unusually) high (in relation to industry standards)591. For
high stockout costs per unit (3), high lead time variability (4), low order quantity and/or
safety stock levels emergency TS perform particularly well compared to OS.592
In case (4) lead times are neither highly variable/uncertain nor long, but rather demand is variable/uncertain and thus demand pooling important, PS593, CP594, CC595, PM596
and CO597 may be appropriate.
590
591
592
593
594
595
Kelle and Silver (1990a, 1990b), Pan et al. (1991: 4), Evers (1999: 132), Thomas and Tyworth (2007:
178, 188).
Thomas and Tyworth (2007: 178, 188).
Evers (1999: 132).
Eynan and Fouque (2003, 2005), Chopra and Meindl (2007: 324ff.), Ganesh et al. (2008: 1124).
Yu et al. (2008: 1).
We will now examine whether CC reduces (the effects of) lead time variability/uncertainty and therefore
should be considered, if it is high:
Benton and Krajewski (1990: 407) show in a computer simulation experiment with 320 observations that
manufacturing “environments with intermediate stocking points and commonality significantly dampen
the effects of lead time uncertainty” (410), “tend[…] to reduce the level of backlogs as well as dampen
their sensitivity to lead time uncertainty” (412), because “commonality causes intermediate inventories to
increase” (413, cf. 410). However, they are more sensitive to vendor quality (“the ability to supply the requested quantity of nondefective parts or raw materials” (404)) and therefore might increase backlogs
(413). Yet, the ambition of risk pooling is to decrease inventory for a given service level or vice versa or a
combination of both. If there are no intermediate stocking points, they are more sensitive to lead time uncertainty (410). Hence, CC by itself does not reduce “the effects of lead time uncertainty”. Benton and
Krajewski (1990) give no intuitive explanation for the increasing total inventory. Usually common components reduce safety and thus total stock, because they are used in several products (Labro 2004: 362).
Eynan and Rosenblatt (1996), Chandra and Kamrani (2004: 175), and Mohebbi and Choobineh (2005:
473) cite Benton and Krajewski (1990) in a truncated manner, aiming at the reduction of lead time uncertainty through CC. Labro (2004) deals with Benton and Krajewski (1990) more accurately.
Although Ma et al. (2002) assume “deterministic replenishment leadtimes” (Ma et al. 2002: 526), they
find “the major benefits of commonality are risk-pooling and lead time uncertainty reduction. These lead
to a safety stock reduction and have been studied extensively by many researchers, including, but not limited to, Baker et al. (1986), Collier (1982), Guerrero (1985), Gerchak et al. (1988), Eynan and Rosenblatt (1996), and Grotzinger et al. (1993)” (Ma et al. 2002: 524).
Like most CC research (e. g. McClain et al. 1984, Eynan 1996, Thonemann and Brandeau 2000, Hillier
2002a, 2002b, Thomas et al. 2003, Labro 2004: 359), all these researchers mention demand uncertainty
reduction as a benefit of CC (Baker et al. 1986: 983, Collier 1982: 1300, 1303, Guerrero 1985: 396, Gerchak et al. 1988: 755), only Eynan and Rosenblatt (1996) lead time uncertainty reduction in the inadequate manner described above.
Under restrictive assumptions, Mohebbi and Choobineh (2005: 476, 481) conclude CC tends to be more
beneficial with both random component procurement order delays and demand uncertainty than with only
one of these uncertainties. They assume, for instance, that the component procurement lead time can
only be longer not shorter than the planned one. Actual uniformly distributed demand for finished
products, however, can be higher or lower than the forecast (476). Costs (481), safety stock and safety
lead times are neglected. Backorders are filled after current demand (475). These researchers do not explain the causes for their observations. Lead time delays mostly reduce average total inventory per component per period (477f.), as they perhaps reduce the time a component remains in storage. This effect increases with increasing demand uncertainty (477), perhaps because a longer-than-planned delivery time
may be offset by lower-than-forecast actual demand. This may be amplified by CC and lead to a higher
service level than without commonality. However, the product with the lowest number of (three) components and without commonality shows the lowest inventory per component and the highest service levels
(478f.).
Song and Zhao (2009: 22) even find that in dynamic assemble-to-order systems commonality may not
decrease inventories under the first-in-first-out (FIFO) with identical and under the FIFO and modified
FIFO (MFIFO) rule for dynamically allocating common components to demand with non-identical com60
4 Choosing Suitable Risk Pooling Methods
(5) If (2) is “Yes”, (3) “High”, (4) “Yes”, and the fixed cost per order high, TS598, VP,
PM, and CO599 are favorable. If the replenishment order cost is high, one rather resorts to
other cheaper and/or faster possibilities (TS, VP, and PM) than placing a replenishment
order or tries to combine orders by CO to reduce the number of orders and exploit economies of scale (EOS) and thus lower ordering costs. If it is low600 and there are no transportation EOS601, OS may be considered. Due to smaller orders OS cannot take advantage of
quantity and transportation discounts and a long-term partnership with a single supplier,
but several suppliers may guarantee competitive pricing and other advantageous terms.602
TS603, VP, and PM may also be applied, if the fixed order cost is low.
(6) In case (2) is “Yes”, (3) “High”, (4) “Yes”, (5) “High”, and the transshipment or
transportation cost is high and there are EOS in ordering, CO604 or PM605 can be
worthwhile. If the transshipment or transportation cost is low and there are no EOS in
ordering, TS606, VP607 or likewise PM608 can be applied. PM may forego EOS:609 Zinn and
596
597
598
599
600
601
602
603
604
605
606
607
ponent replenishment lead times. “The value of commonality tends to decrease as [… the common component replenishment lead time] increases under either FIFO or MFIFO”.
If the common component replenishment lead time fluctuates strongly and the common component is not
available, all the products using this component cannot be built. Thus lead time variability/uncertainty of
the common component supplier might be more severe than of a specific component supplier (cf. Benton
and Krajewski 1990: 413, Labro 2004: 363).
All these findings led us to not recommend CC by itself for coping with high lead time variability/uncertainty and to only consider it for the low lead time variability/uncertainty case.
Jain and Paul (2001: 595ff.), Anupindi et al. (2006: 193), Chopra and Meindl (2007: 365), Pishchulov
(2008: 24).
If we follow Cachon and Terwiesch (2009: 336, 339, 341f., 349), CO may only pool demands and may
also be applied if lead time (variability) is low. PM or delayed differentiation and CO may increase lead
time and only pool demands during lead time.
Herer and Rashit (1999: 525), Daskin (2003), Herer and Tzur (2003: 419).
Schwarz (1981: 147), Evers (1995: 5, 1999: 133), Gürbüz et al. (2007: 294).
Evers (1999: 132), Thomas and Tyworth (2007: 172, 178, 188).
Evers (1999: 122f.), Thomas and Tyworth (2006, 2007), Sajadieh and Eshghi (2009).
Evers (1999: 122f.).
For TS the fixed order cost is irrelevant (Evers 1999: 132).
Eppen and Schrage (1981: 67), Hu et al. (1997, 2005: 34), Gürbüz et al. (2007: 293), Cachon and Terwiesch (2009: 341).
Allowing online sales to accumulate and postponing assigning them to a fulfillment site can lead to lower
inventory costs (Mahar and Wright 2009), higher utilization of transportation means, and EOS in ordering. PM does not necessarily increase transportation distance, so that transportation costs may be irrelevant. Customers may be willing to wait, so that no premium transportation cost is incurred. The product
and process are usually designed, so that the delayed differentiation can be conducted fast (Lee and Tang
1997), the delivery delay is insignificant, and no premium transportation cost is incurred. PM can exploit
EOS (Piontek 2007: 87).
Jönsson and Silver (1987a: 224), Robinson (1990), Evers (1999: 132f.), Grahovac and Chakravarty
(2001), Jung et al. (2003), Hu et al. (2005), Anupindi et al. (2006: 191), Kutanoglu (2008: 356f.). Still TS
may save fixed and variable replenishment costs (Herer and Rashit 1999: 525, Herer and Tzur 2003: 419),
if e. g. one location makes a larger replenishment order to transship some of it to other locations especially in a dynamic deterministic demand environment (Herer and Tzur 2003: 419). Herer and Rashit (1999)
consider a single period random demand environment.
Anupindi et al. (2006: 191). In VP small-orders may be drop-shipped more expensively than full truck
loads (Randall et al. 2002, Cachon and Terwiesch 2009: 328f.).
61
4 Choosing Suitable Risk Pooling Methods
Bowersox (1988: 124f.) find that labeling, packaging, and manufacturing PM can lead to
lost EOS. In case of large EOS in the manufacturing and/or logistics processes some
speculation should be applied instead of manufacturing and full PM. Speculation, the opposite strategy to PM, rather leads to EOS: “Speculation permits goods to be ordered in
large quantities rather than in small frequent orders. This reduces the costs of sorting and
transportation”610.
(7) If (2) is “Yes”, (3) “High”, (4) “Yes”, (5) “High”, and (6) “Yes”, do you prefer redesigning your products and/or processes611 to achieve leagility, both agility (responsiveness) and leanness (cost minimization), (PM)612 to a less expensive, fast implementable and changeable solution that keeps inventory closer to customers (CO)613? If yes, you
may implement PM (8), otherwise CO (9). Time and form PM are appropriate, if welltimed product delivery to and differentiation for the customer are more important than
company-internal cost issues.614 On the one hand, CO may decrease responsiveness because of a lack of local knowledge about sales615 when ordering. On the other hand, it may
increase responsiveness because of allocating the joint order to the delivery warehouses,
retailers, or stores according to more recent demand information and because aggregate
forecasts usually are more accurate than disaggregate ones616. It is more likely that CO
leads to EOS in ordering than PM. While CO and speculation lead to consolidation of
goods in jointly used transfer and transformation processes and EOS617, PM tends to singularize batches of goods in separate transfer and transformation processes618. To determine
which PM strategy might be most appropriate, you may turn to Zinn and Bowersox (1988),
Cooper (1993), Pagh and Cooper (1998), Yang et al. (2004), and Yeung et al. (2007).
(10) In case (6) is answered in the negative, and the less expensive, fast implementable
and changeable, less cross-functional solution is preferred to redesigning products
608
609
610
611
612
613
614
615
616
617
618
Bucklin (1965: 27), Zinn and Bowersox (1988: 126), Christopher (1992), Feitzinger and Lee (1997),
Delfmann (1999: 195), Van Hoek (2001: 161).
Zinn and Bowersox (1988: 124), Yang et al. (2005b: 994).
Bucklin (1965: 27).
Products and/or processes may have to be redesigned for PM (Lee and Tang 1997, Van Hoek 1998a, Kim
and Benjaafar 2002, Yang et al. 2005b: 994, Davila and Wouters 2007, Piontek 2007). PM might lead to
higher manufacturing costs (Chopra and Meindl 2007: 365).
Feitzinger and Lee (1997), Fliedner and Vokurka (1997), Van Hoek et al. (1999a), Christopher (2000),
Van Hoek (2000a), Christopher and Towill (2001), Herer et al. (2002), Graman and Sanders (2009: 206).
Eppen and Schrage (1981), Pishchulov (2008: 22), Cachon and Terwiesch (2009: 349).
Alderson (1957), Rabinovich and Evers (2003b: 34).
Ganeshan et al. (2007).
Cf. footnote 456.
Bucklin (1965: 27), Pagh and Cooper (1998: 14), Delfmann (1999: 195), Klaas (2002: 157).
Cooper (1983: 71), Bowersox and Closs (1996: 475), Klaas (2002: 157).
62
4 Choosing Suitable Risk Pooling Methods
and/or processes619 and there is no or no significant lead time (uncertainty) reduction
benefit in PM after all, TS and VP are considered. If in addition your supplier, wholesaler,
or warehouse locations have small-order drop-shipping or cross-filling capabilities620
(11), VP (12) may be appropriate. If not, TS (13) may do, especially if the TS cost is lower
than the VP cost. VP may reduce investment in inventory and fulfillment capabilities as
well as overall handling and warehousing costs621 more than TS. However, VP is only recommendable, if your company possesses the necessary IS capabilities and is powerful
within the supply chain, because it might lose product margin and control to the dropshipping party, which could negatively affect service quality. The drop-shipping party
might bypass the company and directly sell to customers as it possesses all the information
transparency it needs.622 “Virtual inventories provide little benefit in product categories,
such as grocery, where consolidation of orders is necessary but impossible to accomplish
from a few consolidated wholesalers”623.
TS and PM might be used in combination, as emergency TS, an important type of time
PM, support implementing form PM624.
If you do not mind redesigning products and/or processes and a more expensive midto long-term cross-functional implementation and your PM strategy may reduce lead
time uncertainty (10), PM (14) might be the right method to reduce both demand and lead
time uncertainty. TS can increase leagility like PM625, but perhaps more inexpensively and
faster.
Returning to (5), if the fixed order cost is low, and (15) both demand uncertainty reduction and lead time (uncertainty) reduction and fewer order placements are preferred to only lead time uncertainty reduction, but avoiding premium transportation
and in-transit inventory costs, TS626, VP627, and PM628 come into question and the al-
619
620
621
622
623
624
625
626
627
628
Lee and Tang (1997: 40, 1998), Van Hoek (1998a), Kapuscinski and Tayur (1999), Jain and Paul (2001),
Swaminathan (2001: 129f.), Herer et al. (2002), Kim and Benjaafar (2002: 12), Yang et al. (2005b: 994),
Davila and Wouters (2007: 2245), Shao and Ji (2008), Simchi-Levi et al. (2008: 345f.).
Randall et al. (2002: 56), Cachon and Terwiesch (2009: 328f.).
Randall et al. (2002: 55).
Randall et al. (2002: 56).
Randall et al. (2002: 57).
Rabinovich and Evers (2003b: 41f.).
Herer et al. (2002: 201), Zhao et al. (2008).
Tagaras (1989), Tagaras and Cohen (1992), Evers (1997, 1999), Hong-Minh et al. (2000), Herer et al.
(2002), Çömez et al. (2006).
Randall et al. (2002: 56).
Jain and Paul (2001: 595ff.), Yang et al. (2004: 1054), Dilts (2005: 43), Anupindi et al. (2006: 193), Caux
et al. (2006: 3243), Chopra and Meindl (2007: 365), Pishchulov (2008: 24).
63
4 Choosing Suitable Risk Pooling Methods
ready explained decision process (10) through (14) starts. If (15) is negated, OS629 (16)
may be implemented.
Moving upwards again, in case (3) is low and (17) inventory reduction is more important than agility (customer responsiveness), IP630 and PS631 are considered. If (17) is negated, PM, PS, CO, and OS come into consideration. PM improves agility632 and flexibility633 and enables product variety634, but may not decrease inventory as much as IP or PS. PS
performs better than IP in terms of location accessibility and lost sales (customer responsiveness)635, but may not decrease inventory as much as IP. With PS the customer may get a
product right away, but not the originally desired one. CO performs worse than IP in terms of
inventory reduction, but keeps inventory near customers636. The allocation of the central order to the delivery warehouses, retailers, or stores can be postponed and made more responsively according to more recent demand information. Reducing lead time uncertainty OS
may lower (safety) stock for a given service level637, but not as much as IP, as the former
only pools lead times, not demands638. Simultaneously splitting an order among suppliers
can reduce cycle stock due to successive deliveries of smaller split orders639, but not the sum
of in-transit and cycle stock in the system640. OS may be more responsive than IP, because it
reduces lead time variability and keeps inventory close to customers. However, OS may increase stockouts, if demand variability is high due to successive deliveries.641
In case (17) is confirmed, and (18) the fast implementable, changeable, less expensive
(especially in terms of transportation cost) solution with higher location accessibility and
629
630
631
632
633
634
635
636
637
638
639
640
641
Evers (1999: 132), Thomas and Tyworth (2007: 172, 178, 188).
IP may reduce inventory more than PS, but creates distance between inventory and customers and therefore may reduce product availability and profits (Bowersox et al. 1986: 278f., McKinnon 1989: 104,
Fawcett et al. 1992: 36ff., Evers 1999: 122f., Schulte 1999: 80, 377, Vahrenkamp 2000: 31f., Ballou
2004b: 573f., Schmitt et al. 2008a: 14, Cachon and Terwiesch 2009: 336).
PS might be seen as not as responsive as PM because the customer does not receive his original wish and
is persuaded to buy a substitute, which may cause some customer dissatisfaction, but might reduce inventory more than PM.
Zinn and Bowersox (1988), Herer et al. (2002), Davila and Wouters (2007).
Lee and Tang (1997: 52), Feitzinger and Lee (1997: 117ff.), Van Hoek (2001: 162), Ma et al. (2002:
534), Graman and Magazine (2006: 1078), Piontek (2007: 86f.).
Cachon and Terwiesch (2009: 341).
Eynan and Fouque (2003, 2005).
Eppen and Schrage (1981), Cachon and Terwiesch (2009: 349), Pishchulov (2008: 22).
Evers (1999: 122, 132), Thomas and Tyworth (2006: 245).
Evers (1999: 122, 132).
Moinzadeh and Nahmias (1988), Pan and Liao (1989), Ramasesh (1990), Sculli and Shum (1990), Pan et
al. (1991), Ramasesh et al. (1991), Hong and Hayya (1992), Zhou and Lau (1992), Lau and Zhao (1993),
Ramasesh et al. (1993), Chiang and Benton (1994), Lau and Zhao (1994), Gupta and Kini (1995), Chiang
and Chiang (1996), Hill (1996), Ganeshan et al. (1999), Chiang (2001), Ghodsypour and O'Brien (2001),
Ryu and Lee (2003), Thomas and Tyworth (2006: 245).
Thomas and Tyworth (2006: 254).
Chiang and Chiang (1996) and Chiang (2001: 67, 73).
64
4 Choosing Suitable Risk Pooling Methods
fewer lost sales is preferred to product functionality and inventory reduction, PS (19)
may be suitable. If (18) is negated, IP (20) might be the right method. In contrast to PS, IP
entails aggregate and thus more accurate forecasts642. Individual demand forecasts for controlling the previously separate inventories are replaced by a more accurate aggregate forecast for managing the consolidated inventory. Of course, PS can only be applied, if products or parts are substitutable, which the preceding affirmation of question (2) suggested.
If (17) is negated and (21) lead times are highly variable/uncertain or long, PM, CO,
and OS are considered (cf. (4)). If then (22) the fixed order cost is high (CO and PM may
be appropriate (cf. (5))) and (23) a perhaps cheaper solution, that keeps inventory closer
to customers, is preferred to redesigning products and/or processes to offer customized
products more responsively and there are EOS in ordering643, CO (24) may be chosen. If
(23) is negated, PM (25) might be appropriate.
If (22) is low (OS and PM may be appropriate (cf. (5))) and product and/or process
redesign to reduce demand uncertainty and perhaps lead time (uncertainty) (cf. (4)) is
preferred to only lead time pooling and keeping inventory close to customers, but incurring higher ordering costs (26), then PM (25) might be suitable. Otherwise, OS (27)
may be worthwhile.
If (21) is negated and rather demand pooling is important, PM, PS, and CO are scrutinized (cf. (4)). If then (28) the less expensive, fast implementable, and changeable solution is preferred to giving the customer always the desired product (not a substitute), but
in a longer delivery time and with product and/or process redesign, PS (19) may be
appropriate, otherwise PM and CO are considered. If in this latter case (29) the cheaper
solution that keeps inventory closer to customers is preferred to product and/or
process redesign and leagility and there are EOS in ordering, then CO (24) may be appropriate, otherwise PM (14) (cf. (23) to (25)).
If the importance of product variety is denied in (2) and lead times are highly variable/uncertain or long (30), TS, VP, OS, and CO are considered (cf. (4)). In case (30) is negated and rather demand uncertainty reduction is important, PP644, IP645, CP, and CO646 (cf.
(4)) are considered as they only pool demands and thus reduce demand variability, but not
lead time variability. According to Dilts (2005) CO may also reduce lead times (cf. (4)).
642
643
644
645
646
Cf. footnote 456.
CO may utilize EOS in procurement (Eppen and Schrage 1981: 67, Hu et al. 1997, 2005: 34, Gürbüz et
al. 2007: 293, Cachon and Terwiesch 2009: 341).
Cachon and Terwiesch (2009: 331f.).
Evers (1996: 115, 1997: 57, 60, 1999: 121).
Cf. Cachon and Terwiesch (2009: 336, 339, 341f., 349).
65
4 Choosing Suitable Risk Pooling Methods
If (30) is affirmed, (31) the fixed order cost is high (CO, TS, and VP are considered (cf.
(5))), (32) the transshipment or transportation cost is high and there are EOS in ordering, CO (33) may be reasonable (cf. (6)). If (32) is negated and (34) your supplier, wholesaler, or warehouse locations have small-order drop-shipping or cross-filling capabilities647
(cf. (11)), VP (35) may be appropriate, especially if it is less expensive than TS. If not, TS
(36) may do (cf. (11) to (13)).
If (31) is low (OS, TS, and VP are considered (cf. (5))) and (37) both demand uncertainty and lead time (uncertainty) reduction, fewer stockouts, and order placements are
preferred to only lead time pooling, but avoiding premium transportation and in-transit
inventory costs of stock transfers648, then TS and VP are considered further and the already
explained decision process (34) to (36) is triggered again. If (37) is answered in the negative,
OS (38) may be economically sensible.
If (30) is negated and (39) accommodating demand uncertainty649 is preferred to
reducing inventory and system utilization (arrival divided by service rate) is high, CP and
CO are considered. “While the relative benefit of inventory pooling tends to diminish with
utilization, the relative benefit of capacity pooling tends to increase with utilization” in a
production-inventory system with endogenous supply lead times.650 CP or manufacturing
flexibility is more valuable with approximately equal total capacity and expected demand.651
CO does not reduce inventory as much as IP, but keeps it near customers.652 The postponed
more responsive allocation of the central order to the delivery warehouses, retailers, or stores
according to more recent demand information enables better matching of supply and demand653 (also cf. (17)). If afterwards EOS in ordering and a preference for a possibly less
expensive, fast implementable and changeable solution are affirmed in (40), CO (33) may
be appropriate. If (40) is negated and (41) CP/(manufacturing) flexibility is cheaper than
capacity, CP (42) might be applied654. Goyal and Netessine (2005) may help to choose a
type of manufacturing flexibility (volume and/or product flexibility)655. If capacity is cheap-
647
648
649
650
651
652
653
654
655
Randall et al. (2002: 56).
Evers (1997: 72, 1999: 123f.).
Cachon and Terwiesch (2009: 344, 348).
Benjaafar et al. (2005: 565).
Cachon and Terwiesch (2009: 348).
Eppen and Schrage (1981: 61), Pishchulov (2008: 22), Cachon and Terwiesch (2009: 349).
Cachon and Terwiesch (2009: 341).
Cachon and Terwiesch (2009: 348).
Volume flexibility is “[t]he ability to adjust the output volume of a product without incurring large costs“,
product flexibility “the ability to manufacture different products and to efficiently shift production from
products with low demand to products with high demand” (Goyal and Netessine 2005: 2). For a monopolist, product flexibility reduces uncertainty in demand for individual products more and in aggregate de66
4 Choosing Suitable Risk Pooling Methods
er than CP/flexibity, adding capacity (43) might be a better choice.656 CP may be more
appropriate for manufacturing, CO for trading companies (cf. (48)).
If (39) is negated, PP and IP (cf. (17)) are considered, as inventory reduction is given
priority. If then (44) product availability is preferred to product functionality, PP (45)
may lead to a higher product availability than IP (46): It does not increase the distance between products and customers and may enable EOS in production and procurement of a single universal component or product, but might degrade product functionality, not achieve the
same total demand as a set of focused designs, and eliminate some brand/price segmentation
opportunities.657
Returning to (4), if lead times are not highly variable/uncertain or long, rather demand
pooling is important (PS, CP, CC, PM, and CO are considered), and (47) your products share
components or qualities to satisfy the same or similar needs or you are willing to create these
commonalities, then PS, CP, CC, PM, and CO may be applied.
Substitute goods satisfy the same or similar needs and therefore are seen as an alternative
or replacement by consumers. The reason for this replacement relationship is the functional
replaceability between two goods, if they correspond in price, quality, and utility or performance so that they are able to meet the consumer's need. This thus enables substitution structurally.658
CP is also based on commonalities: Common design, assembly processing, training in
common methods, suppliers capable of coping with common design and processing and
reacting to volume and complexity are needed.659 CC designs products that share components.660
PM advantages partly arise from CC.661 CO does not require (component) commonality.
However, the centrally ordered products usually are needed by several requisitioners (delivery warehouses, stores, or departments). Therefore one could say the products are common
to two or more locations.
656
657
658
659
660
661
mand less than volume flexibility. Moreover, product flexibility copes better with substitutable and worse
with complementary products than volume flexibility. Using both volume and product flexibility can lead
to diseconomies of scope (Goyal and Netessine 2005: 1).
Cachon and Terwiesch (2009: 348).
Cachon and Terwiesch (2009: 335).
Wildemann (2008: 72).
Mayne et al. (2008).
Chopra and Meindl (2007: 326ff.).
Zinn and Bowersox (1988: 124f.), Lee (1996, 1998), Van Hoek (1998b, 2001: 173), Van Hoek et al.
(1998), Feitzinger and Lee (1997), Pagh and Cooper (1998), Swaminathan and Tayur (1998), Aviv and
Federgruen (2001a, 2001b: 579), Swaminathan (2001), Yang et al. (2005b: 993), Simchi-Levi et al.
(2008).
67
4 Choosing Suitable Risk Pooling Methods
PM and CP perform better with similar demand. For PM that means that demand is of
comparable size662 or that the standard deviations of demand for items in the product line
are similar663, for CP approximately equal total capacity and expected demand664 and similar demand variability665. Capacity sharing among independent companies is more beneficial, if they are similar in their characteristics (work content, demand rates, or delay
costs).666 PM may reduce EOS667 or increase the cycle/delivery lead time668.
If then (48) a less expensive, fast implementable and changeable solution is preferred
to product and/or process redesign and leagility and you run a trading or retail company rather than a pure manufacturing company, then PS and CO may be applied, otherwise CP, CC, and PM.
PS can be implemented faster than CP, CC, and PM. It may only incur the costs of persuading a customer to buy a substitute669 and maybe cause customer dissatisfaction with
the substitute purchase670.
CO may be less responsive, but also less expensive, implemented within a shorter time
frame, and involve less departments (mainly purchasing and sales) than CP, CC, and PM.
It does not require a product redesign either. CP671, CC672, and PM673 may necessitate a
costly product and/or process redesign and therefore also involve at least manufacturing
and R&D in addition.
As products are only delivered after a customer order is received, in general PM leads to
a centralized logistics system674 and may increase the distance between inventory and customers relative to CO675 and even more so compared to PS. With CP a product is produced,
662
663
664
665
666
667
668
669
670
671
672
673
674
675
Chopra and Meindl (2007: 363f.).
Zinn (1990: 14), Alfaro and Corbett (2003: 18f., 24), Cachon and Terwiesch (2009: 342).
Jordan and Graves (1995: 583), Cachon and Terwiesch (2009: 348).
Iyer and Jain (2004), Jain (2007).
Yu et al. (2008: 26).
Zinn and Bowersox (1988: 124), Yang et al. (2005b: 994).
Zinn and Bowersox (1988: 126), Van Hoek (2001: 161), Rabinovich and Evers (2003b: 35), Yang et al.
(2005b: 994), Graman and Magazine (2006: 1078), Pishchulov (2008: 13), Mahar and Wright (2009:
3061).
Eynan and Fouque (2003, 2005).
Swaminathan (2001: 133).
Jordan and Graves (1995), Mayne et al. (2008), Cachon and Terwiesch (2009: 349).
Bagchi and Gutierrez (1992: 817), Swaminathan (2001: 129, 131), Ma et al. (2002: 536), Simchi-Levi et
al. (2008: 345f., 348).
Lee and Tang (1997: 40, 1998), Van Hoek (1998a), Kapuscinski and Tayur (1999), Jain and Paul (2001),
Swaminathan (2001: 129f.), Kim and Benjaafar (2002: 12), Davila and Wouters (2007: 2245), Yang et al.
(2005b: 993f.), Piontek (2007), Shao and Ji (2008), Simchi-Levi et al. (2008: 346).
Shapiro and Heskett (1985: 53), Zinn and Bowersox (1988: 126), Pfohl (1994: 145), Pagh and Cooper
(1998: 14), Van Hoek (1998a: 95).
Eppen and Schrage (1981), Pishchulov (2008: 22), Cachon and Terwiesch (2009: 349).
68
4 Choosing Suitable Risk Pooling Methods
stored, or transported, or a customer served where there is capacity, so that the distance
between inventory and customers may increase.
PM research “is highly conceptual”676. Applications are mostly limited to manufacturing677, e. g. in Zinn and Bowersox (1988: 121), Lee et al. (1993), Dröge et al. (1995), Feitzinger and Lee (1997), Garg and Tang (1997), Lee and Tang (1998: 172), Van Hoek
(1997), Dominguez and Lashkari (2004), Caux et al. (2006), Chopra and Meindl (2007:
365), Davila and Wouters (2007), Harrison and Skipworth (2008: 193), Kumar et al.
(2009), and Kumar and Wilson (2009). Bailey and Rabinovich (2005) exceptionally apply
PM in internet book retailing. “Currently, relatively simple postponement applications are
practiced in wholesale and logistics services as supplementary services. More complex,
high value adding manufacturing activities are still the primary domain of manufacturers
and these are not often outsourced to logistics service providers”678.
Our survey results in appendix A support that CC679, PM, and CP680 are predominantly
applied in manufacturing, CO or consolidated distribution681 and PS682 rather in trade, so
that their implementation might be more promising here. PS is more efficient than CC.683
In case (48) is answered in the affirmative (PS and CO are considered) and
(49) matching supply and demand and product functionality are preferred to a less
costly, fast implementable and changeable solution with higher (substitute) product
availability, but possible customer dissatisfaction because of substitution and there are
EOS in ordering, then CO (33) may be appropriate, otherwise PS (50). PS offers the customer a product right away, however, not the originally desired one but a substitute, which
may lead to customer dissatisfaction. CO gives the customer the desired product maybe in
a longer lead time or the sale is lost. PS can be implemented and changed faster and less
expensively than CO. The latter may benefit from EOS in procurement though (cf. (23)).
676
677
678
679
680
681
682
683
Yang et al. (2005b: 994).
Boone et al. (2007: 594).
Van Hoek and Van Dierdonck (2000: 205).
Gerchak and Henig (1989), McDermott and Stock (1994), Tsubone et al. (1994), Sheu and Wacker
(1997), Swaminathan and Tayur (1998), Swaminathan (2001), Hillier (2002b), Ma et al. (2002), Labro
(2004), Mohebbi and Choobineh (2005), Chew et al. (2006), Simchi-Levi et al. (2008: 345-348), Nonås
(2009), Wazed et al. (2008, 2009: 76).
Upton (1994, 1995), Jordan and Graves (1995), Weng (1998), Plambeck and Taylor (2003), Pringle
(2003), Iyer and Jain (2004), Benjaafar et al. (2005), Jain (2007), Goyal et al. (2006), Van Mieghem
(2007), Mayne et al. (2008).
Eppen and Schrage (1981), Cachon and Terwiesch (2009: 336-341).
Anupindi et al. (1998), Smith and Agrawal (2000), Mahajan and Van Ryzin (2001a, 2001b), Rajaram and
Tang (2001), Eynan and Fouque (2003, 2005), Zhao and Atkins (2009).
Eynan and Fouque (2005).
69
4 Choosing Suitable Risk Pooling Methods
If (48) is negated (CP, CC, and PM are considered), (51) the costs to have CP or
(manufacturing) flexibility are lower than the costs for CC (common components, product
redesign, and possible cannibalization) and PM (product and/or process redesign or resequencing), then the already explained decision process (41) through (43) has to be completed.
If (51) is answered in the negative (CC and PM are considered) and the product684 (cf.
(47)) and (52) (manufacturing) process is modular685, “the firm maximizes its performance by adopting”686 PM (53): It “will help to maximize effective forecast accuracy and
minimize inventory costs”687. In case the product is modular688 (cf. (47)) but the process
is not689, then differentiation cannot be delayed, but CC (54) “is the most effective approach”690. Simchi-Levi et al. (2008: 348) express this more cautiously: CC “is likely to be
effective”. However, we follow the primary source Swaminathan (2001: 132). To determine the optimal level of CC you may refer to Boysen and Scholl (2009).
Nevertheless, if the process (and the product) is modular, CC and PM may both be applied. To choose between them the CC691 cost (product redesign692 and possible cannibalization of higher priced components693) has to be traded off against the PM cost (higher
production, transportation, and process and/or product redesign cost (cf. (7))). This be-
684
685
686
687
688
689
690
691
692
693
Feitzinger and Lee (1997), Lee (1998), Van Hoek et al. (1998), Swaminathan (2001: 131), Van Hoek
(1998a, 1998b, 2001: 173), Chiou et al. (2002: 113, 122), Yang et al. (2004: 1053), Simchi-Levi et al.
(2008: 348), ElMaraghy and Mahmoudi (2009: 483).
Feitzinger and Lee (1997), Van Hoek et al. (1998), Swaminathan (2001: 131), Van Hoek (2001: 173),
Simchi-Levi et al. (2008: 348). A modular product, e. g. a personal computer as opposed to a shirt, is assembled from a variety of modules such that there is a number of options the customer is interested in for
each module. This is important for concurrent and parallel processing (Swaminathan 2001: 128, SimchiLevi et al. 2008: 345).
A modular (manufacturing) process, e. g. semiconductor wafer fabrication as opposed to oil refining, consists of discrete operations, so that inventory can be stored in semi-finished form between operations.
Products are differentiated by undergoing a different subset of operations during the manufacturing
process. Modular products are not necessarily made in modular processes (Swaminathan 2001: 128, Simchi-Levi et al. 2008: 345).
Swaminathan (2001: 131).
Simchi-Levi et al. (2008: 348).
Weng (1999), Swaminathan (2001: 131), Yang et al. (2005b: 993), Simchi-Levi et al. (2008: 348).
Swaminathan (2001: 131), Simchi-Levi et al. (2008: 348).
Swaminathan (2001: 132).
The common component may be more expensive than the dedicated ones that it replaces (Hillier 2002a,
2002b, Van Mieghem 2004: 419, Zhou and Grubbström 2004, Mohebbi and Choobineh 2005: 473). Still
component commonality may reduce total cost (Van Mieghem 2004: 419, Hillier 2002a, 2002b).
Sometimes, it is necessary to redesign products and/or processes to achieve commonality (Bagchi and
Gutierrez 1992: 817, Swaminathan 2001: 129, 131, Ma et al. 2002: 536, Simchi-Levi et al. 2008: 345,
348), which may result in a smaller and more economical set of components though (Whybark 1989).
Excessive part commonality can reduce product differentiation, so that less expensive customization
options might cannibalize sales of more expensive parts (Ulrich and Ellison 1999, Kim and Chhajed
2000, 2001: 219, Desai et al. 2001, Krishnan and Gupta 2001, Ramdas and Sawhney 2001, Simpson et al.
2001, Swaminathan 2001: 131, Heese and Swaminathan 2006, Simchi-Levi et al. 2008: 348).
70
4 Choosing Suitable Risk Pooling Methods
comes important if not form, but place and time PM are considered. CC and PM often are
connected and can be applied together. Maybe applying both of them may be more economical than applying only one. PM implementation may require CC694 (“postponement
through standardization”695). According to Caux et al. (2006: 3244), PM in the form of
delayed differentiation can be implemented by “process restructuring, component commonality and product design”.
If (47) is negated, then CO and CP are considered, because they do not require CC, especially if transportation or storage capacity is pooled. Yet, we consider CP related to inventories under IP. If then (55) the costs of CO are lower than both the ones of CP and
adding capacity and there are EOS in ordering, then CO (33) may be effective. Otherwise CP and adding capacity are considered and the already explained decision process
(41) to (43) still has to be followed.
Frequently the risk pooling methods cannot be separated mutually exclusively, because
they are favorable under similar conditions as tables D.3 and D.4 already showed. If the decisions in the RPDST are not selective and disjunctive, the respective risk pooling methods
are considered for both choices. The RPDST only shows tendencies and enables general
statements about the advantageousness of risk pooling design options, since the specific size
of the costs and benefits are unknown and the complex interdependencies are simplified. The
advantageousness of specific risk pooling methods in a specific situation for a specific
company depends on specific cost parameters and their interaction or ratios.696
In a particular company case risk pooling design recommendations might differ from
this RPDST. The identified conditions and recommendations for risk pooling methods depend on the selected reference framework. Therefore a study with the same topic might
attain a different classification and thus different results. The framework gives general recommendations about the advantageousness of risk pooling methods. Afterwards a company should weigh the costs and benefits of the different suitable options expressed in monetary units to reach a decision about which risk pooling strategy to implement. Expenses for
implementing the risk pooling strategy might exceed the achievable savings.697
Some benefits besides decreased (inventory) cost such as increased flexibility, responsiveness, and customer service level are hard to quantify. Resequencing due to PM might
lower inventory levels, but increase the inventory value per unit. However, if customiza694
695
696
697
Swaminathan (2001: 132), Simchi-Levi et al. (2008: 347).
Ma et al. (2002: 534).
Cf. e. g. Wanke (2009) on IP.
Cf. Simchi-Levi et al. (2008: 349).
71
4 Choosing Suitable Risk Pooling Methods
tion is postponed, the generic products may have a lower value than the customized ones.
Tariffs and duties for undifferentiated products might be lower. Still products and
processes might be more expensive under some risk pooling methods.698
Implementing risk pooling might lead to positive or negative effects not studied in detail
in this RPDST, such as human resistance or negative impacts on the whole supply chain.
It might be appropriate to apply risk pooling methods just to certain products (e. g.
the ones with uncertain demand).699
Combining several risk pooling methods might improve performance.700 Using, for
instance, time PM (e. g. emergency TS and inventory centralization), form PM (product
customization), and enterprise-wide information systems together improved “enterprisewide inventory management performance” more than using each of these methods separately in an empirical model based on 216 large and established U.S. manufacturing
firms.701 (Logistics) PM might go hand in hand with IP (inventory centralization) or CO
(centralized distribution).702 A hybrid strategy of pooling demand by centralizing inventories (IP) but splitting supply by multisourcing (OS) can be worthwhile.703 Substitutable
products support the implementation of variety PM.704 Demand substitution furthermore
facilitates flexible manufacturing without competition and may facilitate its adoption with
competition.705 CP may exploit CC.706
Kutanoglu (2008) considers both emergency lateral shipments from other local facilities
and direct shipments (VP in the sense of Netessine and Rudi 2006) from one central warehouse of service parts to repair high-technology hardware systems such as computers and
telecommunication devices in case of a stockout at a local facility within the time window
necessary for the target service level. Alfredsson and Verrijdt (1999: 1430) find conjoint
use of lateral TS and direct deliveries can reduce costs significantly, particularly for slow
moving parts. Investing only in direct delivery flexibility may increase costs dramatically,
unless pipeline flexibility is applied. Pipeline flexibility means that a customer backorder is
satisfied by the part that arrives first either via normal replenishment or via direct delivery.
Similarly, Wong et al. (2007b: 1056) remark emergency direct deliveries from the central
698
699
700
701
702
703
704
705
706
Simchi-Levi et al. (2008: 349).
Cf. Chopra and Meindl (2007: 366).
Cf. e. g. Hong-Minh et al. (2000).
Rabinovich and Evers (2003b: 38, 42f.).
Shapiro (1984), Zinn and Bowersox (1988), Van Hoek (1998a, 2001), Nair (2005: 451).
Benjaafar et al. (2004a: 1442).
Heskett and Signorelli (1984), Kopczak and Lee (1994), Goyal and Netessine (2005: 22).
Goyal and Netessine (2006: 1).
Mayne et al. (2008).
72
4 Choosing Suitable Risk Pooling Methods
warehouse and the plant in case of stockouts in a two-echelon system are only worthwhile,
if lateral TS between local warehouses are not possible.
The RPDST neglects the degree to which the different favorable risk pooling methods
should be applied and their opposite methods. Often two opposing methods are applied in
combination to a certain degree (e. g. centralization and decentralization, consolidation and
singularization, postponement and speculation). Speculative inventories, for instance,
should be held in the logistics channel wherever their costs do not exceed the savings
achievable by postponement.707 Furthermore, the certain part of the product line or the generic product can be made less expensively to stock, the uncertain products or product variants to order.
An empirical verification of the derived results pertaining to the design recommendations appears worthwhile. The theoretical analysis revealed fundamental interdependencies
of risk pooling methods and facilitates the practical risk pooling design. Possible deviations from business practice can be disclosed by empiricism. The analytic process can be
adapted accordingly. Therefore, we will apply the RPDST to a German paper wholesaler to
determine risk pooling methods that may reduce the demand and lead time uncertainty it
faces.
707
Bucklin (1965: 28).
73
5
Applying Risk Pooling at Papierco
In this chapter we will first introduce Papierco to you and some problems it faces. Afterwards
we will determine risk pooling methods with the help of the RPDST developed in the previous
chapter to solve these problems and consider their application at Papierco in more detail. Finally we will summarize our results.
5.1
Papierco
A German paper wholesale company (to protect confidentiality we call it Papierco in the following) pursues the business strategy of a decentralized, differentiated full-line distributor and
system provider of paper, printing accessories, as well as screenprinting and advertising systems, which precludes central warehouses and minimal storage. This corporate strategy seems
to be Papierco's competitive advantage, as its competitors cannot offer such a ubiquitous and
fast delivery service as well as broad assortment. The decentralized warehouse network also
constitutes a competitive advantage in the light of increasing fuel costs, autobahn toll, climate
change, environmental legislation, and increased traffic volume. Papierco delivers its products
from its warehouses with its own truck fleet or has them drop-shipped from paper plants to its
customers.
According to its management, Papierco is a full-line wholesaler, as its 32,739 customers
(mainly printing offices) need all kinds of different product specifications mostly within 24
hours. If a product with a low turnover was eliminated from the assortment, some customers might not buy some other products either anymore due to product interdependencies.
The alliance Papierco of several legally independent paper wholesalers and exchange of
items between 21 regional warehouses in case of a stockout (emergency transshipments)
allow the individual companies and locations to offer a larger product assortment than they
could store on their own. Not every of the 7,000 product specifications Papierco offers is
stored at every location. Products with a low turnover share are only stocked at few locations due to cost considerations.708 This is called “selective stocking”709, selective stock
keeping710, or “specialization”711. The idea behind selective stock keeping is lowering inventory holding costs by treating products differently without impairing the service level
708
709
710
711
Pfohl (2004a: 122f.), Simchi-Levi et al. (2008: 233).
Ross (1996: 310f.).
Pfohl (2004a: 118ff.).
Anupindi et al. (2006: 191f.).
74
5 Applying Risk Pooling at Papierco
considerably.712 Transshipments between Papierco's locations are necessary, so that every
location can offer the complete assortment. The shipping decision is postponed until a customer order is received. Every warehouse thus functions as both a regional and central
warehouse and can access products in every other warehouse as if all warehouses were one
single warehouse (virtual inventory or warehouse). Hence Papierco takes advantage of
inventory pooling, but mitigates some of the disadvantages of a central warehouse
through the use of transshipments and information technology.713
5.2
Problems Papierco Faces
5.2.1
Fierce Competition in German Paper Wholesale
Paper wholesale in Germany is characterized by strong competition especially in office, illustration printing, and offset paper: Sales stagnate, sales prices decrease, raw material, energy,
and logistics costs increase. A lot of customers go bankrupt and there is an ongoing concentration process in the printing industry.714 Paper manufacturers, the paper wholesale's suppliers,
suffer from bad profitability due to increasing costs, overcapacities, and price pressure715, as
well as competition pressure from Asia and Eastern Europe716, which they seek to improve by
mergers and markups. The current international economic downturn intensifies the cost and
competition pressure in all industrial sectors. Insufficient capacity utilization is a strain on the
paper wholesale, its customers, and suppliers. Increasing profit margin pressure is believed to
promote the consolidation tendency on all levels of the value chain.717 Thus paper wholesale
faces strong competition and economically stricken customers and suppliers, whose negotiation power increases because of mergers. Competitiveness and economic success can be secured on this market by efficient supply, storage, and distribution planning enabled by risk
pooling, particularly since logistics incurs the highest costs at Papierco.
5.2.2
Supplier Lead Time Uncertainty
The lead time of paper manufacturers fluctuates strongly, ranges from 14 to 154 days, and is
on average 28.49 days. It fluctuates subject to price increases, drop-shipping sales, (international) demand, and production setup times. Supplier lead times are entered into the enterprise
712
713
714
715
716
717
Pfohl (2004a: 122).
Cf. Sussams (1986: 8f.), Simchi-Levi et al. (2008: 233).
BVdDP (2009).
Kibat (2007).
FPT (2007b: 7).
BVdDP (2009).
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5 Applying Risk Pooling at Papierco
resource planning (ERP) system by a central master data maintenance in three German Papierco locations. The actual lead time of each supplier should rather be recorded for every delivery
to improve the purchasing policy.
Because of long and uncertain lead times for certain products paper merchants sometimes place so called “phantom orders” for product quantities they do not actually need as
a precaution, which intensifies the bullwhip effect718 and leads to even longer and more
variable lead times. This once resulted in all orders having to be cancelled and only entering real orders (with a corresponding real demand) again afterwards. Thus lead times normalized again.
5.2.3
Customer Demand Uncertainty
Total Sales (t)
320,000
2009
2008
290,000
2007
260,000
230,000
200,000
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Months
Figure 5.1: Total Fine Paper Sales in Tons per Month in Germany (BVdDP 2010a: 8)
718
Lee et al. (1997a: 98).
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5 Applying Risk Pooling at Papierco
115000
110000
105000
Total Sales (t)
100000
95000
2007
90000
2008
2009
85000
80000
75000
70000
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Months
Figure 5.2: Papierco's Total Fine Paper Sales to Customers in Germany in Tons per Month
Total demand for fine paper in Germany is seasonal: It is higher in January, February, and
March, lower from April till July, and increases up to November in order to decrease again in
December as figures 5.1 and 5.2 show. Total customer demand depends on the overall economic development, i. e. on the available financial means for e. g. new products and advertising budgets.
Warehouse sales made up 42 %, drop-shipping sales 58 % of all sales in 2007 and
2008,719 respectively 43 % and 57 % in 2009720. Warehouse sales of individual products
per week per warehouse are sporadic without a trend or seasonal pattern as figure 5.3
shows exemplarily.
719
720
BVdDP (2009).
BVdDP (2010b).
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5 Applying Risk Pooling at Papierco
Figure 5.3: Papierco's 2007 Warehouse Sales to Customers per Week of Seven Standard
Paper Products from the Hemmingen Warehouse
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5 Applying Risk Pooling at Papierco
“When demand for items is intermittent, because of low volume overall and a high degree of
uncertainty as to when and at what level demand will occur, the time series is said to be lumpy,
or irregular”721. Among others many products and stocking locations might explain the lumpiness of demand for individual Papierco products.722 “The lumpy demand condition occurs
when two or three times the standard deviation of the historical data exceed the forecast of the
best model that can be fit to the time series”723. Ballou (2003a: 9) states in the PowerPoint
presentation to Ballou (2004b) a time series is lumpy, if the mean of the series is less than or
equal to three times the standard deviation of the series.
Although the items in figure 5.3 are considered standard, on average they did not sell
8.29 weeks or around 16 % of the year 2007 and their standard deviation of sales per week
per warehouse was on average 0.94 times their mean. Fast moving copy papers selling
nearly every week were the least lumpy with the standard deviation being only 0.37 times
the mean on average. Uncoated Cut-Size White Wood-Pulp Paper was the lumpiest with
no sale in 34 weeks or almost two thirds of the year 2007 and a lumpiness factor (standard
deviation of demand divided by mean demand) of 2.11, followed by the Folding Box
Board with no sale in 15 weeks and a lumpiness factor of 1.32.
On average the standard deviation of an item's sale per month per warehouse is 2.24
times the mean sale per month per warehouse in 2007. Nearly one third (31.45 %) of the
products show a standard deviation that is more than three times the arithmetic mean of
sales per month per warehouse. In these cases the standard deviation is on average
3.78 times the mean. Of a lot of articles no unit is sold for several months and then suddenly some month a lot of units are sold. On average 7.83 months or nearly two thirds of the
year 2007 a specific product is not sold. We conclude that demand per product per month
is very random and lumpy or sporadic and therefore “difficult to predict accurately by mathematical methods due to the wide variability in the time series”724. Risk pooling methods
might produce relief here.
Ballou (2004b: 311) suggests to use the reasons for the lumpiness in the forecast, separate forecasting of lumpy and regular demand products, not react quickly to random demand shifts without assignable cause and use slowly reacting forecast methods such as
exponential smoothing with a low smoothing constant or a regression model refit annually
721
722
723
724
Ballou (2004b: 288). For further definitions please refer to e. g. Ghobbar and Friend (2003: 2105), Kukreja and Schmidt (2005: 2059), Bridgefield (2006), Gutierrez et al. (2008: 409, 412).
Cf. Ballou (2004b: 288, 310).
Ballou (2004b: 310).
Ballou (2004b: 310).
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5 Applying Risk Pooling at Papierco
at the most, and maybe make up for forecast inaccuracy by a higher inventory level for low
demand items. Croston (1972) and Johnston and Boylan (1996) recommend an exponential
smoothing constant of 0.05 to 0.20 for lumpy demand. Silver et al. (1998: 127), however,
report pertaining to intermittent and erratic demand that “[t]he exponential smoothing forecast methods […] have been found to be ineffective where transactions (not necessarily
unit-sized) occur on a somewhat infrequent basis. […] Infrequent in the sense that the average time between transactions is considerably larger than the unit period, the latter being
the interval of forecast updating”.
Lumpy or highly uncertain demand can be coped with by obtaining information directly
from customers, collaborating with other supply chain and channel members, collaborative
forecasting, forecasting total demand and apportioning it by regions, delaying supply response, product differentiation, and forecasting as long as possible, supplying the more
certain products first, developing quick response and flexible supply systems, and applying
the forecasting methods with caution.725 Most of these suggested solutions rely on risk
pooling.
5.2.4
Distribution Requirements Planning (DRP)
7000
6000
5000
Inventory
4000
Tons
Sales to Customers
Sales to Colleagues
Total Warehouse Sales
3000
Goods Received from Suppliers
Goods Received from Colleagues
Total Goods Received
2000
1000
0
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Months
Figure 5.4: 2007 Incoming Goods, Warehouse Sales, and Inventory at
Warehouse Hemmingen
725
Ballou (2003a: 39-42, 2004b: 310f., 314-317).
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5 Applying Risk Pooling at Papierco
6000
5000
4000
Tons
Inventory
Sales to Customers
3000
Sales to Colleagues
Total Warehouse Sales
Goods Received from Suppliers
Goods Received from Colleagues
2000
Total Goods Received
1000
0
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Months
Figure 5.5: 2007 Incoming Goods, Warehouse Sales, and Inventory at
Warehouse Reinbek
Figures 5.4 and 5.5 illustrate Papierco's demand forecasting and inventory management problems using two standard Papierco warehouses. The inventory level is always around 1,000 to
2,000 tons higher than total warehouse sales. This may be partly explained by the large product
variety. The Total Goods Received and Total Warehouse Sales curves often are opposite in
phase or time-lagged, i. e. when total warehouse sales go up, often goods receipts go down or
vice versa.
Sales departments, product managers, and purchasing departments of the different
warehouse locations do not collaborate in planning demand and requirements. The sales
departments merely plan the customers' financial development, i. e. sales and contribution
margins per customer. On the basis of the product managers' aggregated sales planning on
the product group level for all German locations skeleton agreements are centrally negotiated with the most important suppliers. The purchasing departments forecast demand on
the product level on the basis of the past six months' sales and order accordingly. These
three planning processes are unconnected. The sales departments do not report any expected exceptional demands to the purchasing departments either. The latter only plan
products sold via warehouses, without considering substitution effects between similar
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5 Applying Risk Pooling at Papierco
products or between warehouse and drop-shipping sales726. Drop-shipping sales are conducted only by the sales departments.
Papierco should create a uniform cross-functional demand planning process, in which
sales, product managers, and purchasing collaborate, to contain extraordinary demands
through the sales assistants' and product managers' profound market knowledge and enable
a better demand forecast and thus order policy. Although Adam and Ebert (1976) show
that objective statistical forecasting models produce more accurate results than subjective
judgemental forecasts, Bunn and Wright (1991) remark expert forecasts had a higher quality than previous research claims. That is why Silver et al. (1998: 133) suggest combining
these two approaches.
The individual locations conduct their distribution requirements planning (DRP) without any coordination, so that inventory reductions at one location strain the transshipment
flows and impair other locations' DRP. Thus, one location might deplete another one's
stock of a specific product via transshipments. In the following week the latter location
might have to obtain this product via transshipments from another warehouse due to a customer demand and so on. Likewise a warehouse may receive a supplier's delivery, although
it has plenty of inventory left, while another one does not. This process seems to have taken on a life of its own in a “vicious circle” with increasing transshipment volumes and inventory variability at most warehouse locations.
The increased transshipments did not reduce the aggregate safety stock, although this
might be assumed because of the demand balancing effect thanks to the creation of a virtual inventory through transshipments. Allegedly the customer service level increased,
which is difficult to verify, as Papierco does not record it in any way.
We will recommend a not necessarily geographically centralized procurement, which
forecasts and orders for all of Papierco's German locations on the product level and directs
the suppliers' deliveries to the warehouses according to current demand in section 5.3.3.
5.2.5
Demand Forecasting Methods
Increasing forecast accuracy decreases the need for risk pooling727 (e. g. emergency transshipments) and safety stock and increases customer service level (product availability).
726
727
Sometimes a drop-shipping sale is converted into a warehouse sale, if the drop-shipping lead times are
high.
Cf. Graman and Magazine (2006: 1081).
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5 Applying Risk Pooling at Papierco
Today Papierco uses the forecast methods 4 (Moving Average) and 10 (Linear Smoothing) of the twelve ones the ERP software JD Edwards OneWorld offers.
Method 1 (Percent Over Last Year), method 2 (Calculated Percent Over Last Year), method 3 (Last Year To This Year) and method 8 (Flexible Method or Percent Over Months
Prior) are so called “naïve estimates” and project sales of previous years into the future
either directly or after multiplying them with a factor.728 These methods are rather inadequate for Papierco, as sales of individual products differ significantly from year to year.
Method 12 (Exponential Smoothing with Trends and Seasonality) is not suitable either, as
demand for individual products does not follow a trend or seasonal pattern.
Method 4 (Moving Average), Method 7 (Second Degree Approximation), which expresses sales in a curve, method 9 (Weighted Moving Average), method 10 (Linear
Smoothing), which assigns weights to the sales numbers linearly decreasingly with a formula, and method 11 (Exponential Smoothing729) are similar. They are suitable for shortterm forecasts for mature products without trends or seasonal patterns.730 They could enable a good demand forecast for Papierco with an order cycle of two weeks.
Method 5 (Linear Approximation) establishes a trend on the basis of two data points.
Small changes influence long-term forecasts strongly. Method 6 (Least Squares Regression) also calculates a linear trend. Turning points and changes in the demand function are
recognized late with the Linear Regression. If the sales data form a curve or show strong
seasonal fluctuations, systematic forecast errors appear.731 Methods 5 and 6 may be suitable for Papierco because of the short order cycle of two weeks, although demand for individual products shows no or only a short-term trend.
Analyzing the forecast methods for the seven standard products, we discovered that a
forecast based on sales of the last twelve months leads to improved results compared to the
current one with six months. This comes as no surprise as Gibson and Horner (2005: 1f.)
state that JD Edwards OneWorld forecasting accuracy improves with the length of the used
sales history. The software is capable of using up to two years of sales history.
Method 11 (Exponential Smoothing) and method 6 (Least Squares Regression) led to
the best results most frequently. Ballou (2004b: 311) also recommends these methods for
forecasting lumpy demand.
728
729
730
731
Oracle (2009).
Exponential Smoothing automatically uses linearly decreasing weights and is a weighted average of actual sales and the previous period's forecast.
Oracle (2009).
Oracle (2009).
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5 Applying Risk Pooling at Papierco
The results of method 11 (Exponential Smoothing) might be improved by letting JD
Edwards OneWorld determine the smoothing constant alpha based on past sales instead of
determining it arbitrarily.
Methods 9 (Weighted Moving Average), 4 (Moving Average), and 10 (Linear Smoothing) also led to good results in order of descending quality. A naïve estimation (projection
of the previous year's sales into the current year) did not give good results. The results
could be improved by multiplying the previous year's sales with a growth factor.
We used the mean absolute deviation (MAD) of the forecast values from the actual
sales in 2006 and 2007 and the forecast error (the sum of the difference of the actual and
the forecast sale per week) to measure the quality of the respective forecast method. For
other forecast performance measures please refer to Gutierrez et al. (2008: 413f.).
Comparison of the forecast accuracy of forecast methods is difficult732, as the forecast
errors of the two methods may be correlated733. Besides “a linear combination of forecasts
from two or more [forecasting] procedures can outperform all of those individual procedures”734. According to Kang (1986) a regular average of forecasts of several methods
leads to high-quality results.
Tiacci and Saetta (2009) evaluate the impact of usually neglected possible interactions
between demand forecasting methods and stock control systems on global system performance. Accordingly, demand forecasting methods cannot be chosen only on the basis of
traditional measures of forecast errors. Total costs and service level of the global inventory
control system should also be considered. However, this is beyond the scope of this thesis
and remains for further research.
The products still have a lumpy demand pattern also according to Ballou's (2004b: 310)
definition: “[T]he forecast of the best model that” could “be fit to the time series” was 3.39
times “the standard deviation of the historical data”.
The MAD was on average half the size of the mean actual demand per week, i. e. even
with the best tested forecast method, we would have ordered half a week's average demand
too much or too little per product per week on average. The absolute forecast error was on
average four times the mean actual demand per week, i. e. even though the forecast errors
balance each other to a certain extent we would have had four week's average demand too
much or too little over the whole year per product on average.
732
733
734
Silver et al. (1998: 131).
Peterson (1969).
Silver et al. (1998: 131).
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5 Applying Risk Pooling at Papierco
Methods 11 (Exponential Smoothing), 6 (Least Squares Regression), and 9 (Weighted
Moving Average) should be admitted to the DRP forecast run besides today's exclusively
used methods 4 (Moving Average) and 10 (Linear Smoothing), as they gave good results.
Gibson and Horner (2005: 4) recommend using as many forecast methods as possible “to
maximize the chances that the Best Fit forecast that is calculated is really close to what
reality will be”. Of course, this has to be traded off with calculation time and software performance.
“The statistical forecast techniques discussed earlier may work well for stable, mature
products with significant demand history, whereas qualitative methods based largely on
human opinion and direct marketing intelligence (not a part of JD Edwards) usually make
more sense for new or unstable demand products. […] In fact, conventional wisdom is that
sales and marketing should ʻown the forecastʼ. Their input is especially important for new
products or products with unstable demand. Sales and marketing should participate in the
development of forecasts and they should also be formally ʻgradedʼ on their forecast accuracy performance results. […] And one final comment: always remember that there is far
more to be gained by people collaborating and communicating well than there is by using
all of the advanced formulas and algorithms yet developed”735.
Since our analysis is only based on seven standard products, as no further data were
provided, it should be extended to a larger, more representative number of products before
implementation.
Simple forecasting methods outperform statistically sophisticated procedures for individual items. The reverse is true for macro-level data and medium and long-term forecasting. Consequently, sophisticated forecasting methods do not outperform simpler ones in
terms of forecast accuracy in general.736 Nevertheless, one could check whether more sophisticated forecasting methods not available in JD Edwards OneWorld and developed for
products with lumpy demand lead to more accurate results.
The Croston (1972) method forecasts intermittent demand well737 and is available in forecasting software packages738. It “generates separate forecasts for the demand size and the
number of periods between demands, and uses the ratio as an estimate for the expected demand per period. It also updates the mean absolute deviation of the forecast error for the de-
735
736
737
738
Gibson and Horner (2005: 9).
Makridakis et al. (1982).
Willemain et al. (1994), Johnston and Boylan (1996).
Syntetos et al. (2005).
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5 Applying Risk Pooling at Papierco
mand size”739. Teunter and Sani (2009: 82) call Croston's method “the standard method for
forecasting intermittent demand” and use its forecasts to calculate order-up-to levels that lead
to close to target customer service levels. Gutierrez et al. (2008) apply neural network modeling to forecasting lumpy demand. Neural network forecasts generally outperform single
exponential smoothing, Croston's method, and the Syntetos–Boylan approximation740. Syntetos and Boylan (2001, 2005) approximately correct an error in the mathematical derivation of
and the resulting bias in Croston's estimates of expected demand.
Gutierrez et al. (2008: 418) find neural network models generally perform better than
the traditional methods. The Syntetos–Boylan approximation performs better than Croston's and single exponential smoothing methods in lumpy demand forecasting. If the average nonzero demand is considerably smaller in the test than in the training sample, the traditional forecast methods perform better than the neural network forecasts with lower
smoothing constants. However, Gutierrez et al. (2008: 412) only consider 24 SKUs.
Analyzing other methods for lumpy demand forecasting not available in JD Edwards
OneWorld lies beyond the scope of this thesis. Furthermore, it would be difficult and expensive to integrate these forecasting methods into the current ERP system and DRP.
A better demand forecast leads to a higher product availability (customer service level)
at the primary warehouse and thus reduces transshipments. Customer service level can be
increased and at least safety stock can be reduced.
Of course it would be desirable to always have the desired product at the right time at
the right warehouse, so that no transshipments would be necessary at all. This however is
impossible741, as forecasts are generally incorrect742. The longer the forecast horizon, the
worse the forecast is743. Aggregate are more precise than individual forecasts.744
As the suggested forecast methods in JD Edwards OneWorld only lead to a limited
forecast improvement and the more sophisticated methods for lumpy demand are difficult
to implement at least in the short run and their benefit for Papierco is unknown, this company could resort to risk pooling methods that reduce demand uncertainty relying on aggregate forecasting745, such as central ordering.
739
740
741
742
743
744
745
Teunter and Sani (2009: 82).
Syntetos and Boylan (2001, 2005, 2006), Syntetos et al. (2005).
Evers (2001: 316).
Anupindi et al. (2006: 168).
Anupindi et al. (2006: 169).
Cf. footnote 456.
Sheffi (2004: 95).
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5 Applying Risk Pooling at Papierco
5.3
Solving Papierco's Problems
Papierco could cope with lead time and demand uncertainty and its related forecasting and
inventory problems and ensure its competitiveness and economic success by risk pooling.
5.3.1
Determining Suitable Risk Pooling Methods for Papierco
The RPDST developed in section 4.4 is used to determine appropriate risk pooling methods for
Papierco, which suffers from customer demand and supplier lead time uncertainty (1). Both
demand and lead times fluctuate strongly.
Product variety is important (2) for Papierco's competitive advantage and because its
customers, who are mostly printing offices, need all kinds of paper specifications.
Stockout penalty costs are high compared to inventory carrying costs and thus attainable
inventory cost savings (3) from e. g. inventory pooling: The stockout cost (209 €) is estimated by the average contribution margin of one ton of warehouse sales to customers minus the sales assistant's premium. The average length of time a ton stays in inventory is
estimated by the average inventory level divided by average annual demand. Papierco has
an annual average turnover rate of 8, i. e. on average a ton of paper remains in storage for
one eighth of a year or one and a half months. Storing one ton of paper costs 22 € per
month, so that the cost of holding a ton of paper in storage is 33 € on average.
The supplier lead time means and variabilities are high and therefore their reduction is
important to Papierco (4). Papierco declared costs per order did not accrue. However, if all
2007 expenses of the purchasing departments are divided by the total amount of warehouse
purchases from suppliers, we arrive at an order cost of 3.31 € per ordered ton. This cost per
order is relatively low (5) compared to the average value per ton of 1,058 € in 2007. Demand uncertainty and lead time (uncertainty) reduction and fewer orders are preferred to
only lead time pooling, but lower premium transportation cost and in-transit inventory cost
(15), as Papierco suffers from both demand and lead time uncertainty, minimum order and
saltus quantities have to be observed, and the in-transit carrying cost per unit and emergency transfer cost per unit are low.
Order splitting (16) is not feasible because of among others the required minimum order
quantities and full truck load supplier deliveries. The cheaper, faster implementable and
changeable, and less cross-functional solution to cope with both demand and lead time uncertainty is preferred to product and/or process redesign of a postponement (14) strategy
(10). Besides, manufacturing and assembly postponement can rather be applied by the paper
producer, not the paper wholesaler. Papierco could postpone the labeling, packaging (ream
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5 Applying Risk Pooling at Papierco
wrapping paper), or delivery of products, e. g. by central ordering the allocation of ordered
products can be delayed and conducted according to more current demand information. Mixing printer's ink from base colors can also be postponed to the delivery warehouses until a
customer order arrives instead of ordering already mixed colors from the supplier. Cutting
paper to the desired format could also be delayed until an order arrives. However, this can
only be applied to an insignificant part of the product line. The other postponement options
for Papierco will not reduce demand and lead time uncertainty much either.
The paper producers do not possess small-order drop-shipping capabilities (11). They
only drop-ship full truck loads to customers. However, there are endeavors of some paper
wholesalers to conduct drop-shipping sales via its warehouses to gain the higher profit
margin of warehouse sales and of paper producers to drop-ship less than truck load to paper wholesale customers to increase their profit. This causes resentment on both sides.
Virtual pooling (12) by not holding any inventory, only arranging sales, and having all
products drop-shipped from the paper producers to the customers is no viable strategy for
the paper wholesaler, as it would make him dispensable and the paper producers do not
possess the necessary distribution infrastructure. Furthermore, the restriction to deliver to
customers usually within 24 hours could not be kept. Therefore lateral transshipments
(13) or cross-filling seem to be the risk pooling method of choice for Papierco to deal with
both demand and lead time uncertainty.
Order costs may also be considered high in (5), because minimum order and saltus
quantities make (placing) an order more expensive, as frequently more than forecast demand minus on hand inventory has to be ordered by the individual locations to meet these
order restrictions, which results in unnecessary inventory costs. Increasing the needed order quantity per order by postponement (8) or central ordering (9) for several locations
may better exhaust minimum order and saltus quantities and lead to economies of scale in
ordering (6) due to price discounts. As Papierco prefers the less expensive, fast implementable and changeable solution and the possibilities for postponement (8) are still limited as
described above, central ordering (9) might be a viable risk pooling method to achieve both
efficiency and responsiveness to customers. Some of the transportation cost otherwise incurred for emergency transshipments between warehouses may be shifted unto the suppliers who deliver to Papierco's delivery warehouses. Therefore (9) central ordering might
make sense, especially against the background of increasing fuel prices.
Today Papierco's average transportation cost to deliver one ton of paper with its truck
fleet within Germany is 15.88 €. We arrived at this figure by dividing Papierco Germany's
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5 Applying Risk Pooling at Papierco
total transportation cost (driver costs, capital commitment, depreciation, maintenance and
repair, motor vehicle tax, insurance, diesel, lubricant, tires, autobahn toll, parking, and
miscellaneous operating costs) by the total annual warehouse sales in 2008. The transshipment cost per ton (transportation, shipment documentation, receiving, handling and
administration costs) amount to 69.48 € per transshipped ton of paper on average. This is
still relatively moderate (6), so that the decision process (10) through (13) can be followed
again, which reconfirms transshipments (13) as a favorable risk pooling method.
Papierco's management thinks that (2) product variety might be reduced in the office
paper segment and where product specifications just differ in their format in one or two
centimeters. The Paper Technology Research Association Forschungsvereinigung Papiertechnik e. V. (FPT) also denies the necessity of the current large product variety in German
paper wholesale.746 Affirming the importance of lead time (uncertainty) reduction (30)
afterwards leads to the same train of thoughts in (31) to (38) as in (5) to (16) without considering postponement (cf. 2), which favors transshipments (36) and perhaps central ordering (33).
If Papierco gives priority to reducing demand uncertainty, as demand variability is more
severe and lead times and their variability are not recorded accurately nowadays, and therefore (30) is denied and accommodating demand uncertainty is preferred to inventory reduction (39) due to the fierce competition for customers, then central ordering (33) is favored
again: It is less expensive, faster implementable and changeable than capacity pooling
(41f.) and permits to achieve economies of scale in ordering (40). Besides, capacity pooling is rather suitable for manufacturing companies than for wholesalers. Papierco's locations cannot pool manufacturing capacity, as they do not produce paper. They could, however, pool or share printer's ink mixing, paper cutting, or ream wrapping capacity. This
might not be economically worthwhile, since the costs of shipping mixed paint or cut to fit
or ream wrapped paper between locations might destroy the capacity pooling benefits. Furthermore, delivery time to the customer might suffer, and this can only be applied to an
insignificant part of the product line. Papierco's locations could pool transportation capacity, which is operationalized by transshipments, and inventory storage capacity, which corresponds to inventory pooling.
Papierco's management would also like to reduce inventory. One has to carefully check
whether this intention does not conflict with Papierco's business strategy and competitive
746
FTP (2007a, 2007b).
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advantage of being a 24-hour delivery full-range paper wholesaler in Germany and inventory savings outweigh possible lost sales. Remember that Papierco's inventory carrying
costs are moderate relative to stockout and transshipment costs per ton. If one concludes
that inventory reduction is more important than accommodating demand uncertainty (39),
product pooling (45) and inventory pooling (46) might be suitable. Product pooling
keeps inventory close to customers in the delivery warehouses, thus enables the nationwide
24-hour delivery service and product availability (44), pools demands, and improves forecast accuracy, but perhaps degrades product functionality. Because of the mentioned shortcomings and because it only pools demands, product pooling should not be applied on its
own but together with another risk pooling method that reduces lead time uncertainty and
only within a product segment that can be rationalized without hurting customer service
level and product purchase interdependencies substantially. Rationalization in this context
means deleting products from the product line or replacing several product variants by a
universal product.
Physical inventory pooling in a single central warehouse would preclude the 24-hour delivery service. However, selective stock-keeping in several delivery warehouses may be feasible, pool demands, enable to reduce at least safety stock and maintain the product variety
and delivery speed, but increase transportation costs. Fast movers could be stored at every
warehouse, while slow movers could be held at a limited number of warehouses only.
If Papierco disavows the importance of lead time (uncertainty) reduction in (30), it may
also do so in (4). Papierco's products share common qualities (47). The less expensive, fast
implementable and changeable solution is preferred to product and/or process redesign and
leagilty, and Papierco is a trading company (48). It does not produce its paper products
itself and its products neither are modular nor do they share common components besides
the raw materials, so that it cannot redesign the products and/or production processes.
Hence, component commonality (54) or manufacturing postponement (53) is not sensible
for Papierco. Postponing cutting paper to the right format, mixing printer's ink, and labeling and ream wrapping paper are conceivable but not expected to reduce demand or lead
time uncertainty significantly.
Product substitution (50) can be implemented quickly and cheaply, but displease customers as they do not receive the desired product in case of a stockout, but a substitute. In
contrast to product substitution, central ordering (33) might reduce lead time (uncertainty) in addition to demand uncertainty and lead to economies of scale in ordering, but be
more expensive, particularly since transaction and coordination costs are higher.
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5 Applying Risk Pooling at Papierco
On the whole, lateral emergency transshipments seem to be the most suitable risk pooling method for Papierco, followed by central ordering, especially if fuel and transportation
costs continue to rise. Both methods may be applied in combination and enable to achieve
the seemingly conflicting aims of reducing demand and lead time uncertainty as well as
inventory investment and maintaining customer service level in terms of product variety,
inventory availability, and delivery speed. Product substitution, product pooling, inventory
pooling, and postponement may also be suitable in order of descending favorability, but
not as a sole method due to their mentioned drawbacks. They may not reduce lead times or
lead time uncertainty by themselves.
In the following we will deal with the suitable risk pooling methods determined for Papierco in more detail.
5.3.2
Emergency Transshipments between Papierco's German Locations
Papierco's German locations exchange products in case of a stockout, which supports the result
of the RPDST.
As the quantities exchanged by transshipments have risen over the last years, Papierco's
management asked whether these transshipments are economically sound and whether they
can be reduced or improved.
In our opinion this stock exchange must not be considered detachedly from sales747,
demand, demand forecast, order policy and storage policy, as it is influenced by these factors. Therefore the systemic approach of logistics should be accommodated and the interdependencies between single components and the whole should be considered.748 It is desired to contribute to a preferably spatially and temporally smooth, continuous, and aligned
sequence of activities and processes which target satisfying customer needs.749
5.3.2.1 Optimizing Catchment Areas
A business policy has evolved historically that if the sales department of one location attends to
a customer, the same location's logistics department also delivers products to this customer.
Therefore, today some of Papierco's customers in the same five-digit zip code areas are allocated inefficiently to several of the current 21 German warehouse locations. Customers should,
however, be supplied standardly by the warehouse closest to them. There is a high potential for
747
748
749
The sales assistant triggers a transshipment order, i. e. he orders stock from another warehouse, if he
cannot satisfy a customer's demand from the primary warehouse.
Delfmann (2000: 322).
Delfmann (2000: 325).
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5 Applying Risk Pooling at Papierco
transportation cost degression in switching from today's suboptimal to the determined optimal
customer allocation to Papierco's current 21 warehouses. Unfortunately, it cannot be numeralized exactly due to today's inefficient customer allocation to multiple locations, erroneous data
management, and ignorance of the number of delivery trips to each customer, delivery routes
and quantities, and truck utilization before and after optimization.
Optimizing the customer allocations can lead to cost reductions fast and without much
investment burden. The delivery route numbers merely have to be changed for some customers in the customer master data of the ERP software. Furthermore, optimal customer
allocations may reduce transshipments.
The optimal customer allocation according to the shortest distance was found with the
software NCloc750 and Euclidean metric and visualized with the zip code diagram Das
Postleitzahlen-Diagramm 3.7751 in figure 5.6. The colored areas represent today's, the ones
outlined in black the optimal catchment areas.
750
751
ATL (2009).
Wessiepe (2009).
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5 Applying Risk Pooling at Papierco
Figure 5.6: Comparison of Current and Optimal Catchment Areas of Papierco's Warehouses
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5 Applying Risk Pooling at Papierco
5.3.2.2 Increase in Transshipments and Its Causes
Year
Warehouse Sales
to Customers (t)
Transshipments (t)
Transshipments
(% of Sales to Customers)
2005
381,694
53,636
14.05
2006
405,116
58,755
14.50
2007
428,491
71,967
16.80
Table 5.1: The Extent of Transshipments at Papierco
We can confirm that the transshipment quantities rose from 2005 to 2007 by 34.18 % (from
2005 to 2006 by 9.54 % and from 2006 to 2007 by 22.49 %). The warehouse sales to customers also increased from 2005 to 2007 by 12.26 % (from 2005 to 2006 by 6.14 % and from
2006 to 2007 by 5.77 %). However, this does not fully explain the increase in transshipments,
as the percentage of warehouse sales to customers enabled by transshipments increased as well
(cf. table 5.1).
In interviews with chief operating officers and directors of purchasing, sales, and logistics at Papierco's different locations it became clear that the increase in transshipments is
caused by changing transshipment operations to direct invoicing in June of 2006752, some
locations decreasing their inventory levels, and including more and more products in the
product line753. According to one chief executive officer the “dramatic increase” in transshipment volumes was “the manifestation of the sales department's service delusion”.
However, thanks to transshipments Papierco had also gained market share in warehouse
sales. Papierco's better development compared to its competitors was based on transshipments, as they enabled a higher product availability, broader product assortment, and faster
delivery. This confirms that transshipments can lead to a competitive advantage as Guglielmo (1999), Kroll (2006), and Alvarez (2007) already insinuate.
The cost that locations are charged for using an emergency transshipment (transshipment cost rate) is based on quantity units (positions, pallets, and kilograms) and purchase
prices and does not reflect the actual logistical costs (picking, transportation, and reloading
costs). Within a company group only the costs really incurred by the transshipments should
752
753
Sales people do not search at the own warehouse for an alternative product to the one originally desired
by the customer in case of a stockout anymore. Today sales assistants order more via transshipments for
reasons of simplicity than prior to the introduction of direct invoicing. This puts a strain on the product
exchange flows between warehouses in terms of volume and costs.
These products tend to have small sales volumes and to steal sales from substitutes. Nonetheless, at least
small quantities have to be stored at every location, which increases average stock, or the product has to
be obtained via transshipments, which increases transshipment quantities.
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5 Applying Risk Pooling at Papierco
be charged, so that there is no incentive to prefer or reject the use of transshipments due to
inadequate charges.
Although Rudi et al. (2001) find transshipment prices that are supposed to always induce local deciders to make globally optimal inventory and transshipment decisions, Hu et
al. (2007) give a counterexample. There may exist coordinating prices for only a small
range of problem parameters, e. g. if the two locations are symmetric (both locations have
the same cost and revenue coefficients, demand distributions, and capacity constraints, and
changes in either demand or capacity distributions are simultaneously implemented in both
locations). The higher the capacity uncertainty is, the higher the coordinating prices are.
Increasing demand variability may increase or decrease coordinating prices depending on
the distribution. A linear transshipment price schedule often will not achieve coordination
of two locations' production and transshipment.
Apart from this the transshipment lead time tends to be shorter than the supplier lead
time. In Papierco's case the transshipment lead time ranges from a few hours to 4 work
days at the most. The supplier lead time for the various products ranges from 14 to 154
days and is 28.49 days on average. Therefore a transshipment from a sister location is preferred to a replenishment from a supplier in case of a stockout, as otherwise the sale is lost
due to the usual delivery time restriction of 24 hours.
Some managers remark that for some Papierco locations other ones were their “best
customers“, as they made profits by transshipping products. One director of logistics
claimed only locations obtaining a lot of products via transshipments criticized the transshipment charge rate as too high. It would be even higher, if the really incurred logistical
costs were charged. This supports the call for fair transshipment charge rates.
The transshipment costs ought to be debited to the sales assistants (deducted from the
contribution margin which determines the sales assistants' premium) who release a transshipment order or at least made transparent to them. The objection that one should not inhibit the sales assistants in their sales function can be countered that other wholesalers
commonly set up guidelines for the sales personnel.
Furthermore, if a sales assistant chooses, for instance, a paper with a one centimeter
larger format as an alternative to a stocked out product desired by a customer, the higher
purchase price cannot be charged. Therefore, the contribution margin that determines the
sales assistant's premium is lower and the sales assistant is enticed to obtain the originally
demanded product via transshipment from another warehouse location. This highlights that
the implementation of risk pooling methods is influenced by human resource and business
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5 Applying Risk Pooling at Papierco
policy factors. Managers should formulate clear guidelines for the usage of transshipments
in case a desired item is not available at the primary stocking location.
A software tool should be created to help the sales assistant in deciding whether it is
more economical to obtain a stocked out item via transshipments from another warehouse,
search for a substitute at the own warehouse, cut paper to the right format, or ream wrap
paper at the own location if possible.
5.3.2.3 Transshipments Are Worthwhile for Papierco
A high customer service level at the warehouses can be achieved by either holding sufficient
inventory there, which entails high inventory investment and carrying costs, or by postponement through centralized inventory holding, which presumes fast and thus expensive delivery
of any amount of any product to any customer. A better alternative might be to hold some inventory at the warehouses and let the warehouses transship products in case of a stockout.754
“A mathematical model of the exact implications [… of transshipments] is extremely
complicated”755. Evers (2001), Minner et al. (2003), and Minner and Silver (2005) consider
transshipments between two locations for a specific product in a specific situation only and
not whether transshipments might be worthwhile for a company with more locations and
products in general at all. Minner et al. (2003: 394) note that their model may be extended
to multiple locations with no fixed transshipment costs by successively determining which
location maximizes the savings for each transshipped unit. The problem becomes more
difficult with fixed costs, unless there are only a small number of warehouses as in Tagaras
(1999). The structures in all past transshipment research are much simpler than the practical ones.756
If the outlets use complete pooling, the exact form of the lateral transshipment policy
does not significantly affect total system performance.757 Deciding between never transshipping or always transshipping as many units as disposable if one location faces a stockout while another one has stock on hand758 is almost as good as a more extensive investigation that considers the transshipment's prospective effect on the transshipping location's
cost759. Burton and Banerjee (2005: 169) also find that an ad hoc emergency transshipment
approach may lead to lower shortage (higher customer service) and transshipment cost
754
755
756
757
758
759
Cf. Evers (2001).
Minner et al. (2003: 385).
Chiou (2008: 442).
Tagaras (1999).
Cf. Olsson (2009).
Minner et al. (2003: 394f.), Minner and Silver (2005: 1).
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(number of lateral transshipments) than a more systematic transshipment technique based
on stock level equalization760. Transshipping is better than not transshipping, but it increases transportation activity.761 Backordered demand should not be partially fulfilled by transshipments.762 In practice pull systems may offer simpler and more practical joint replenishment/transshipment policies than the push systems mostly considered in the literature.763
At Papierco the charged transshipment costs (for transportation, shipment documentation, receiving, handling, and administration) amounted to 5 Mio. € in 2007, i. e. about
69.48 € per ton that was delivered via transshipments (5 Mio. €/71,967 t = 69.48 €/t). According to its inventory turnover curve (figure 5.7), Papierco needs around 10,291 t of average inventory for 71,967 t of warehouse sales to customers. This suggests that without
transshipments Papierco would have had to store at least 10,291 t of additional average
inventory.
This derivation might not be fully justified, as we derive inventory figures for the system without transshipments from the figures for the existing system with transshipments
and while safety stocks will be lower in general, regular stocks may increase with crossfilling of demand764.
Before transshipments were used, average inventory turnover in German paper wholesale was 5.4 from 1975 to 1984765. Therefore one might estimate that Papierco would have
needed 13,327 t (= 71,967 t/5.4) extra average inventory without transshipments. Consequently, Papierco would have incurred approximately 3.5 Mio. € of additional inventory
carrying costs in order to sell 71,967 t without transshipments: 13,327 t × 1,058 €/t (average product purchase price in the warehouse sales business division) × 0.25 (average
inventory carrying cost rate) = 3,524,992 €. However, these additionally stored tons would
not necessarily have been the demanded ones in the right location. As the estimate of additional inventory carrying costs without transshipments is lower than the 2007 total transshipment cost, the latter should be reduced, e. g. by storing fast-movers such as copy papers at all locations (cf. section 5.3.5), avoiding unnecessary and uneconomical transshipments, improving demand forecasts, and using less expensive alternative risk pooling methods.
760
761
762
763
764
765
See, e.g., Jönsson and Silver (1987a).
Burton and Banerjee (2005: 169).
Wee and Dada (2005: 1529).
Bhaumik and Kataria (2006).
Ballou and Burnetas (2000, 2003), Ballou (2004b: 385-389).
Röttgen (1987: 109).
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5 Applying Risk Pooling at Papierco
Centralizing all inventories in one or several central warehouses would decrease warehouse fixed costs, safety stock and thus inventory holding costs as well as inbound transportation costs to these central warehouses, but also the customer service level due to
greater delivery distances to the customers (the stockout costs would be higher and the
profit possibly lower) and increase outbound transportation costs to customers. Besides, a
central warehousing strategy would conflict with Papierco's corporate strategy of a decentralized full-line 24-hour-delivery distributor.
As stockout costs could not be estimated in the aggregate consideration without transshipments in general, we now consider the costs of transshipping versus not transshipping.
Transshipments entail transportation, shipment documentation, receiving, handling and
administration costs, the sending location's cost of reordering the transshipped product
from the supplier, as well as an increased probability of a stockout at the sending location.766
Transportation, shipment documentation, receiving, handling, and administration costs
amount to 69.48 € per transshipped ton of paper on average. As derived in section 5.3.1 the
order cost per ton amounts to 3.31 €. Even though Papierco's locations order and receive
stock regularly about every two weeks and thus it is unlikely to place an order merely to
make up for transshipped items, we consider this value as an upper bound to the order cost
caused by transshipping.
The increased probability of a stockout at the sending location is difficult to quantify in
general and on average. In Papierco's case this cost is rather another transshipping cost
again, as the sending location would ask another location for a transshipment, if later it ran
out of stock of the product it had just transshipped. The increased stockout likelihood depends on the transshipment quantity, the current on-hand inventory of the transshipped
product, customer demand for this item, and the stock receipts of this item (quantity on
order and its arrival time).
Transshipments made up 16.8 % of warehouse sales to customers in 2007, i. e. one could
assume that Papierco had an average overall stockout probability of 16.8 % and therefore an
inventory availability or fill rate before transshipments of 83.2 %. We assume that every
location faces a stockout probability of 16.8 % for an item, neglecting the different influencing factors just mentioned, the derivation of this stockout probability from the situation with
transshipments, and the difference between alpha and beta service level. If two locations
766
Evers (2001: 312f.).
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5 Applying Risk Pooling at Papierco
transship, they face a stockout with a probability of 0.168
probability of 0.168
100
100
2.82 %, three with a
0.47 %, four with 0.08 %, five with 0.013 %, six with
0.002 %, seven with 0.0004 %, and 21 with 5.3888354 10
%. This affirms that emer-
gency transshipments lead to a high effective fill rate for the customer (97.18 % for two,
99.53 % for three, and 99.92 % for four locations that transship), even if the item fill rate is
relatively low (83.2 %).767 The main benefit (reduced stockouts and safety stock levels) can
be reaped having just a few locations transship. It is neither necessary nor economical to
have all 21 locations transship due to diminishing marginal returns to transshipping768.
If we consider the worst but unlikely case that at every location one after another a
stockout occurs for the same item after having transshipped one ton of that item to the preceding location, then the reorder cost due to transshipment only accrues at the last (21st)
location. The cost of increased probability of a stockout can be estimated by another transshipping cost of 69.48 €, since the likelihood that one transshipment triggers more than one
additional stockout and thus transshipment is negligible as the example above shows.
Therefore the average cost of transshipping can be estimated as: 142.27 €/t = 69.48 €/t
(transportation and related costs) + 3.31 €/t (reorder cost) + 69.48 €/t (increased transshipment usage/stockout probability).
Without transshipments Papierco incurs the cost of a stockout and the cost of holding a
ton in inventory until later at the not transshipping location. The stockout cost (209 €) is
estimated by the average contribution margin of one ton of warehouse sales to customers
minus the sales premium. The impact of stockouts on the future purchasing behavior of
customers is difficult to grasp and neglected here. Holding the ton of paper in storage until
later costs 33 € on average (cf. section 5.3.1). Therefore, the cost of not transshipping
amounts to approximately 242 €/t.
Transshipping is on average economically sensible for Papierco, as it generally is less
expensive (142.27 €) than not transshipping (242 €) a ton of paper in case of a stockout.
If only transportation-related costs evoked by transshipments and stockout costs due to
not transshipping are considered and the other costs are neglected, a sales assistant should
only make a transshipment order in case of a stockout, if the contribution margin is equal
to or larger than 69.48 €/t. Then at least the average transportation-related costs for the
transshipment are covered.
767
768
Cf. Ballou and Burnetas (2000, 2003), Ballou (2003b: 81, 2004b: 385-389).
Tagaras (1989), Evers (1997: 71f.), Ballou and Burnetas (2000, 2003), Ballou (2004b: 385-389), Kranenburg and Van Houtum (2009).
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In order to decide more accurately on emergency transshipments for a specific item in a
specific situation the methods proposed by Evers (2001), Minner et al. (2003), and Minner
and Silver (2005) can be used, provided that the necessary data are available. Minner et al.
(2003: 395) present a heuristic decision rule for the quantity and source of a transshipment.
In simulations, Minner et al.'s (2003: 390f., 393) method generally achieves lower average
annual costs than Evers' (2001) one. Since the cost parameters are likely to remain constant
in the short run, whether or not a particular transshipment is made depends principally on
the on-hand inventory level at the shipping location.769
However, before using transshipments, sales assistants should check their own warehouse for substitutes for the customer wish and try to persuade the customer to buy another
product, which only incurs transaction costs (searching for substitutes in the information
system). This product substitution might cause a slight dissatisfaction on the customer's
part, but is certainly cheaper than a transshipment. If the alternative product is more expensive than the original customer wish, a higher profit is gained. If only the sales price for the
originally desired product can be charged or the substitute is less expensive than the original purchase wish, Papierco has to accept a lower contribution margin. Of course the product should not be sold beneath cost price.
If no substitute can be found, it should be checked whether the paper can be cut to the
right size (form postponement770), which costs around 56.25 €/t (neglecting waste), or
ream wrapped (packaging postponement) for 33.50 €/t on average. Both options are
cheaper than and therefore should be preferred to a transshipment in general.
In order of increasing costs incurred by the considered risk pooling methods, Papierco's
sales assistants should first try to substitute an unavailable product, then to customize or
differentiate products, and then to resort to transshipments in case of a stockout. This
shows that risk pooling methods can be combined effectively.
Although this is a rather crude general average analysis, because exact data (especially
probabilities) were not available, and we advert to the perils of using averages as noted
e. g. by Savage et al. (2006), it shows some general relationships. Of course a decision for
a particular risk pooling method (product substitution, postponement, or transshipment) in
a certain situation depends on the specific cost parameters.
769
770
Evers (2001: 313).
See e. g. Chauhan et al. (2008).
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5.3.3
Centralized Ordering
5.3.3.1 Papierco's Current Order Policy
At Papierco a replenishment order is placed with a supplier (the daily DRP run generates an
order message) whenever the reorder point is reached or in possibly short intervals (every two
weeks) within the suppliers' minimum order quantity restrictions. The reorder point is the sum
of safety stock, which is set by every Papierco member company independently, and average
lead time demand (average sales per day during the lead time times the lead time in days).
The purchase order planning code for a specific product is 1, if it is planned with DRP,
and 0, if it is not planned with DRP. The latter case applies to about 20 % of the warehouse
products, as for them the minimum order quantity is usually higher than the planned order
quantity, e. g. if they have fixed order dates or the minimum order quantity is a full truck
load. These products are planned manually with order lists.
Safety stock is calculated as the product of average sales per day during the lead time,
supplier lead time in days, and a safety factor. Thus double average demand during lead
time results in double safety stock. According to experience the safety factor is set to ¼ for
ream wrapped paper and 1/3 for not ream wrapped one. The safety factor is not entered
into the ERP system for every product, but for parts of the product line manually every
three months.
However, safety stock should not be set arbitrarily, but according to a target customer
service level (e. g. 90 % product availability for A items) and the statistical behavior of
demand during lead time or rather the forecast error in the case of Papierco, because demand is forecast. The actual supplier lead time and whether and how often the safety stock
is touched is not recorded either. No cost optimal order quantities or times are determined.
Folding Box Board (cf. figure 5.3) has an average demand during one week lead time of
819.23 sheets, a current safety stock of 204.81 (= 819.23 × 1/4) sheets, and a reorder point of
1024.04 (= 819.23 + 204.81) sheets. According to the empirical distribution function this corresponds to a service level of approximately 76 % or a stockout probability during lead time of
24 %. A reorder point of 1.460 sheets or safety stock of 640.77 (= 1460 - 819.23) sheets would
be needed to reach an inventory availability of 80.8 % during lead time. According to the respective empirical distribution functions, the Uncoated Cut-Size White Wood-Pulp Paper has an
inventory availability during lead time of 86 %, one continuous roll of approximately 84 %, the
other of 73.1 %, Woodfree Matte Coated Cut-Size Paper of 72 %, the Woodfree White CutSize C-Quality Copy Paper of 76.9 %, and the Woodfree White Cut-Size A-Quality Copy Paper
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of 86.5 % with today's calculation of safety stock. The safety stock can be determined more
definedly based on a target customer service level.
According to the nonparametric Kolmogorov–Smirnov test for the second continuous
roll (asymptotic significance (two-tailed) p = 0.700) and the copy papers (p = 0.741 and
0.616) the hypothesis H0 that the sample stems from a population with normally distributed
weekly demands cannot be rejected with a level of significance of 5 %. The Kolmogorov–
Smirnov test is also applicable to small samples, but might not be very definite if the unknown distribution function is not continuous (as in this case) or the data are not metric.771
The hypothesis H0 that the sample stems from a population with uniformly, Poisson, or
exponentially distributed weekly demands is rejected with a level of significance of 5 %
for all products but the second continuous roll (for the exponential distribution p = 0.436).
However, there is one value outside the specified exponential distribution range that is
skipped. In the Kolmogorov–Smirnov test of exponential distribution for the other paper
grades (variables) there are also values outside the specified distribution range that are
skipped.
The used Order Policy Code 4 (Periods of supply) combines the order quantities (forecast demands) for the time period defined in the Value Order Policy (for most Papierco
products 10 days). The JD Edwards OneWorld manual says “This order policy code was
designed to use with high-use/low cost items for which the user is not concerned about
carrying excess inventory”772. This partly explains why Papierco carries so much inventory, although it mainly sells low-turnover and not necessarily low-cost products.
The other available Order Policy Codes are 0 (The DRP system will not plan this item.),
1 Lot-for-lot or as required (The system will create messages for purchase orders for the
exact amount needed.), 2 Fixed order quantity (The system will create messages for purchase orders based on the value entered in the Value Order Policy in the Plant Manufacturing Data. If demand exceeds the fixed order quantity, the system will generate purchase
orders in multiples of the fixed order quantity.), 3 Economic Order Quantity (EOQ), and 5
Rate scheduled item (The system will generate messages based on existing rates and rate
generation rules for parent rate-scheduled items only.).
The order quantity is the maximum of the ten day demand forecast and the minimum
order quantity, which is rounded to the next higher order quantity that is divisible by the
saltus quantity. For instance, if the minimum order and saltus quantity are 500 kg (only
771
772
Duller (2008: 108, 112).
Oracle (2009).
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complete pallets must be ordered) and forecast demand for ten days is 1,150 kg, then
1,500 kg are ordered. Such a policy that determines and controls the inventory level at each
warehouse location in direct proportion to (forecast) demand is called stock-to-demand.773
Papierco's inventory turnover curve in grey in figure 5.7 confirms this. For all its
warehouses the average annual inventory in dependence of the annual throughput is plotted
with green squares. A linear regression line is adequate for these data as the coefficient of
determination R2 = 0.8362 shows. However, it also suggests that not all warehouses execute this order policy consistently.774 Individual turnover rates range from 5 to 21 with an
average of 8.24. Deviations of the individual turnover rates might be explained by different
service levels or replenishment rules.775 Warehouses, whose data points lie above the turnover curve, might attain a higher turnover and lower inventory holding costs, if they followed the stock-to-demand order policy more consistently. Warehouses, whose data points
are plotted beneath the turnover curve, exhibit a higher-than-average turnover rate than
attainable by this stock-to-demand policy.
An EOQ policy would lower the average turnover rate to 6.53 as the turnover curve in
black shows (a power function with the normative exponent suggested by Ballou (2000:
75) fitted to Papierco's data), probably because the stock-to-demand order policy is not
followed consistently today and some warehouses have an unusually high turnover rate of
11, 15, or 21.
Nevertheless, this paper distributor's average inventory levels appear rather high for the
annual throughputs. The annual average turnover rate of the German wholesale of paper,
cardboard, and office supplies from 1999 to 2006 was 17.3.776 However, this group contains stationary wholesalers, which might raise the average turnover rate and make it unsuitable as a benchmark for just paper wholesalers. The U.S. merchant wholesalers of paper and paper products had an annual average turnover rate from 1992 to 2008 of 12.75.777
Papierco has a rather low average turnover rate of 8.24. This might be explained by the
large product variety it offers. Papierco sells at least 7,000 different product specifications.
Thus it is difficult to forecast demand for individual products. Furthermore, minimum order and saltus quantities have to be met.
773
774
775
776
777
Ballou (2000: 74).
Cf. Ballou (2000: 76).
Cf. Ballou (2000: 78f.).
Statistisches Bundesamt Deutschland (2009a, 2009b, 2009c, 2009d, 2009e, 2009f, 2009g, 2009h), calculated by us.
U.S. Census Bureau (2009), calculated by us.
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10000
9000
y = 0.143x
R² = 0.8362
Average Inventory (t)
8000
7000
y = 3.1756x 0,7
6000
5000
4000
3000
2000
1000
0
0
10000
20000
30000
40000
50000
60000
70000
Annual Warehouse Throughput (t)
EOQ
Current Stock-to-Demand Policy
Pot.(EOQ)
Linear (Current Stock-to-Demand Policy)
Figure 5.7: Inventory Turnover Curves for Papierco
EOQ = economic order quantity, Pot. = regression power function, Linear = linear regression line.
Papierco has 196 sum suppliers, but 83 % of the annual procurement quantity is sourced from
ten, 52 % from three, 40 % from two suppliers, and 20 % just from a single supplier. With big
suppliers a quantity structure is negotiated. There is a one-to-one product-supplier relationship,
i. e. every product is sourced from only exactly one supplier.
Therefore, Papierco should collaborate closer with its suppliers, conduct a better supplier management, to enable shorter lead times, a better forecast, inventory policy and
product availability. One Papierco member company's director of purchasing had created
such a collaboration with Papierco's most important supplier that supplied the highest
quantity. A monthly demand forecasting for product groups and a guaranteed maximum
lead time of 14 days for fast and 28 days for slow movers was established. Previously this
supplier's lead time had been 4 to 6, sometimes 8 to 12 weeks. Inventories could be reduced considerably. Unfortunately, the business relationship to this supplier was broken
due to price policy reasons. This concept was neglected, and inventories rose again.
One director of purchasing is against a partner-like collaboration with suppliers for they
already took advantage of Papierco due to their big negotiation power. One director of
sales remarked, paper wholesalers and manufacturers did not cope with recurring demand
peaks correctly, such as in election times. When there were vacation close-downs, they
could not prevent supply bottlenecks. This shows again that a close collaboration with
104
5 Applying Risk Pooling at Papierco
suppliers is indispensable. Not least Weng and McClurg (2003) showed the value of supplier–buyer coordination (in ordering) in coping with uncertain delivery time and demand.
5.3.3.2 Stock-to-Demand Order Policy with Centralized Ordering and Minimum
Order and Saltus Quantities
Risk pooling models are based on economic-order-quantity (trading off inventory holding
against order costs) or newsvendor models (trading off overage against underage costs).
In practice, however, a stock-to-demand order policy is followed frequently778 as we also detected in interviews with logistics and purchasing managers and at Papierco. Orders
and therefore cycle inventories are proportional to demand at each warehouse.779 Expected
demand at each warehouse location is forecast. Order quantities result from the difference
of forecast demand and available inventory. Maister (1976: 132) and Evers (1995: 5) refer
to this order policy as the “replacement principle”, where orders are set equal to demand
during a certain time period. Such an order policy leads to a constant turnover. It is frequently pursued, as it is simple and easily executable780 and because automated ordering
systems have very low ordering costs and thus the EOQ is not used781. The replacement
principle is followed e. g. in Zinn et al. (1990: 139), Evers (1996: 117, 1997: 59), and Rabinovich and Evers (2003a: 226).
If it is applied, centralization usually does not reduce cycle stocks:782 The system wide
order quantity of n warehouses and therefore average cycle stock in the decentralized system are equal to the ones in the centralized system, if exactly the forecast demand is ordered.
Following a stock-to-demand order policy, safety stock is often calculated as the product of a safety factor and average demand during lead time at each warehouse as our interviews with logistics and purchasing managers showed. Doubling demand results in double
safety stock. Safety stock is not determined by a desired target customer service level and
the statistical behavior of demand during lead time or the forecast error. Centralization
does not reduce system wide safety stock, if the safety factor is equal for all warehouses
778
779
780
781
782
Wanke (2009: 108).
Ballou (2000: 74).
Ballou (2000: 77f., 2004a: 20f.).
Herron (1987), Evers (1995: 14). Researchers disagree whether the EOQ model is rarely used (Herron
1987, Woolsey 1988, Zinn et al. 1990: 139, Evers 1995: 14) or often used (Osteryoung et al. 1986, Pan
and Liao 1989, Lee and Nahmias 1993: 48, Dubelaar et al. 2001: 98, Slack et al. 2004). Of eleven companies that we surveyed (table D.1) five use a stock-to-demand, four an EOQ, one a dynamic order policy, and one the newsvendor model.
Maister (1976: 132), Evers (1995: 2, 14f.).
105
5 Applying Risk Pooling at Papierco
and remains the same. The service level increases, however, due to the risk pooling effect.
Perhaps this service level is higher than necessary.
Often the stock-to-demand policy is subject to minimum order and saltus quantity constraints as in the case of Papierco. Then the order quantity qi for a specific product at warehouse i = 1, …, n results from forecast demand minus available inventory di for a specific
period at warehouse i and a constant minimum order quantity m and saltus quantity s. The
saltus quantity demands that only certain multiples are ordered like in Köchel (2007), e. g.
only full pallets.
If a stock-to-demand order policy with minimum order and saltus quantities is followed,
centralization may lead to a reduction in average cycle stock. The order quantity and therefore average cycle stock in the decentralized system, where every location places orders for
itself, is more than or equal to the ones in the centralized system, where a common joint
order is placed for all locations783, since often more than forecast demand minus available
inventory is ordered in order to meet minimum order and saltus quantities. In the centralized system the constant minimum order and saltus quantities may be exhausted more.
The order quantity qi for a specific product at warehouse i is
,
(5.1)
.
The total system wide order quantity in the decentralized system therefore is:
∑
∑
,
(5.2)
.
The total system wide order quantity in the centralized system is:
∑
,
(5.3)
.
The total system wide order quantity in the centralized system is less than or equal to
the one in the decentralized system, because the order quantity function (5.1) is subadditive:
∑
,
∑
,
.
(5.4)
For the proof please refer to appendix E.
The centralized ordering effect (COE), the percent reduction of the order quantity by
centralized ordering, is:
783
For Özen et al. (2005: 1) inventory centralization also is a byword for joint ordering: “Groups of retailers
might increase their expected joint profit by inventory centralization, which means that they make a joint
order to satisfy total future demand”.
106
5 Applying Risk Pooling at Papierco
∑
1
100
1
∑
,
,
100.
(5.5)
Centralized ordering can reduce demand and supply uncertainty and thus inventory and
stockouts and increase customer service level by demand pooling, aggregate forecasting
across all locations, and postponement of order allocation to the delivery warehouses. This
will be shown in the following section.
5.3.3.3 Benefits of Centralized Ordering for Papierco
The example of a woodfree white cutsize A-quality copy paper in table 5.2 demonstrates that
the centralized ordering effect for a stock-to-demand order policy with minimum order and
saltus quantities can be significant. This copy paper has the highest annual sales and contribution margin in warehouse sales of all products at most Papierco locations.
Table 5.2 shows the actual warehouse sales for this copy paper for Papierco's 22 German locations and one Dutch location per month in 2007. The sales forecasts were obtained with exponential smoothing. The forecast method was initialized with the 2006 actual warehouse sales per month per location, i. e. data from 2006 were used to determine
starting values for the exponential smoothing model. The exponential smoothing constant
(column O) that minimized the forecast error (the standard error of the forecast (RMSE))
for the monthly forecasts of 2006 warehouse sales for every location was used for forecasting 2007 sales.784
784
Cf. Ballou (2004b: 299).
107
5 Applying Risk Pooling at Papierco
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
A
Minimum order quantity
Saltus order quantity
B
C
22,500 kg
500 kg
Work days
22
20
Warehouse Location
Jan
Feb
Aalen
Actual sales
43,300
32,608
Forecast
27,465
27,624
Forecast error
15,835
4,984
Order quantity
27,500
43,500
Net stock
-15,800
-4,908
Sales rate
1,968
1,630
Average cycle stock (CS)
8,952
11,868
Berlin
Actual sales
40,165
44,888
Forecast
35,059
35,110
Forecast error
5,106
9,778
Order quantity
35,500
40,000
Net stock
-4,665
-9,553
Sales rate
1,826
2,244
Average cycle stock
15,788
14,097
Bielefeld
Actual sales
44,288
28,438
Forecast
28,440
28,599
Forecast error
15,848
-161
Order quantity
28,500
44,500
Net stock
-15,788
274
Sales rate
2,013
1,422
Average cycle stock
9,397
14,493
Bremen
Actual sales
22,150
17,000
Forecast
19,224
19,253
Forecast error
2,926
-2,253
Order quantity
22,500
22,500
Net stock
350
5,850
Sales rate
1,007
850
Average cycle stock
11,425
14,350
Cologne
Actual sales
127,123 114,645
Forecast
105,695 107,838
Forecast error
21,428
6,807
Order quantity
106,000 129,000
Net stock
-21,123
-6,768
Sales rate
5,778
5,732
Average cycle stock
44,605
50,926
Dietzenbach (Frankfurt)
Actual sales
37,325
44,800
Forecast
36,609
36,616
Forecast error
716
8,184
Order quantity
37,000
37,000
Net stock
-325
-8,125
Sales rate
1,697
2,240
Average cycle stock
18,352
15,183
Dortmund
Actual sales
2,238
2,775
Forecast
3,625
3,611
Forecast error
-1,387
-836
Order quantity
22,500
0
Net stock
20,262
17,487
Sales rate
102
139
Average cycle stock
21,381
18,875
Ernstroda (Erfurt)
Actual sales
6,900
4,888
Forecast
18,712
12,806
Forecast error
-11,812
-7,918
Order quantity
22,500
0
Net stock
15,600
10,712
Sales rate
314
244
Average cycle stock
19,050
13,156
Fellbach (Stuttgart)
Actual sales
32,800
37,603
Forecast
36,395
36,035
Forecast error
-3,595
1,568
Order quantity
36,500
32,500
Net stock
3,700
-1,403
Sales rate
1,491
1,880
Average cycle stock
20,100
17,465
Garching (Munich)
Actual sales
56,395
51,943
Forecast
40,932
48,664
Forecast error
15,463
3,279
Order quantity
41,000
64,500
Net stock
-15,395
-2,838
Sales rate
2,563
2,597
Average cycle stock
15,147
23,280
Hemmingen (Hanover)
Actual sales
60,453
62,338
Forecast
41,620
45,386
Forecast error
18,833
16,952
Order quantity
42,000
64,000
Net stock
-18,453 -16,791
Sales rate
2,748
3,117
Average cycle stock
14,881
16,949
Kiel
Actual sales
17,728
19,563
Forecast
23,673
23,614
Forecast error
-5,945
-4,051
Order quantity
24,000
22,500
Net stock
6,272
9,209
Sales rate
806
978
Average cycle stock
15,136
18,991
Leizen
Actual sales
2,488
2,388
Forecast
4,920
4,896
Forecast error
-2,432
-2,508
Order quantity
22,500
0
Net stock
20,012
17,624
Sales rate
113
119
Average cycle stock
21,256
18,818
Lohfelden (Kassel)
Actual sales
4,650
1,288
Forecast
2,252
2,276
Forecast error
2,398
-988
Order quantity
22,500
0
Net stock
17,850
16,562
Sales rate
211
64
Average cycle stock
20,175
17,206
Lunteren (NL)
Actual sales
1,513
100
Forecast
437
652
Forecast error
1,076
-552
Order quantity
22,500
0
Net stock
20,987
20,887
Sales rate
69
5
Average cycle stock
21,744
20,937
D
E
F
G
0.93 €/kg
Value
0.23 €/kg
Contribution margin
H
I
J
K
L
M
N
O
All values in kg except for the exponential smoothing constant (sm. const.).
Average monthly positive net stock (sum of the positive net stocks divided by twelve).
22
Mar
19
Apr
20
May
21
Jun
22
Jul
23
Aug
20
Sep
22
Oct
22
Nov
44,833
27,674
17,159
33,000
-16,741
2,038
9,037
26,535
27,845
-1,310
45,000
1,724
1,397
14,992
26,935
27,832
-897
26,500
1,289
1,347
14,757
23,490
27,823
-4,333
27,000
4,799
1,119
16,544
27,773
27,780
-7
23,000
26
1,262
13,913
34,888
27,780
7,108
28,000
-6,862
1,517
11,380
19,350
27,851
-8,501
35,000
8,788
968
18,463
36,420
27,766
8,654
22,500
-5,132
1,655
13,539
29,615
27,852
1,763
33,000
-1,747
1,346
13,154
8,140
27,870
-19,730
30,000
20,113
428
24,183
353,887
333,162
20,725
374,000
3,062
37,418
35,208
2,210
45,000
-1,971
1,701
16,835
39,375
35,230
4,145
37,500
-3,846
2,072
16,122
33,300
35,271
-1,971
39,500
2,354
1,665
19,004
41,138
35,252
5,886
33,000
-5,784
1,959
15,307
34,318
35,311
-993
41,500
1,398
1,560
18,557
39,308
35,301
4,007
34,000
-3,910
1,709
16,019
41,488
35,341
6,147
39,500
-5,898
2,074
15,392
40,243
35,402
4,841
41,500
-4,641
1,829
15,847
42,313
35,451
6,862
40,500
-6,454
1,923
15,323
8,241
35,519
-27,278
42,000
27,305
434
31,426
442,195
423,454
18,741
469,500
2,588
53,200
28,597
24,603
28,500
-24,426
2,418
8,073
25,388
28,843
-3,455
53,500
3,686
1,336
16,380
27,913
28,809
-896
25,500
1,273
1,396
15,230
21,163
28,800
-7,637
28,000
8,110
1,008
18,692
22,028
28,723
-6,695
22,500
8,582
1,001
19,596
45,038
28,657
16,381
22,500
-13,956
1,958
10,930
18,665
28,820
-10,155
43,000
10,379
933
19,712
40,700
28,719
11,981
22,500
-7,821
1,850
13,425
31,663
28,839
2,824
37,000
-2,484
1,439
13,501
15,838
28,867
-13,029
31,500
13,178
834
21,097
374,322
344,713
29,609
387,500
3,790
22,450
19,231
3,219
22,500
5,900
1,020
17,125
12,913
19,263
-6,350
22,500
15,487
680
21,944
13,988
19,199
-5,211
22,500
23,999
699
30,993
17,938
19,147
-1,209
0
6,061
854
15,030
12,663
19,135
-6,472
22,500
15,898
576
22,230
24,038
19,070
4,968
22,500
14,360
1,045
26,379
11,238
19,120
-7,882
22,500
25,622
562
31,241
14,188
19,041
-4,853
0
11,434
645
18,528
24,013
18,993
5,020
22,500
9,921
1,092
21,928
16,825
19,043
-2,218
22,500
15,596
886
24,009
209,404
229,721
-20,317
225,000
12,540
105,668 176,203
84,720 139,303 113,465
97,890
118,967 117,637 123,493 119,616 121,585 120,773
-13,299
58,566 -38,773
19,687
-8,120 -22,883
111,000 104,000 182,500
80,500 141,500 112,500
13,678 -58,525
39,255 -19,548
8,487
23,097
4,803
7,661
4,236
6,332
5,158
5,152
66,512
40,147
81,615
51,851 65,220
72,042
1,532,903
1,405,010
127,893
1,556,000
9,882
241,830
108,519
133,311
115,500
-133,098
10,992
25,768
96,180 123,998 111,878
121,850 119,283 119,754
-25,670
4,715
-7,876
255,000
94,000 124,500
25,722
-4,276
8,346
5,062
6,200
5,328
73,812
57,927
64,285
19
Dec
Total/Average Sm. Const.
P
Q
R
MAD
BIAS
S
RMSE Safety Stock
15,835
0.01
7,523
1,727
9,922
0.01
6,602
1,562
9,362
0.01
9,472
2,467
11,780
0.01
4,382
-1,693
4,790
30,095 10,658
45,742
14,232
6,862
17,476
16,381
15,044
4,968
21,265
58,566
0.10
57,893
36,765
36,698
67
45,000
110
1,671
18,493
35,105
36,699
-1,594
37,000
2,005
1,848
19,558
28,875
36,683
-7,808
35,000
8,130
1,444
22,568
58,725
36,605
22,120
28,500
-22,095
2,796
11,743
26,413
36,826
-10,413
59,000
10,492
1,201
23,699
82,000
36,722
45,278
26,500
-45,008
3,565
8,784
23,588
37,174
-13,586
82,500
13,904
1,179
25,698
37,725
37,039
686
23,500
-321
1,715
18,555
34,888
37,045
-2,157
37,500
2,291
1,586
19,735
39,073
37,024
2,049
35,000
-1,782
2,056
17,844
485,282
441,738
43,544
483,500
3,078
8,503
3,603
4,900
0
8,984
387
13,236
3,800
3,652
148
0
5,184
200
7,084
4,050
3,653
397
0
1,134
203
3,159
6,040
3,657
2,383
22,500
17,594
288
20,614
4,225
3,681
544
0
13,369
192
15,482
3,300
3,686
-386
0
10,069
143
11,719
3,440
3,682
-242
0
6,629
172
8,349
5,190
3,680
1,510
0
1,439
236
4,034
2,813
3,695
-882
22,500
21,126
128
22,533
2,690
3,686
-996
0
18,436
142
19,781
49,064
43,911
5,153
67,500
11,809
15,125
8,847
6,278
0
-4,413
688
3,865
7,213
11,986
-4,773
22,500
10,874
380
14,481
11,788
9,599
2,189
0
-914
589
5,039
10,650
10,694
-44
22,500
10,936
507
16,261
14,313
10,672
3,641
0
-3,377
651
4,236
16,263
12,492
3,771
22,500
2,860
707
10,992
27,225
14,378
12,847
22,500
-1,865
1,361
11,860
18,238
20,801
-2,563
23,000
2,897
829
12,016
18,525
19,520
-995
22,500
6,872
842
16,135
19,263
19,022
241
22,500
10,109
1,014
19,741
170,391
169,529
862
180,500
5,905
41,795
36,192
5,603
38,000
-5,198
1,900
16,130
39,615
36,752
2,863
42,000
-2,813
2,085
17,172
39,400
37,039
2,361
40,000
-2,213
1,970
17,604
30,535
37,275
-6,740
39,500
6,752
1,454
22,020
45,043
36,601
8,442
30,000
-8,291
2,047
15,143
49,350
37,445
11,905
46,000
-11,641
2,146
14,603
42,663
38,636
4,027
50,500
-3,804
2,133
17,788
49,505
39,038
10,467
43,000
-10,309
2,250
15,706
52,850
40,085
12,765
50,500
-12,659
2,402
15,502
14,850
41,361
-26,511
54,500
26,991
782
34,416
476,009
452,854
23,155
503,000
3,120
69,108
50,303
18,805
53,500
-18,446
3,141
18,871
46,790
59,706
-12,916
78,500
13,264
2,463
36,659
53,673
53,248
425
40,000
-409
2,684
26,447
53,540
53,460
80
54,000
51
2,550
26,821
56,500
53,500
3,000
53,500
-2,949
2,568
25,446
47,680
55,000
-7,320
58,000
7,371
2,073
31,211
50,575
51,340
-765
44,000
796
2,529
26,084
59,443
50,958
8,485
50,500
-8,147
2,702
22,287
41,563
55,200
-13,637
63,500
13,790
1,889
34,572
37,363
48,382
-11,019
35,000
11,427
1,966
30,109
624,573
620,693
3,880
636,000
3,892
75,190
48,777
26,413
66,000
-25,981
3,418
16,490
42,813
54,059
-11,246
80,500
11,706
2,253
33,113
52,063
51,810
253
40,500
143
2,603
26,175
47,125
51,861
-4,736
52,000
5,018
2,244
28,581
59,500
50,914
8,586
46,000
-8,482
2,705
22,038
76,913
52,631
24,282
61,500
-23,895
3,344
18,625
41,063
57,487
-16,424
81,500
16,542
2,053
37,074
45,175
54,202
-9,027
38,000
9,367
2,053
31,955
56,228
52,397
3,831
43,500
-3,361
2,556
24,934
36,325
53,163
-16,838
57,000
17,314
1,912
35,477
655,186
614,307
40,879
672,500
5,008
26,308
23,573
2,735
22,500
5,401
1,196
18,555
21,080
23,601
-2,521
22,500
6,821
1,109
17,361
17,575
23,575
-6,000
22,500
11,746
879
20,534
24,715
23,515
1,200
22,500
9,531
1,177
21,889
27,015
23,527
3,488
22,500
5,016
1,228
18,524
29,045
23,562
5,483
22,500
-1,529
1,263
13,068
21,305
23,617
-2,312
25,500
2,666
1,065
13,319
18,883
23,594
-4,711
22,500
6,283
858
15,725
29,563
23,547
6,016
22,500
-780
1,344
14,035
14,013
23,607
-9,594
24,500
9,707
738
16,714
266,793
283,006
-16,213
276,500
6,054
6,025
4,871
1,154
0
11,599
274
14,612
5,100
4,882
218
0
6,499
268
9,049
4,075
4,885
-810
0
2,424
204
4,462
3,700
4,876
-1,176
22,500
21,224
176
23,074
3,238
4,865
-1,627
0
17,986
147
19,605
4,375
4,848
-473
0
13,611
190
15,799
5,613
4,844
769
0
7,998
281
10,805
8,563
4,851
3,712
0
-565
389
3,749
7,550
4,888
2,662
22,500
14,385
343
18,160
3,125
4,915
-1,790
0
11,260
164
12,823
56,240
58,542
-2,302
67,500
12,052
4,700
2,266
2,434
0
11,862
214
14,212
2,763
2,290
473
0
9,099
145
10,481
1,950
2,295
-345
0
7,149
98
8,124
388
2,292
-1,904
0
6,761
18
6,955
2,013
2,273
-260
0
4,748
92
5,755
2,775
2,270
505
0
1,973
121
3,361
1,963
2,275
-312
22,500
22,510
98
23,492
2,200
2,272
-72
0
20,310
100
21,410
2,900
2,271
629
0
17,410
132
18,860
2,400
2,277
123
0
15,010
126
16,210
2,625
542
2,083
0
18,262
119
19,575
100
959
-859
0
18,162
5
18,212
0
787
-787
0
18,162
0
18,162
1,163
629
534
0
16,999
55
17,581
2,150
736
1,414
0
14,849
98
15,924
513
1,019
-506
0
14,336
22
14,593
963
918
45
0
13,373
48
13,855
2,138
927
1,211
0
11,235
97
12,304
1,863
1,169
694
0
9,372
85
10,304
1,075
1,308
-233
0
8,297
57
8,834
22,120
0.01
9,555
3,629
15,739
0.01
1,218
429
1,757
0.50
4,756
72
6,254
0.10
8,071
1,930
10,450
0.50
7,933
323
10,054
0.20
13,119
3,407
15,279
0.01
4,505
-1,351
5,009
0.01
1,611
-192
1,896
0.01
870
223
1,206
0.20
833
343
988
18,351
2,383
13,854
6,278
12,236
11,905
18,637
15,463
26,411
24,282
25,524
5,483
16,988
2,662
14,351
29,990
27,309
2,681
45,000
12,604
2,398
13,853
14,203
10,083
4,120
22,500
15,410
1,414
16,002
108
5 Applying Risk Pooling at Papierco
1
6
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
A
Warehouse Location
Mannheim
Actual sales
Forecast
Forecast error
Order quantity
Net stock
Sales rate
Average cycle stock
Nuremberg
Actual sales
Forecast
Forecast error
Order quantity
Net stock
Sales rate
Average cycle stock
Ottendorf-Okrilla (Dresden)
Actual sales
Forecast
Forecast error
Order quantity
Net stock
Sales rate
Average cycle stock
Queis (Halle)
Actual sales
Forecast
Forecast error
Order quantity
Net stock
Sales rate
Average cycle stock
Reinbek (Hamburg)
Actual sales
Forecast
Forecast error
Order quantity
Net stock
Sales rate
Average cycle stock
Sasbach (Strasbourg)
Actual sales
Forecast
Forecast error
Order quantity
Net stock
Sales rate
Average cycle stock
Tettnang (Lake Constance)
Actual sales
Forecast
Forecast error
Order quantity
Net stock
Sales rate
Average cycle stock
Trierweiler (Trier)
Actual sales
Forecast
Forecast error
Order quantity
Net stock
Sales rate
Average cycle stock
Total demand
Aggregate forecast
Forecast error
Pooled order quantity
Non-pooled order quantity
Net stock
Sales rate
Average CS central ordering
Average CS decentral ordering
B
Jan
C
Feb
D
Mar
E
Apr
F
May
G
Jun
H
Jul
I
Aug
J
Sep
K
Oct
L
Nov
M
Dec
Negative net stock
Pooled system
Non-pooled system
654,175 kg
845,636 kg
N
O
Total/Average Sm. Const.
14,475
16,620
-2,145
22,500
8,025
658
15,263
8,225
16,598
-8,373
22,500
22,300
411
26,413
21,500
16,514
4,986
0
800
977
11,550
23,625
16,564
7,061
22,500
-325
1,243
11,504
18,025
16,635
1,390
22,500
4,150
901
13,163
18,463
16,649
1,814
22,500
8,187
879
17,419
17,050
16,667
383
22,500
13,637
775
22,162
22,575
16,671
5,904
22,500
13,562
982
24,850
12,025
16,730
-4,705
22,500
24,037
601
30,050
16,913
16,683
230
0
7,124
769
15,581
23,900
16,685
7,215
22,500
5,724
1,086
17,674
11,188
16,757
-5,569
22,500
17,036
589
22,630
207,964
199,773
8,191
225,000
10,382
2,540
10,388
-7,848
22,500
19,960
115
21,230
4,488
9,603
-5,115
0
15,472
224
17,716
8,425
9,092
-667
0
7,047
383
11,260
9,135
9,025
110
22,500
20,412
481
24,980
9,488
9,036
452
0
10,924
474
15,668
8,668
9,081
-413
0
2,256
413
6,590
10,638
9,040
1,598
22,500
14,118
484
19,437
6,400
9,200
-2,800
0
7,718
278
10,918
10,188
8,920
1,268
22,500
20,030
509
25,124
7,843
9,047
-1,204
0
12,187
357
16,109
11,113
8,926
2,187
0
1,074
505
6,631
7,675
9,145
-1,470
22,500
15,899
404
19,737
96,601
110,503
-13,902
112,500
12,258
1,613
810
803
22,500
20,887
73
21,694
200
818
-618
0
20,687
10
20,787
650
812
-162
0
20,037
30
20,362
1,188
810
378
0
18,849
63
19,443
625
814
-189
0
18,224
31
18,537
500
812
-312
0
17,724
24
17,974
1,200
809
391
0
16,524
55
17,124
63
813
-750
0
16,461
3
16,493
1,188
805
383
0
15,273
59
15,867
2,463
809
1,654
0
12,810
112
14,042
963
826
137
0
11,847
44
12,329
500
827
-327
0
11,347
26
11,597
11,153
9,765
1,388
22,500
16,723
34,400
28,771
5,629
29,000
-5,400
1,564
12,331
33,738
29,334
4,404
35,000
-4,138
1,687
13,081
34,800
29,774
5,026
34,000
-4,938
1,582
12,908
40,538
30,277
10,261
35,500
-9,976
2,134
11,720
24,025
31,303
-7,278
41,500
7,499
1,201
19,512
28,750
30,575
-1,825
23,500
2,249
1,369
16,624
30,938
30,393
545
28,500
-189
1,406
15,288
36,663
30,447
6,216
31,000
-5,852
1,594
13,056
25,863
31,069
-5,206
37,000
5,285
1,293
18,217
29,650
30,548
-898
25,500
1,135
1,348
15,960
39,575
30,458
9,117
29,500
-8,940
1,799
12,009
23,238
31,370
-8,132
40,500
8,322
1,223
19,941
382,178
364,321
17,857
390,500
2,041
60,375
43,764
16,611
44,000
-16,375
2,744
16,294
50,345
48,748
1,597
65,500
-1,220
2,517
24,011
55,478
49,227
6,251
50,500
-6,198
2,522
22,021
48,475
51,102
-2,627
57,500
2,827
2,551
27,065
64,020
50,314
13,706
47,500
-13,693
3,201
20,053
62,413
54,426
7,987
68,500
-7,606
2,972
24,232
70,720
56,822
13,898
64,500
-13,826
3,215
23,142
81,763
60,991
20,772
75,000
-20,589
3,555
23,218
41,658
67,223
-25,565
88,000
25,753
2,083
46,582
61,405
59,553
1,852
34,000
-1,652
2,791
29,122
62,938
60,109
2,829
62,000
-2,590
2,861
28,992
42,615
60,958
-18,343
64,000
18,795
2,243
40,103
702,205
663,237
38,968
721,000
3,948
16,790
15,090
1,700
22,500
5,710
763
14,105
16,953
16,790
163
22,500
11,257
848
10,734
18,805
16,953
1,852
22,500
14,952
855
24,355
18,165
18,805
-640
22,500
19,287
956
28,370
14,225
18,165
-3,940
0
5,062
711
12,175
15,950
14,225
1,725
22,500
11,612
760
19,587
15,005
15,950
-945
22,500
19,107
682
26,610
12,015
15,005
-2,990
0
7,092
522
13,100
7,950
12,015
-4,065
22,500
21,642
398
25,617
10,223
7,950
2,273
0
11,419
465
16,531
13,553
10,223
3,330
0
-2,134
616
4,643
12,723
13,553
-830
22,500
7,643
670
14,005
172,357
174,724
-2,367
180,000
11,232
5,238
3,306
1,932
22,500
17,262
238
19,881
4,900
3,692
1,208
0
12,362
245
14,812
6,425
3,934
2,491
0
5,937
292
9,150
2,238
4,432
-2,194
0
3,699
118
4,818
3,513
3,993
-480
22,500
22,686
176
24,443
4,968
3,897
1,071
0
17,718
237
20,202
4,235
4,111
124
0
13,483
193
15,601
4,313
4,136
177
0
9,170
188
11,327
4,300
4,171
129
0
4,870
215
7,020
4,988
4,197
791
0
-118
227
2,381
3,200
4,355
-1,155
22,500
19,182
145
20,782
3,163
4,124
-961
0
16,019
166
17,601
51,481
48,349
3,132
67,500
11,866
19,150
21,553
-2,403
22,500
3,350
870
12,925
654,097
571,613
82,484
572,000
721,000
-82,097
29,732
251,782
411,112
19,728
21,529
-1,801
22,500
6,122
986
15,986
603,842
588,110
15,732
670,500
668,000
-15,439
30,192
287,217
430,134
41,668
21,511
20,157
22,500
-13,046
1,894
10,029
873,626
591,256
282,370
607,000
599,000
-282,065
39,710
204,515
352,512
19,038
21,713
-2,675
35,000
2,916
1,002
12,435
567,172
647,730
-80,558
930,000
892,000
80,763
29,851
364,349
466,755
21,400
21,686
-286
22,500
4,016
1,070
14,716
594,904
631,619
-36,715
551,000
542,500
36,859
29,745
334,311
428,452
22,665
21,683
982
22,500
3,851
1,079
15,184
614,565
624,276
-9,711
587,500
636,000
9,794
29,265
317,077
463,209
27,153
21,693
5,460
22,500
-802
1,234
12,809
619,799
622,334
-2,535
613,000
614,500
2,995
28,173
312,895
458,833
27,925
21,748
6,177
23,000
-5,727
1,214
8,923
823,406
621,827
201,579
619,000
599,500
-201,411
35,800
238,270
369,495
8,113
21,809
-13,696
28,000
14,160
406
18,217
505,144
662,143
-156,999
864,000
872,000
157,445
25,257
410,017
541,441
30,838
21,672
9,166
22,500
5,822
1,402
21,241
682,237
630,743
51,494
473,500
449,500
-51,292
31,011
292,938
401,898
18,025
21,764
-3,739
22,500
10,297
819
19,310
663,079
641,042
22,037
692,500
718,500
-21,871
30,140
310,619
446,266
23,425
21,727
1,698
22,500
9,372
1,233
21,085
441,638
645,449
-203,811
667,500
661,500
203,991
23,244
424,810
551,405
P
MAD
Q
BIAS
R
S
RMSE Safety Stock
7,061
0.01
4,148
683
4,957
0.10
2,094
-1,158
3,014
0.01
509
116
649
0.10
5,378
1,488
6,151
0.30
11,003
3,247
13,547
1.00
2,038
-197
2,390
0.20
1,059
261
1,308
0.01
5,687
1,587
8,062
19,022
1,598
16,283
803
17,187
9,117
15,054
16,611
27,070
2,273
17,486
1,932
14,002
279,128
260,088
19,040
288,500
4,992
15,238
7,643,509
7,478,140
165,369
7,847,500
7,974,000
40,987
9,166
SUM(S7:S184) =
245,561
201,579
0.2
95,502 13,781 130,602
43,982
312,400
443,459
Table 5.2: Effects of Centralized Ordering at Papierco
The order quantity for every month is the demand forecast for that month minus the
net stock (at the end of the period after demand has been satisfied but before the order arrives at the beginning of the new period) left from the previous period plus the quantity to
meet the minimum order and saltus quantity. Supplier lead time is neglected785. If net cycle
stock is negative (the actual sales exceeded the order quantity and the cycle stock on hand),
this demand is either satisfied via transshipments, covered by safety stock786, or backor785
786
Actually a location might run out of stock before the end of the period and have to wait until the beginning of the next period to place and receive a new order. This time might be seen as a replenishment order
lead time.
Safety stock is neglected here at first. However, safety stock may also be “defined as the average level of
the net stock just before a replenishment arrives” (Silver et al. 1998: 234, cf. Chopra and Meindl 2007:
305). Here we adhere to the definition “Safety inventory is inventory carried to satisfy demand that exceeds the amount forecasted for a given period” (Chopra and Meindl 2007: 304).
109
5 Applying Risk Pooling at Papierco
dered. In any case this quantity has to be ordered in addition for the next period to replenish the stock of the location that has transshipped this item or the safety stock or satisfy
the backordered demand. It is assumed that there are no available inventories or backorders
of the copy paper at the beginning of the year 2007. The net stock of the respective period
is the order quantity minus the actual sales plus the previous period's net stock. If the forecast of next period's sales can be met with net stock no order is placed with the supplier
(the order quantity is zero). This occurs at the locations Bremen, Dortmund, Ernstroda,
Leizen, Lohfelden, Lunteren, Mannheim, Nuremberg, Ottendorf, Sasbach, and Tettnang,
where the monthly forecasts and actual sales are lower than the minimum order quantity
(except in Bremen in August and November and Ernstroda in September).
For central ordering (total demand) the monthly actual sales are the sum of the individual locations' monthly sales (row 191). The total 2007 order quantity of this copy paper
with central ordering for all locations (pooled order quantity) 7,847,500 kg (cell N194) is
lower than the sum of the total order quantities of the individual locations ordering separately (non-pooled order quantity) 7,974,000 kg (cell N195). The centralized ordering
effect (equation (5.5)) amounts to 1.59 %. With central ordering Papierco could have saved
ordering 126,500 kg, 117,645 € (= 126,500 kg × 0.93 €/kg) purchasing costs, as well as
average cycle inventory and the associated inventory carrying cost just for this one product
by improved exhausting of the minimum order and saltus quantity.
For some months the non-pooled order quantity is lower than the pooled one. This is
evoked by some locations not placing an order in some months and serving demand from a
minimum order quantity and net stock, as the forecasts and actual sales are much lower
than the minimum order quantity. However, in these cases higher inventory carrying costs
have to be borne, as the ordered minimum order quantity minus sales remains in stock for
several periods. Negative net stock also postpones order quantities to later periods. Besides, a higher order quantity than the forecast to meet minimum order and saltus quantities
works as a buffer for positive forecast errors (if the actual demand exceeds the forecast):
The absolute value of the negative net stock is always less than the forecast error in these
cases. Nevertheless, on the whole a lower total order quantity is needed to serve the same
total annual demand with central than with decentral ordering.
We approximated the average cycle stock per warehouse location as follows: We calculated
the sales rate (actual sales divided by work days). Sales can only occur on work days. We determined the work days per month for the year 2007 (row 5). In case the work days in the different German federal states differed, we took the maximum. We then determined the inventory
110
5 Applying Risk Pooling at Papierco
level at the end of each working day after sales, deducting the sales rate from the previous end
of day inventory. Whenever the end of day inventory was negative we replaced it with zero
physical inventory. The inventory level at the beginning of the month is the order quantity plus
the previous month's end inventory level. We thus assumed that backordered demand (negative
end of month net stock) is satisfied instantaneously at the beginning of the new month when
the order quantity arrives. Finally we determined the arithmetic mean of the end of work
day inventory levels as the average cycle inventory. This also confirms that today average
inventory at Papierco is so high relative to actual sales partly due to minimum order and
saltus quantities.
The total average cycle stock with central ordering (row 198) is lower than with decentral ordering (row 199) in every month and for the whole year 2007, because of improved
exhausting of minimum order and saltus quantities. For this copy paper Papierco could
have saved 131,059 kg of average cycle stock and the corresponding inventory carrying
costs of 30,471 € (= 131,059 kg × 0.93 €/kg × 0.25) in 2007.
The sum of the average monthly positive net stock of the individual locations
(184,234 kg) in column N is larger than the average monthly positive net stock with central
ordering in cell N196 (40,987 kg).
The sum of the forecast error statistics mean absolute deviation (MAD 142,459), bias
(BIAS 29,560), and root mean square error (RMSE 190,306) for the individual locations in
columns P, Q, and R is higher than the error statistics for the central order (95,502, 13,781,
and 130,602 respectively) in cells P, Q, and R192.787
This confirms788 that the aggregate forecast of monthly sales of this copy paper for all
23 considered locations is more accurate than the disaggregate forecast for the individual
locations. This leads to a higher inventory availability, i. e. a smaller total stockout or
backorder quantity (negative net stock) and thus smaller stockout or backorder costs in the
system with central ordering (654,175 kg) than in the system with decentral ordering
(845,636 kg), if safety stock is neglected.
According to the One-Sample Kolmogorov-Smirnov Test, the H0-hypothesis that the
forecast error at the locations Aalen, Berlin, Bielefeld, Bremen, Cologne, Dietzenbach,
Dortmund, Ernstroda, Fellbach, Garching, Hemmingen, Kiel, Leizen, Lohfelden, Lunteren,
Mannheim, Nuremberg, Ottendorf, Queis, Reinbek, Sasbach, Tettnang, and Trierweiler
787
788
“MAD is […] the average of the absolute differences between the actual […] and the forecast” sales.
“BIAS is the average of the differences between actual and forecast” sales. “RMSE is [the] square root of
the average of the squared differences between the actual and the forecast” sales (Ballou 2004c: 5f.).
Cf. footnote 456.
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5 Applying Risk Pooling at Papierco
and of total demand is normally distributed cannot be rejected with an asymptotic significance (two-tailed) p of 0.984, 0.317, 0.879, 0.872, 0.485, 0.268, 0.582, 0.996, 0.513, 0.974,
0.970, 0.922, 0.973, 0.695, 0.966, 0.984, 0.681, 0.864, 0.832, 0.711, 0.758, 0.991, 0.851,
and 0.968 respectively. The One-Sample Kolmogorov-Smirnov Test for the exponential
distribution shows a higher asymptotic significance (two-tailed) for Cologne (p = 0.820),
Dortmund (p = 0.936), Fellbach (p = 0.824), Leizen (p = 0.993), Lohfelden (p = 0.911),
Nuremberg (p = 0.839), Reinbek (p = 0.830), Trierweiler (p = 0.977), and total demand
(p = 0.993). However, for Fellbach and Reinbek there are 3, for Cologne, Dortmund, Lohfelden, Trierweiler, and total demand 6, for Leizen and Nuremberg 7 values outside the
specified distribution range. These values are skipped. Kiel shows a higher asymptotic significance (two-tailed) of 0.958 in the One-Sample Kolmogorov-Smirnov Test for the uniform distribution. As Poisson variables are non-negative integers and negative values occur
in the data, the One-Sample Kolmogorov-Smirnov Test cannot be performed for the Poisson distribution. In conclusion, the forecast error can be assumed to be rather normally
distributed at the different locations. According to Thonemann (2005: 258) most applications assumed a normally-distributed forecast error.
Nevertheless, we use the empirical distribution function of the forecast error to determine the safety stock. The empirical distribution function F(y) gives the probability that
the forecast error is less than or equal to y, i. e. F(y) = P (forecast error Y ≤ y). In order to
have an inventory availability of 91.7 %, we determine the y for P = 91.7 %. If we carry y
as safety stock, this will cover demand that exceeds the forecast with a probability of
91.7 %, as the forecast error is less than or equal to this safety stock with the probability of
91.7 %. The safety stock that ensures a service level of 91.7 % is shown in column S for
every location. The sum of the individual locations' safety stocks (245,561 kg) in cell S188
is larger than the safety stock with central forecasting and ordering for all locations
(201,579 kg) in cell S191, as the aggregate forecast is more accurate than the disaggregate
one. Papierco could have saved 43,982 kg of safety stock and the associated inventory
holding cost of 10,226 € (= 43,982 kg × 0.93 €/kg × 0.25) just for this copy paper in 2007.
Although Papierco forecasts demand and therefore should use safety stock as protection
against the forecast error and not demand uncertainty789, it uses the average past demand
for the copy paper to determine safety stock.
789
Cf. Thonemann (2005: 255f.).
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5 Applying Risk Pooling at Papierco
With decentralized ordering there would have been 123,215 kg negative net stock that
could not have been absorbed by the safety stock for all locations in 2007. We arrived at
this figure by adding the negative net (cycle) stock and safety stock for every location for
every month, whenever the absolute value of the former was greater than the one of the
latter, and then adding up all the negative sums. With centralized ordering 80,486 kg of
demand would have exceeded available inventory (cycle stock and safety stock). In the
decentralized system the 123,215 kg of demand could have been satisfied by transshipments from other warehouses, backordered, or lost. In the centralized system, transshipments would not have been possible, as demand would have exceeded the order quantity
and safety stock for all locations, and demand could have been only backordered or lost.
Therefore one could argue that in this regard the service level in the decentralized system
would have been higher. Transshipping 123,215 kg of this copy paper in the decentralized
system would have cost at least 8,561 € = 123.215 t × 69.48 €/t (cf. section 5.3.2.3). Losing
the contribution margin of selling the 80,486 kg of this copy paper would have cost
80,486 kg × 0.23 €/kg = 18,512 € in the centralized system. Thus the net stockout costs
(lost contribution margin in the centralized system minus the transshipment cost in the decentralized one) amount to 9,951 € = 18,512 € - 8,561 € at the most. If all the unsatisfied
demand had been backordered in both systems, backorder costs would have been higher in
the decentralized than in the centralized system because of the backordered volume.
Overall, Papierco could have saved at least 30,746 € in inventory holding costs just
for this one copy paper in 2007, if it had used centralized planning and ordering instead of
the current decentralized one: 30,746 € = 30,471 (saved inventory holding costs for average cycle stock) + 10,226 € (saved inventory holding costs for safety stock) - 9,951 € (net
stockout costs).
This example highlights that centralized ordering enables to reduce order quantities and
thus average cycle inventory and inventory carrying costs by exhausting minimum order
and saltus quantities better as well as to reduce safety stock and improve overall customer
service level (inventory availability) or reduce negative net stock as the aggregate forecast
is more accurate than the disaggregate one.
Therefore, we propose a central distribution requirements planning with aggregate
forecasting and central ordering for all Papierco locations. After placing a joint order, central planning would receive a notification of dispatch from the producer when the ordered
products are produced and the trucks are ready to deliver them. Then Papierco tells the
supplier which warehouses to deliver to according to current demand. Full truck loads can
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5 Applying Risk Pooling at Papierco
be delivered to single warehouses or one truck can deliver to several warehouses on a delivery route. The delivery destination decision is postponed until the ordered products are
produced and ready to be delivered from the production facility to the delivery warehouses
(geographic or logistics postponement).
Today each warehouse location forecasts its warehouse sales and places orders with the
suppliers individually. The warehouse receives a dispatch notification from the supplier
before the delivery truck leaves the production facility to deliver the ordered products to
the warehouse. The delivery destination is determined at the time of placing the order.
With today's decentralized release orders within the centrally negotiated framework
contracts every Papierco location orders all products for itself.
With centralized ordering each location or company of the eight ones comprising Papierco could process the orders for one part of the product line, e. g. a main product group,
for all considered 23 locations. This would lead to the following advantages:

Fewer orders at the suppliers (1/23 of today's decentralized orders), lower order
costs, improved utilization of minimum order and saltus quantities, lower average
inventory, higher turnover, lower capital commitment, lower inventory holding
costs.

Only one procurement manager per product line part or product, higher specialist
knowledge about this part of the assortment, improved forecasting, improved
matching of supply and demand, improved potential utilization (negotiation power),
closer collaboration with suppliers, long-term planning with suppliers, cost degression potentials for Papierco and its suppliers, reduced lead times.

Directing supplier deliveries to certain warehouse locations at short notice (higher
flexibility, product availability, and customer service level, reduced transshipments
and inventories).
This approach would maintain the importance of the legally independent companies
forming Papierco and their decentral locations. The employees of the purchasing departments do not have to relocate to a physically central ordering department, but can remain at
their locations. They may become more motivated by their increased responsibility, as they
do not place replenishment orders for their own location only anymore, but for all Papierco
locations albeit just for a certain part of the product line. Thus possible disadvantages of
centralized ordering such as decreased responsiveness and sales due to lacking local know-
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5 Applying Risk Pooling at Papierco
ledge790 can be mitigated as well. Procurement employees may have more time for improved forecasting and collaboration with suppliers and other departments or their number
may be reduced.
The number of the suppliers' trips to the warehouses would probably remain unchanged.
Perhaps the supplier would charge a fee for delivery routes, if a truck load is to be transported to more than one Papierco location. This charge is unlikely to outweigh all the other
stated benefits. The products, however, have to be managed more intensively by procurement managers. Operations and rules in all locations have to be standardized. Necessary
data have to be available and correct.
Orders would still be placed according to order suggestions generated by DRP consistent with customer orders, demand forecasts, inventory levels, and supplier lead time. Of
course the ERP software has to be adapted to plan across all Papierco locations.
The paper industry shows long production lead times, expensive holding costs for inventory surplus, and highly random demand at the retailers. Orders can be backlogged only
for a few days at the most in case of a stockout or the sale is lost. These conditions favor
centralized ordering according to Eppen and Schrage (1981: 51) and Schoenmeyr (2005:
5). Total demand is less variable than demand at the individual stores, which makes consolidated distribution most effective according to Cachon and Terwiesch (2009: 340). The
time from placing an order with the supplier until production of the order is finished is
longer than the delivery time from the production facility to the delivery warehouses. This
corresponds to Cachon and Terwiesch's (2009: 340) observation that consolidated distribution “is most effective […] if the lead time before the distribution center is much longer
than the lead time after the distribution center”. Replenishment coordination is most beneficial for high fixed order/transportation cost, large truck capacities, and many retailers.791
The minimum order and saltus quantity restrictions Papierco has to observe can be subsumed under large fixed order or transportation cost and truck capacities, and Papierco has
many delivery warehouses in Germany.
In contrast to Eppen and Schrage (1981), Gürbüz et al. (2007: 305), and Cachon and Terwiesch (2009) our considerations do not contain a distribution center (here we follow
Schonmeyr's (2005: 4) proposition), Papierco uses a stock-to-demand order policy with minimum order and saltus quantities and transshipments between regional warehouses, weekly
demand often does not follow a theoretical distribution (cf. section 5.3.3.1), demand at the
790
791
Ganeshan et al. (2007: 341).
Gürbüz et al. (2007: 305).
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5 Applying Risk Pooling at Papierco
different warehouses is correlated, and supplier lead time is largely neglected. Our centralized ordering model does not increase the distance a unit must travel from the supplier to the
delivery warehouses, unless it is delivered on a delivery route with several stops.
Eppen and Schrage (1981) consider centralized ordering policies in a periodic-review
base-stock multi-echelon, multi-period system in the conglomerate for steel industry with
independent normally distributed stationary random demands and identical proportional
costs of holding and backordering at N warehouses, and no transshipments between the
warehouses. In Eppen and Schrage (1981) products are ordered and quantity discounts are
possible. Papierco just calls quantities of products from the supplier within the bounds of
previously centrally negotiated skeleton agreements. Possible quantity discounts have been
granted before.
Diruf (2005, 2007) and Heil (2006: 169) examine only the demand-pooling savings of
postponement, centralized ordering, and lateral transshipments between cooperating possibly independent fashion retailers with normal and lognormal792 demand, equally big sales
areas793, and a newsboy structure. In their model the central ordering system leads to lower
costs than the local ordering system with transshipments unless over- and underage costs
are equal. In this case both systems achieve the same improvements compared to a system
without risk pooling.794
Hu et al. (2005) deal with the impact of emergency transshipments on (s, S) (order-upto) ordering policies and centralized ordering.
Gürbüz et al. (2007: 296, 305) consider only one outside supplier, but inventory and
transportation costs and four order-up-to policies.
Cachon and Terwiesch (2009) consider consolidated distribution in retail with 100
stores, an order-up-to-model, Poisson demand at the retail stores per week795, normallydistributed demand at the retail distribution center796, lead times, and backordering797.
One could still determine an optimal delivery allocation procedure and order policy for
Papierco, but this would go beyond the scope of this thesis. The reader is referred to e. g.
Silver et al. (1998) for a detailed treatment of inventory control policies.
792
793
794
795
796
797
Heil (2006: 145f.).
Heil (2006: 169).
Diruf (2005: 59f.), Heil (2006: 110).
Cachon and Terwiesch (2009: 336).
Cachon and Terwiesch (2009: 338).
Cachon and Terwiesch (2009: 336f.).
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5 Applying Risk Pooling at Papierco
Alfaro and Corbett (2006: 24) find that within certain quite wide ranges of suboptimality of inventory control policies, risk pooling is better than optimizing the policy. This
range expands with the number of SKUs. Papierco carries thousands of SKUs.
Harrison and Skipworth (2008: 193) also find that form postponement in three companies
improved responsiveness of manufacturing, although it had not been implemented theoretically ideally.
Finally, risk pooling reduces decision errors, biases, and local suboptimization of boundedly rational decision makers and thus total costs “by pooling decision errors across locations”, even if demands are perfectly positively correlated or deterministic (behavioral
benefits of inventory pooling)798.
Therefore, introducing risk pooling methods at Papierco at first, does not hurt.
5.3.4
Product Pooling
For the last years more and more products have been added to Papierco's product line without
dropping any other ones. The product range meanwhile comprises around 20,000 current
products, some with few sales, and is planned to be diversified further especially in the business units printing accessories and screens and signs. This diversification leads to higher inventories, as every warehouse has to store at least some units of every product in order to be
able to deliver every product specification, or more transshipments. Product availability decreases as forecasts for more and more individual items are less accurate.
“Every firm wishes to be ʻcustomer focusedʼ or ʻcustomer oriented,ʼ which suggests
that a firm should develop products to meet all of the needs of its potential customers. Truly innovative new products that add to a firm's customer base should be incorporated into a
firm's product assortment. But if extra product variety merely divides a fixed customer
base into smaller pieces, then the demand–supply mismatch cost for each product will increase. Given that some of the demand–supply mismatch costs are indirect (e.g., loss of
goodwill due to poor service), a firm might not even realize the additional costs it bears
due to product proliferation”799.
Already in 1987 Röttgen remarked due to the cut-throat competition fine paper wholesalers are forced to distinguish themselves from their competitors. This is possible by intensifying some selected distribution functions rather than accepting additional ones. Thus
paper wholesalers seek to diversify their product line more and more to exhaust the cus798
799
Su (2008: 33).
Cachon and Terwiesch (2009: 335f.).
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5 Applying Risk Pooling at Papierco
tomer potential as much as possible.800 Fine paper wholesale has to abandon the idea to be
a specialist for all paper grades. This implies prioritizing within the product range instead
of a sprawling product line diversification. An escalating diversification will lead to disproportionately high costs and continue to keep the return low.801
According to the FPT-Workshop No. 4 in Munich on October 24, 2007 the variety of
paper grades is narrower in the U.S. and is not demanded by customers (printing offices) in
Germany either. The majority of printing offices deny the necessity of the present variety
of grades. For them operativeness, color consumption, quality consistency, and mixability
of paper grades are decisive and not a new brand or grade.802
A FPT study supports this: A change in demand behavior for paper grades seems to gain
momentum away from the unclear vast variety of grades towards a homogenization. The
printing industry foremost demands good operability and printability of the paper in the
printing machine. Paper grades with standard functionality (reproducible operability and
printability) and multifunctionality are the focus of the forthcoming development.803
Furthermore a too large product variety might backfire, as customers might not like to
choose from many alternatives.804 Toyota's and Nissan's fast introduction of a series of
products, for instance, was counterproductive as it confused customers.805
For all these reasons Papierco should rationalize its product line by product pooling
taking into account its business strategy, demand and buying interdependencies between
products, customer needs, and cooperation with suppliers806 also in order to simplify its
procurement planning. Serving “demand with fewer products” reduces “demand variability, which leads to better performance in terms of matching supply and demand (e.g., higher
profit or lower inventory for a targeted service level)”807.
5.3.5
Inventory Pooling
Nowadays there are bilateral agreements between some Papierco member companies to store
slow-moving items for one another. However, there is no transparency, which articles are
stored at which location, and the partly sought selective stock keeping is not pursued strategically and economically.
800
801
802
803
804
805
806
807
Röttgen (1987: 83).
Röttgen (1987: 124).
FPT (2007b).
FPT (2007a).
Chain Drug Review (2009a), Hamstra (2009), Ryan (2009).
Pine II et al. (1993), Lau (1995).
Kulpa (2001), Hamstra (2009), MMR (2009), Pinto (2009a, 2009b), Thayer (2009: 23).
Cachon and Terwiesch (2009: 330, 335).
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5 Applying Risk Pooling at Papierco
If a new product is launched, it is stored at only three locations first. If it has been selling well for half a year, further locations start inventorying it and it may be stocked at
every Papierco location in the end.
Papierco's uniform price list suggests immediate availability of all paper grades at every
warehouse location. Due to the increasing range of products, however, availability of every
product at every location cannot be assured anymore. Some products are only available at
one warehouse in Germany. Thus demands for transshipments rise and the 24-hour delivery
service cannot be guaranteed anymore. Transshipment errors increase, especially if a product
is transshipped via other warehouses. Often truck capacity is exceeded. Papierco's competitive advantage of delivering any paper grade mostly within 24 hours is fading.
The product master record contains 61,132 different products. Thereof merely 23,740
ones show stock on hand at at least one warehouse. Of these only 9,868, of the 61,132 only
14,565 ones, are planned automatically with DRP. The product master record should be rid
of inactive products with no sales.
Product purchase planning and storing is distributed unequally between the eight Papierco member companies as figures 5.8 and 5.9 show. If it was distributed more evenly
at least for fast movers, product availability could be increased and transshipments decreased (cf. section 5.3.2.3).
Along the same line, Pasin et al. (2002) simulate pooling of equipment for homecare
service for a group of local community service centers (CLSCs) in the Montreal, Canada
region. Overall pooling reduces shortages (rental costs) with the same inventory level, but
the larger CLSCs with considerable equipment overcapacity may lose, because they almost
never need to borrow equipment from other CLSCs, but have to bear the disadvantages
(wear-and-tear costs). A more even distribution of over-capacity reached by inter-CLSC
sales or an equivalent financial compensation is much more effective than minimum stock,
maximum contribution or maximum debt rules in producing an overall reduction in costs
without penalizing any of the partners in the pooling process.
We would have liked to design an optimal policy of strategic stock-keeping (inventory
pooling through selective stock keeping). However, the necessary data such as the turnover
or (average) inventory per SKU were not available.
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5 Applying Risk Pooling at Papierco
7000
6057
6000
4879
5000
Number of Products
4624
4261
4197
3936
3872
4000
3124
3003
3000
2651
2000
1668
959
926
1000
939
703
296
0
100
200
300
400
500
600
700
800
Papierco Member Company (Code)
Number of products planned with DRP (planning code = 1)
Number of products not planned with DRP (planning code = 0), but with stock on hand
Figure 5.8a: Product Purchase Planning at Papierco's Member Companies
8000
7537
7000
Number of Planned Identical Products
6000
5000
4000
3000
2229
2000
1487
992
1000
735
639
656
288
0
1
2
3
4
5
6
7
8
Number of Papierco Member Companies
Figure 5.8b: Product Purchase Planning at Papierco's Member Companies
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5 Applying Risk Pooling at Papierco
11083
12145
14000
12000
8596
5029
5960
6208
5021
4853
5077
4831
4835
4835
5407
0
0
0
0
50
0
0
295
848
443
11
1
1131
2367
3424
4033
1357
1983
4025
4029
3915
3223
1687
492
782
96
322
418
840
2000
7303
7309
6555
6144
6152
4464
4459
4970
3036
3791
3274
2972
2972
4000
4974
6000
5339
4970
6447
8000
2982
3567
Number of SKUs
Inventory (t)
8446
8664
10000
0
101
102
103
201
202
203
301
302
401
402
501
502
503
601
602
603
701
702
703
704
801
Warehouse
Number of routinely stocked SKUs (product code P = purchase including raw materials)
Number of SKUs with stock on hand
Inventory (t)
Figure 5.9: Stockkeeping at Papierco's Warehouses in February 2008
5.3.6 Challenges in IT and Organization
Today too little process-oriented information exchange between departments inhibits business
processes. Data are not transparent enough. If they are recorded at all, often they can only be
obtained from the diverse, little integrated electronic data processing (EDP) systems with great
effort. Too many subsystems and interfaces result in data transfer problems, too much data
maintenance, and high costs. A lot of workarounds were programmed in the standard ERP
system for Papierco, as many locations wanted to keep some unique business processes. However, the standard ERP system should standardize the business processes or one does not derive the full benefit from the standard software.808 CLM (1995: 6) also concludes that “the vast
majority of available technology capable of facilitating process integration is underutilized”.
Papierco's different data analysis tools often show different numerical results for the
same data query specifications. Data are often not available on a disaggregate individual
product basis, but only for product groups. Analyses are hampered by different product
codes for the same product for drop-shipping and warehouse sales, different periods (days,
weeks, and months), units (sheets and kilograms), and product groupings and levels in dif808
Fleisch et al. (2004), Laudon and Laudon (2010: 369).
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ferent parts of the EDP system, too little knowledge about the analysis tools at Papierco's
locations, as well as a bad data structure and maintenance. The delivery situation is not
transparent enough: There are customer and delivery addresses. The delivery addresses are
not assigned to customers uniquely. Sales can only be attributed to customer and not to
delivery addresses. Some data are not recorded at all, such as cycle, safety, and average
stock, as well as turnover per product, utilization of safety stock, cycle time, actual supplier
lead times, and actual transshipment costs. Some computerized reports give wrong (calculated, not actual) safety stock levels for product groups, so that often the shown safety
stock is higher than the actual total inventory on hand. Certain costs can only be obtained
by checking every single cost unit. Higher cost awareness might lead to higher return. Setting up a systematic controlling might be worthwhile.
Data and information are passed on by employees only hesitantly and after direct request. Important extra information to get a complete idea often is omitted. This might be
interpreted as a defense strategy to secure the job and power position by exclusive knowledge. Any criticism can be invalidated by pointing out that certain information had not
been considered. Similar “micropolitical games” were observed e. g. by Reihlen (1997: 3)
in a heating technology company. Change in logistical practices often faces resistance.809
This can be remedied with a company culture that promotes transparency.
Papierco consists of eight different and legally independent companies, but is and
wants to be seen as a single uniform company. However, employees rather feel obliged to
their individual member companies that pay their salaries. This sometimes leads a member
company to transship products for its own warehouse locations first and leave the goods
bound for other member companies' locations behind. Products ought to be transshipped
according to urgency and not company affiliation. Papierco should not optimize locally but
globally.
Logistics is seen very restrictively within Papierco as storing, handling, and transporting goods. Taking on its interdepartmental function, logistics should collaborate closely
with and support management, sales, purchasing, finance, accounting, and controlling.
During this study differences in managing Papierco's different locations became obvious.
Papierco should standardize its operational policy, measure performance uniformly, and restructure its distribution system cautiously. For this a consistent and faultless data maintenance and accessibility is essential. Some data are deficient for logistical management.
809
CLM (1995: v, 6), Ballou et al. (2004b: 550), Graman and Magazine (2006: 1077).
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Most of these challenges are common in a lot of companies. Papierco is addressing
them successfully and is a profitable company.
5.4
Summary
The paper wholesale company Papierco can increase its competitiveness and reduce customer
demand and supplier lead time uncertainty by the risk pooling methods transshipments, product substitution, postponement, centralized ordering, product pooling, and inventory pooling.
The proposed optimization of the customer allocation to the individual warehouses can
lead to considerable transportation cost savings near-term and without much investment
burden. Customers should be served by the warehouse nearest to them.
The following suggestions can be made to reduce inventory and transshipments, which
have increased for the last years, and maintain or improve the customer service level and
profitability:
(1)
The organizational structure and logistics should support the business
processes as well as possible.
(2)
The company culture should promote transparency and a process view.
(3)
Improve the fragmented, little integrated, little standardized, not process- but
function-oriented system landscape. This would also lower the disproportionately high IT costs.
(4)
Necessary data should be collectable faultlessly.
(5)
The demand planning810 and purchasing policy should be improved, as this
will result in higher product availability (customer service level) and less
transshipments and inventory.
(6)
Create a uniform cross-functional demand planning process, in which sales,
product managers, and purchasing collaborate to contain extraordinary demands through the sales assistants' and product managers' profound market
knowledge and enable a better demand forecast and thus order policy.
(7)
Communicate and coordinate inventory reductions at the different member
companies and warehouses. If a company is member of a purchasing group, it
cannot act autonomously anymore.
810
Methods 11 (Exponential Smoothing), 6 (Least Squares Regression), and 9 (Weighted Moving Average)
should be admitted to the DRP forecast run besides today's exclusively used methods 4 (Moving Average) and 10 (Linear Smoothing), as they gave good results. The forecast should be based on the last 12 to
24 months of sales history, if system performance permits this.
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5 Applying Risk Pooling at Papierco
(8)
Establish (not necessarily physically) centralized procurement, which forecasts and orders for all of Papierco's German locations on the product level
and directs the suppliers' deliveries to the warehouses according to current
demand (consolidated distribution with pooling over the outside-supplier lead
time).
(9)
Foster a close, reliable, long-term collaboration and exchange of information
between suppliers, Papierco, customers, and individual departments.
(10)
Safety stock and transshipments can be reduced without hurting product availability by decreasing lead time (uncertainty) through improved collaboration
with suppliers and reducing demand uncertainty by better forecasts and information gathering and usage.
(11)
Determine safety stocks more definedly according to the target customer service level, forecast error, supplier lead time, and lead time variability.
(12)
Enable determining the correct inventory levels per product and utilization of
safety stock.
(13)
Rationalize the product line considering the business strategy, customer needs,
product interdependencies, and cooperation with suppliers (product pooling).
(14)
Establish transparency regarding the storage locations of products.
(15)
Pursue selective stock keeping (inventory pooling) strategically economically.
(16)
Use alternatives to transshipments (product substitution and form postponement).
(17)
Papierco's emergency transshipments are economically worthwhile on average.
(18)
However, they should only be used, if the contribution margin of a sale is at
least 69.48 €/t.
(19)
Establish transshipment cost rates that reflect the true costs.
(20)
Set up clear rules for the sales assistants for using transshipments.
(21)
Transshipment costs should be made transparent to the sales assistants and
perhaps be deducted from the premium-determining contribution margin.
We would have liked to always evaluate the cost savings attainable by these suggestions for
improvement in money units, but necessary cost data and information were not provided. A
consultancy described similar problems of obtaining data at Papierco.
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Human resource factors, transaction costs, and local suboptimization seem to be important in risk pooling and transshipments. These factors are commonly neglected in the risk
pooling literature.
This application shows that risk pooling can be used effectively as a guiding umbrella
principle in systematically restructuring a distribution system to cope with supplier lead
time, customer demand, and forecast uncertainty, as well as product variety and reduce
costs and inventory, increase customer service, and make a company more competitive.
Risk pooling methods can be used side by side to take advantage of their benefits, while
making up for disadvantages of other ones.
Our Risk Pooling Decision Support Tool is suitable to determine appropriate risk pooling methods for a company that faces lead time and demand uncertainty. Some of the methods determined with the help of this tool are already applied by Papierco nowadays
(transshipments, product substitution, inventory pooling, and postponement), but can and
should be improved. The other ones still make sense after a more thorough investigation
(centralized ordering and product pooling).
Centralized ordering can reduce average cycle inventory, even if a stock-to-demand order policy is followed and minimum order and saltus quantities have to be observed. It also
enables to decrease safety stock and improve inventory availability, as the aggregate forecast for the central order is more accurate than the disaggregate one for the decentral orders.
125
6
Conclusion
Our main novel contributions lie in the (1) comprehensive and concise definition of risk pooling distinguishing between variability, uncertainty, and risk, (2) holistic review and valuechain-oriented structuring of the plethora of research on risk pooling methods in business logistics, especially on inventory pooling, according to their uncertainty reduction abilities,
(3) developing tools to help in comparing and choosing appropriate risk pooling methods and
models for different economic conditions based on a contingency approach, (4) applying these
tools to German paper wholesale, and (5) conducting a survey on the recognition and usage of
the various risk pooling concepts and their associations in 102 German trading and manufacturing companies.
Risk pooling in business logistics can reduce total variability of demand and/or lead
time and thus uncertainty and the possibility of not achieving business objectives (risk) by
consolidating individual variabilities (measured with the standard deviation) of demand
and/or lead time. These individual variabilities are consolidated by aggregating demands
(demand pooling) and/or lead times (lead time pooling).
This reduction in uncertainty allows to reduce inventory without reducing the customer service level (product availability) or to increase the service level without increasing the
inventory or a combination of both and to cope with product variety. Risk pooling is explained by the Minkowski-inequality, the subadditivity property of the square root of nonnegative real numbers, and the balancing effect of higher-than-average and lower-thanaverage values of a random variable.
Risk pooling usually shows increasing returns, but diminishing marginal returns. Its
benefit generally increases with decreasing correlation of pooled demands and/or lead
times and concentration of uncertainty as well as increasing variability.
Risk pooling in business logistics comprises well over 600 publications mostly containing modeling research. After the concept borrowed from modern portfolio and insurance
theory has been mainly applied to inventory pooling, meanwhile research focuses on postponement, transshipments, and the coordination of risk pooling arrangements and cost and
profit allocation through contracts. The researchers are of different backgrounds, orientation, and prominence, so that they use inconsistent terms, frameworks, and structures and
make our thorough literature review, structuring, and definitions essential.
We identified ten risk pooling methods: (1) inventory pooling, (2) virtual pooling,
(3) transshipments, (4) centralized ordering, (5) order splitting, (6) component commonali126
6 Conclusion
ty, (7) postponement, (8) capacity pooling, (9) product pooling, and (10) product substitution.
These methods can be implemented everywhere along the supply chain and mainly pertain to the value activities storage (inventory pooling), transportation (virtual pooling and
transshipments), procurement (centralized ordering and order splitting), production of
goods and services (component commonality, postponement, and capacity pooling), and
sales (product pooling and product substitution). We presented a classification of risk
pooling methods according to their ability to pool demands and/or lead times.
They all but order splitting can reduce demand uncertainty, order splitting only lead
time uncertainty, capacity pooling, component commonality, inventory pooling, product
pooling, and product substitution only demand uncertainty. Transshipments, virtual pooling, postponement, and central ordering may dampen both uncertainties.
(1) Inventory pooling is the consolidation of inventories, e. g. by inventory or warehouse system centralization or selective stock keeping, in order to reduce inventory holding and shortage costs through risk pooling. Its risk pooling effect in terms of inventory
savings can be quantified with the square root law (SRL), portfolio effect (PE), and inventory turnover curve.
The SRL states that the total system wide stock of n decentralized warehouses is equal
to that of a single centralized one multiplied with the square root of the number of warehouses n. Despite confusion in the literature it applies to regular stock, if an economic
order quantity (EOQ) order policy is followed, the fixed cost per order and the per unit
stock holding cost, demand at every decentralized location, and total system demand is the
same both before and after centralization. It is valid for safety stock, if demands at the
decentralized locations are uncorrelated, the variability (standard deviation) of demand at
each decentralized location, the safety factor, and average lead time are the same at all locations both before and after consolidation, average total system demand remains the same
after consolidation, no transshipments occur, lead times and demands are independent and
identically distributed random variables and independent of each other, the lead time variance is zero, and the safety-factor approach is used to set safety stock for all facilities
both before and after consolidation. It applies to total stock (the sum of regular and safety
stock), if the assumptions stated above of the SRL both as applied to regular and safety
stock hold (cf. appendix B). It does not hold, if its assumptions are not fulfilled.
If an EOQ policy is followed and constant fixed costs per order, holding costs, and total
demand are assumed for all locations before and after centralization, the total order fixed
127
6 Conclusion
cost usually is lower because of less orders and the inventory holding cost is lower due to
a smaller total EOQ in the centralized than in the decentralized system (cf. appendix C).
Savings in safety stock through inventory pooling stem from balancing demand variabilities (risk pooling).
Although some researchers811 claim the SRL estimated real savings well, in 13 of 14
practical cases we reviewed it overestimated actual inventory savings often significantly.
This means its assumptions are not fulfilled in these cases or there were other inventory- or
service-related changes. In a survey that we conducted with eleven companies from different countries and industries (see table D.1) only one fulfilled all, two fulfilled none of the
five assumptions necessary for applying the SRL to regular stock. The participants fulfilled
at least two and at the most seven of the eleven assumptions of the SRL when applied to
safety stock.
It seems that seldom is it appropriate to apply the SRL, because mostly not all its assumptions are fulfilled. Nonetheless, the other SRL- and PE-models that we synoptically
compared in terms of their assumptions in table D.2 might be applied as their assumptions
are fulfilled.
Researchers questioning the SRL either question its assumptions or do make other assumptions and therefore arrive at different results.
Zinn et al.'s (1989) PE shows the reduction in aggregate safety stock by centralizing
several warehouses' inventories in one warehouse in percent, if lateral transshipments are
not usual, there is no lead time uncertainty, customer service level is not affected by a
change in the warehouse number, demand at each warehouse is normally distributed, and
the order quantity equals demand during lead time.
The inventory turnover curve shows average inventory in dependence of the inventory
throughput for a specific company. It can be constructed from a company's stock status
reports and be used to estimate the average inventory (not only safety stock as with the PE)
for any (planned) warehouse throughput without the limitations of the SRL.
(2) Virtual pooling extends a company's warehouse or warehouses beyond its or their
physical inventory to the inventory of other own or other companies' locations by means of
information and communication technologies, drop-shipping, and cross-filling.
(3) Transshipments are inventory transfers among locations (e. g. between warehouses
or stores) for example in case of a stockout.
811
For example Sussams (1986: 10), Pfohl (1994: 141).
128
6 Conclusion
(4) Centralized ordering places joint orders for several locations and later allocates the
orders (perhaps by a depot) to the requisitioners or distribution points in consolidated distribution according to current demand information.
(5) Order splitting is partitioning a replenishment order into multiple orders with multiple suppliers or into multiple deliveries.
(6) Component commonality designs products sharing parts or components. This reduces the variability of demand for these components.
(7) Postponement delays decisions in production, logistics, or distribution as long as
possible, e. g. developing, purchasing, ordering, fulfillment assignment, production, manufacturing, assembly, packaging, labeling, pricing, and shipping. Because of a shorter forecast period and an aggregate forecast more accurate information can be used.
(8) Capacity pooling is consolidating production, service, or inventory capacities of
several facilities. Without pooling every facility fulfills demand just with its own capacity.
With pooling demand is aggregated and fulfilled by a single (perhaps virtually) joint facility. A higher service level can be attained with the same capacity or the same service level
can be offered with less capacity.
(9) Product pooling is unifying several product designs to a single generic or universal
design or reducing the number of products thereby serving demands that were served by
their own product variant before with fewer products.
In (10) product substitution one tries to make customers buy another alternative product, because the original customer wish is out of stock or although it is available (demand
reshape).
Using contingency theory, we explored conditions that favor these individual risk
pooling methods, their advantages and disadvantages, and basic trade-offs in detail. Based
on this synopsis the Risk Pooling Decision Support Tool (RPDST) was developed for
choosing an appropriate risk pooling strategy for a specific situation.
This tool was effectively utilized to choose suitable risk pooling methods for a large
German paper distributor. This application showed that risk pooling can be used effectively as a guiding umbrella principle in systematically restructuring a distribution system
to cope with supplier lead time, customer demand, and forecast uncertainty, as well as
product variety and reduce costs and inventory, increase customer service, and make a
company more competitive. Human resource factors, transaction costs, and local suboptimization seem to be important in risk pooling and transshipments. These factors are commonly neglected in the risk pooling literature. Risk pooling methods can be and are used
129
6 Conclusion
side by side to take advantage of their benefits, while making up for disadvantages of other
ones. This is in line with our survey findings.
Centralized ordering can reduce average cycle inventory even if a stock-to-demand
order policy is followed and minimum order and saltus quantities have to be observed. It
also enables to decrease safety stock and improve inventory availability as the aggregate
forecast for the central order is more accurate than the disaggregate one for the decentral
orders.
The literature review and this application showed the theoretical benefits risk pooling
can bring. However, survey research on the knowledge and application of risk pooling is
scarce. Therefore, we explored whether the different risk pooling concepts are known, applied, and associated in a survey of 102 German manufacturing and trading companies:
A lot of respondents do not perceive all the questioned concepts as risk pooling ones. It
appears that mainly transshipments and postponement are associated with risk pooling.
Although at least in our sample the risk pooling concepts are known fairly well (central
ordering, product substitution, and selective stocking the most), only selective stocking,
transshipments, and central ordering are widely applied. Transshipments are more, postponement and product pooling less applied than suggested by some publications mostly for
other regions.
Less sample companies have centralized their warehouse system than European ones.
For our sample we cannot confirm a major decentralization trend as one may expect due to
increasing fuel costs. Companies seem to be consistent in their strategy of centralization,
decentralization, or no change in warehouse number over time.
The utilization and knowledge of a risk pooling concept are correlated. This suggests
that improving the knowledge of risk pooling may increase its application. Research needs
to convey under what conditions and how the different risk pooling concepts can be applied successfully. This research constitutes one step in this direction.
Prominently associated is past decentralization with future decentralization, the utilization of product substitution and demand reshape, past centralization and decentralization
(the only negative correlation), the application of the inventory turnover curve and transshipments, commonality and product pooling, risk pooling and transshipments, turnover
curve and order splitting, selective stocking and virtual pooling, transshipments and virtual
pooling, risk pooling and postponement, product substitution and transshipments, product
substitution and virtual pooling, as well as postponement and commonality and vice versa.
130
6 Conclusion
We can support Rabinovich and Evers' (2003b) finding that time postponement (emergency transshipments and inventory centralization) contributes to the implementation of
form postponement at best only weakly for our sample.
Trading companies seem to apply product substitution and transshipments more than
manufacturing companies. The opposite is true for commonality and postponement. This
was considered in the RPDST. In contrast to Van Hoek (1998b) our sample shows no significant difference in the application of postponement by electronics, automotive, food, and
clothing manufacturers.
More large companies appear to use risk pooling and postponement than smaller ones,
perhaps because they can better afford to invest in expensive risk pooling methods as suggested by Huang and Li (2008b: 12). More small companies have centralized their warehouse or logistics system in the past than large ones in our sample.
The survey is of limited representativeness and generalizability, as a genuine simple
random sample of the relevant population of German manufacturing and trading companies could not be drawn. Survey research is very laborious and prone to many biases and
errors and has low response rates that disappoint the researcher and impair the results. Our
experience supports that face-to-face methods tend to achieve higher response rates.
As this treatise constitutes a first attempt to structure the vast risk pooling research in
business logistics, develop tools to choose between the various risk pooling methods, and
get an idea about their recognition and application in German companies, we make the
following suggestions for further research:
Our RPDST and its underlying contingency factors should be empirically validated
with additional companies in different industries. Conditions and implementation modalities favoring the different risk pooling methods should be further explored, especially for
product pooling, central ordering, (particularly non-manufacturing) capacity pooling, virtual pooling, and substitution/demand reshape, as our considerations are not exhaustive.
The effectiveness and efficiency of the different methods should be compared. Evers
(1999), Swaminathan (2001), Eynan and Fouque (2005), and Wanke and Saliby (2009)
made a good start here.
Perhaps a normative model could be developed that integrates and compares the ten
identified methods in terms of their costs and benefits in order to choose an optimal one.
However, such a model might be either too complex or simple. Perhaps combining simulation and analytic frameworks may better account for the complicated interaction effects
131
6 Conclusion
among various factors.812 Centralized ordering and transshipments at Papierco could be
simulated as well.
In general, risk pooling models should become more realistic in terms of their assumptions, accessibility for practitioners, and allowing (practitioners) to quantify the benefits of
risk pooling.813
We considered choosing suitable risk pooling methods for individual companies for certain economic conditions and sometimes their relation to their immediate supply chain
members at the most. However, a risk pooling strategy that is beneficial for an individual
supply chain member might not be profitable for others or the whole supply chain.814
Therefore, it should not be implemented by one company unilaterally and further research should focus on the supply chain as a whole: Which conditions render a risk pooling method or a combination of risk pooling methods beneficial for all members of a
supply chain? How do you get independent parties to agree on or join a risk pooling strategy? If some supply chain members are better and other ones worse off after risk pooling,
how do you distribute the gains to encourage risk pooling and make it beneficial for everybody? The contracting side of risk pooling still leaves room for further research.
Another interesting question to explore would be whether the risk pooling methods
make individual companies and the whole supply chain more resilient to external uncertainties other than demand and lead time uncertainty. Sheffi (2006, 2007) explores this
question for several risk pooling methods and individual companies815. Snyder and Shen
(2006: 42) conclude that “[s]upply chain resilience [to supply disruptions and demand uncertainty] can be improved significantly without large increases in cost” by centralization
(risk pooling) and decentralization (risk diversification). How should supply chains or logistics systems be designed, so that risk pooling is exploited optimally and uncertainties
are minimized?
812
813
814
815
Cf. Hwarng et al. (2005).
Cf. Heil (2006: 81, 169).
Some or all supply chain members may be hurt by centralized ordering (Gürbüz et al. 2007: 305), inventory pooling (Anupindi and Bassok 1999, Pasin et al. 2002, Simchi-Levi et al. 2008: 234-238), postponement (García-Dastugue and Lambert 2007), transshipments (Grahovac and Chakravarty 2001, Dong and
Rudi 2002, 2004, Zhang 2005, Shao et al. 2009), and virtual pooling (Randall et al. 2002: 56).
He examines how an enterprise can be made more resilient to disruptions (supply shortages, production
disruptions, energy price increases, exchange rate fluctuations, strikes, and natural disasters) especially by
risk pooling (Sheffi 2006: 117f., 210, 212, 248, 303, 317), flexibility (Sheffi 2006: 117ff., 199ff.), postponement (Sheffi 2006: 297), commonality (Sheffi 2007: 184-186), standardization (Sheffi 2007: 186193), interchangeability (Sheffi 2006: 210), multiple suppliers (Sheffi 2007: 99f., 215-222), inventory/forecast aggregation (Sheffi 2006: 117f.), exchange of parts (Sheffi 2006: 248), and reduction of product variants (Sheffi 2006: 119).
132
6 Conclusion
An empirical analysis of risk pooling in the German auto industry might be interesting,
because of the current changes in model mix (high gas prices), production volume (recession), and steel prices. How can you prepare your production system for something like
this?
How does the current economic downturn affect risk pooling? We already noted that
this might have contributed to increased research and implementation of risk pooling.
How do increased transportation costs affect risk pooling? If they are lasting and
warehouse networks are therefore decentralized, how is this decision affected by risk pooling and how does network redesign affect risk pooling?
Another more representative survey with a higher response rate could also shed light
onto the companies' reasons for and against as well as the manner, degree, benefits, and
costs of applying the risk pooling concepts, as we intended in the six-page version of our
survey that yielded a uselessly low response rate. As risk pooling can affect the whole
supply chain, another survey could consider a supply chain wide perspective rather than
single companies.
Risk pooling is usually shown or proved with the standard deviation. For other measures of dispersion, such as the variance of independent random variables or the range,
there might be no risk pooling effect. Therefore one could consider risk pooling with
measures of dispersion other than the standard deviation. Risk pooling should also be further explored with different order policies.
Finally, the SRL- and PE-models can be extended to include further assumptions. One
should also check whether the conditions or assumptions necessary for the SRL to hold
(necessary conditions) are also sufficient conditions, i. e. if the SRL holds, these conditions
also automatically apply.
133
Appendix A: A Survey on Risk Pooling Knowledge and
Application in 102 German Manufacturing and Trading
Companies
134
1
Introduction
After reviewing the limited recent survey research in OR, business logistics, SCM, and particularly risk pooling mostly with low response rates, we describe our findings from a survey on
risk pooling knowledge and application we conducted among 102 German manufacturing and
trading companies. Such a survey has been demanded by some researchers and – to our knowledge – has not been conducted before.
1.1
Motivation: Scarce Survey Research on Risk Pooling
There is little empirical and especially survey research in OR816, business logistics817, and risk
pooling818. The samples and response rates are usually small or not mentioned819.
No surveys have been conducted on risk pooling in business logistics in general yet.
Only few surveys touch types of risk pooling. Most of these surveys deal with postponement, although the majority of empirical research on postponement relies on case stu-
816
817
818
819
Cachon (2004), Netessine (2005).
Griffis et al. (2003: 237).
Labro (2004: 358).
The following researchers conducted surveys on logistics topics with the following returns: Jackson
(1985, 53 usable responses), Dubelaar et al. (2001, 72 usable of 101 surveys), Griffis et al. (2003: 241f.,
response rate: 13.25 %), Kisperska-Moroñ (2003: 130, 538 questionnaires, on average three respondents
in one company), Bagchi and Skjoett-Larsen (2005, 149 responses, response rate: 5.7 %), White (2005,
429 answers, response rate: 10.93 %), Hilmola and Szekely (2006, 67 usable responses, response rate:
8.9 %). Johnson et al. (2006, 297 usable responses, response rate: 55 %, 305 usable responses, response
rate: 51 %, 284 usable responses, response rate: 44 %), Shao and Ji (2006, 321 surveys, response rate:
89.2 %), Böhnlein and Lünemann (2008, 51 responses), Chikán (2009, 51 responses, response rate:
20.82 %).
Surveys on postponement received 65 (Kisperska-Moroñ 2003: 130), 76 (Yang et al. 2005b), 80 (Van
Hoek 1998b), 102 (Chiou et al. 2002), 106 (Huang and Li 2008b), 111 (completed 24-page workbooks in
interviews with world class companies, CLM 1995: 8, 384), 129 (McKinnon and Forster 2000: 5, Delphi
survey with logistics experts), 256 (Rabinovich and Evers 2003b), 306 (Nair 2005), 322 (in the base-line
survey in Germany, CLM 1995: 381f.), 358 (Oracle 2004, response rate: 2.24 %), 782 (Van Hoek 2000b,
Van Hoek and Van Dierdonck 2000, response rate: 53 %), and 3,693 (altogether in the base-line survey,
CLM 1995: 381f.) usable responses. The surveys with high returns were conducted via logistics associations (CLM 1995, Rabinovich and Evers 2003b, Oracle 2004, Nair 2005) or via phone with very few
questions (Van Hoek 2000b). They were administered in Europe (McKinnon and Forster 2000: 5),
Greater China (Mainland China, Hong Kong, and Taiwan) (Huang and Li 2008b), Taiwan (Chiou et al.
2002), the U. S. (an expert study by Morehouse and Bowersox 1995, Van Hoek 1998b, Rabinovich and
Evers 2003b, Nair 2005), the UK (Yang et al. 2005b), the Netherlands (Van Hoek 2000b, Van Hoek and
Van Dierdonck 2000), and Upper Silesia, Southern Poland (Kisperska-Moroñ 2003) among manufacturing (Van Hoek 1998b, Van Hoek and Van Dierdonck 2000, Chiou et al. 2002, Kisperska-Moroñ 2003,
Rabinovich and Evers 2003b, Nair 2005, Yang et al. 2005b, Huang and Li 2008b), trading (Van Hoek and
Van Dierdonck 2000, Nair 2005), and transport and logistics services companies (Van Hoek 2000b, Van
Hoek and Van Dierdonck 2000). Graman and Magazine (2006: 1068, 1070f., 1075) conducted depth interviews with five managers of a small U.S. manufacturer of mops and brooms on issues influencing successful postponement implementation.
135
Appendix A
dies820, such as Dapiran (1992), Cooper (1993, examples), Feitzinger and Lee (1997), Garg
and Tang (1997), Van Hoek (1997, 1998a, 1998b), Van Hoek et al. (1998), Magretta
(1998), Brown et al. (2000), Waller et al. (2000), Ghemawat and Nueno (2003), Huang and
Lo (2003), and Huang and Li (2008a).
Whereas some researchers find postponement application has increased, will increase,
or postponement is widely applied821, others state it is not applied as much (as expected)822
and will be even less used in the future823. This is explained by “a general lack of understanding of postponement” regarding its conception, gains, and costs824, perceived technology limitations, ineffective organization alignment825, as well as difficulties in managing
the relations to suppliers and customers826 and in estimating the costs and benefits of postponement827.
Van Hoek (1998b: 513) finds that “[d]ownstream activities such as distribution and
packaging are largely postponed (56.93 per cent of the flow of goods and 53.95 per cent).
Upstream activities such as engineering and purchasing are postponed to a lesser extent
(37.49 per cent of the flow of goods and 37.42 per cent). Overall however, the findings
indicate that postponement is applied at multiple points in the chain and to a significantly
high share of the flow of goods”. Yang et al. (2005b: 1000) remark that postponement is
mostly applied as make to order and ship to order.
820
821
822
823
824
825
826
827
Van Hoek (2001).
CLM (1995: 213), Morehouse and Bowersox (1995), Van Hoek (1998b, 2000b), Van Hoek and Van
Dierdonck (2000), McKinnon and Forster (2000: 7f.), Chiou et al. (2002), Huang and Li (2008b). CLM
(1995: 213) finds “Research clearly supports the generalization that firms are rapidly adopting both form
and time postponement”, although 10.3 % of North American and 85 % of non-North American world
class companies have decreased or substantially decreased the use of postponement and 31 % of North
American and 0 % of non-North American (European/Pacific Basin) world class companies have increased or substantially increased the use of postponement (Workbook Section 4: Organization, Question
31, “Electronic Appendix” Disk to CLM 1995). Yet, only few non-North American companies completed
the workbook (CLM 1995: 384).
Van Hoek et al. (1998: 34, 51), Bowersox et al. (1999), Battezzati and Magnani (2000: 423), Brown et al.
(2000: 78), Van Hoek (2000b, in third party logistics or TPL), Van Hoek and Van Dierdonck (2000, in
TPL), Oracle (2004), Yang et al. (2004, 2005a, 2005b: 991), Boone et al. (2007: 594), Yang et al. (2007:
972). Van Hoek et al. (1998: 51, 34) observe that although “the theoretical benefits of postponement
[were] introduced [already] in the 1950s and 60s”, this “highly attractive principle has hardly been applied to date”. “[P]ostponement applications are still in the infancy stage” (Van Hoek et al. 1998: 51). It
“has an enormous potential, still largely under-exploited, in Italy” (Battezzati and Magnani 2000: 423).
Boone et al. (2007: 594) remark “the slow rate of postponement adoption among practitioners”.
„[P]ostponement is an underutilized concept“ (Yang et al. 2007: 972).
“Postponement applications are still not as widespread as expected. […] The respondents also expected
postponement to be less used in three years” (Yang et al. 2005b: 991).
Oracle (2004: 2, 7).
Capgemini (2003), Matthews and Syed (2004: 30).
Yang et al. (2005b: 991), Waller et al. (2000), Van Hoek et al. (1998).
Van Hoek et al. (1998).
136
Appendix A
Rabinovich and Evers (2003b: 41f.) find that time postponement (emergency transshipments) contributes to the implementation of form postponement.
Huang and Li (2008b: 5, 16f.) discover that the degree of postponement application is
higher in China than CLM (1995), Yang et al. (2005a), and Van Hoek (1998b) remarked in
Western countries and increases. Chiou et al. (2002: 122) also conclude “that form postponement strategies are practiced widely by IT firms in Taiwan”. Huang and Li (2008b:
12) sent their questionnaires only to 411 companies that had confirmed on the phone that
they applied postponement. They, Chiou et al. (2002), and Yang et al. (2005b) do not state
how many companies in their research countries actually apply postponement. In a personal correspondence on September 4, 2009 Dr. Biao Yang, The York Management School,
University of York, UK, explained that speaking from their experience, given the working
definitions of different postponement strategies they provided828, very few companies
would claim that they are not using any postponement.
The Council of Logistics Management (CLM) conducted a base-line survey in North
America (Canada and the U.S.), Europe (France, Germany, the Netherlands, Norway,
Sweden, and the UK), and the Pacific Basin (Australia, Japan, and Korea) from May to
September 1993. Of the 21,592 mainly manufacturing companies contacted, 3,693 answered (response rate: 17.1 %). In Germany 3,000 surveys were mailed and 322 returned
(response rate: 10.7 %).829
It also did interviews with 111 companies from 17 countries in North America, Europe,
and the Pacific Basin from early 1994 until spring 1995 that were believed “by a group of
logistics experts to have a high potential to possess world class logistical capabilities” and
asked them to complete a 24-page workbook.830
35.3 % of North American and 29.1 % of non-North American world class companies
consider location flexibility (“[t]he ability to service customers from alternative warehouse locations”, i. e. in our opinion transshipments or virtual pooling) less or least impor828
829
830
In their survey Yang et al. (2005b: 1002f.) ask for “the percentages of goods related to” engineer, purchase, make, final manufacturing/assembling, package/label, and ship to order to elicit the extent of postponement application in the respondents' companies. Thus they equate make-to-order with postponement
or delayed differentiation, while Cachon and Terwiesch (2009: 344) distinguish these strategies: Although “they are conceptually quite similar”, “[d]elayed differentiation is thought of as a strategy that
stores nearly finished product and completes the remaining few production steps with essentially no delay. Make-to-order is generally thought to apply to a situation in which the remaining production steps
from components to a finished unit are more substantial, therefore involving more than a trivial delay.
Hence, delayed differentiation and make-to-order occupy two ends of the same spectrum with no clear
boundary between them”.
CLM (1995: 381f.). CLM was named Council of Supply Chain Management Professionals (CSCMP) in
2005.
CLM (1995: 8f., 384).
137
Appendix A
tant, 35.3 % or 37.5 % respectively more or most important. The North American and nonNorth American world class companies see mostly the logistics department as responsible
for location flexibility (77.19 and 74.76 % responsibility). Fifty-one percent of North
American and 58.3 % of non-North American world-class companies believe they perform
better or much better than their competitors in terms of location flexibility.831
According to McKinnon and Forster (2000: 17), “the proportion of retail sales bypassing conventional shops and being delivered directly to the home is likely to increase significantly” until 2005. “Direct distribution to the home from nationally based suppliers is likely to experience the fastest growth”832. That means that virtual pooling in the form of
drop-shipping is expected to increase.
In a small phone survey by Randall et al. (2006) of 64 (56 responses, 54 usable responses, response rate: 84.4 %) publicly held e-tailers that made up 60 % to 70 % of U.S.wide e-tailing revenue, 36 companies (67.7 %) chose to hold inventory. That means 33.3 %
of the surveyed e-tailers conducted virtual pooling.
In the CLM base-line survey, 62.81 % of North American, 68.31 % of European, and
47.26 % of Pacific Rim companies agree or strongly agree that on an equal volume basis
they had inventory located at fewer sites in 1993 (today) than in 1988 (five years ago).833
That means that 68.31 % of the surveyed European companies conducted inventory pooling.
The world class companies' “[l]ogistics strategy includes a priority to reduce […] [t]he
number of logistics facilities” more so in Europe and the Pacific Basin, where the mean
answer was 3.55 than in North America, where the mean answer was 3.23 on a scale from
1 (Strongly Disagree) to 5 (Strongly Agree).834
McKinnon and Forster (2000: 6f.) find “The centralisation of inventory is likely to outstrip that of production. At a European level, the degree of inventory concentration is forecast to increase by a third, twice as much as at a national level. A significant minority of
the panel (around 15 %) indicated that within countries there would be net decentralisation
of inventory, with firms increasing their number of stockholding points. The prevailing
view, however, was that inventory centralisation, which has been one of the main logistical
trends over the past 30 years, would continue apace for at least the next 5 years”.
831
832
833
834
Workbook Section 3: Relative Performance Competencies, Question 20, “Electronic Appendix” Disk to
CLM (1995).
McKinnon and Forster (2000: 9).
Logistics Practices Results, Question 7, “Electronic Appendix” Disk to CLM (1995).
CLM (1995: 387).
138
Appendix A
A Warehousing Education and Research Council survey with 139 U.S. participants in
manufacturing, retail, wholesale, public utilities and government showed that the number
of warehouses continues to shrink, although there are a few new large facilities in West or
Mid Atlantic regions.835
Contrarily, according to a survey by Lemoine and Skjoett-Larsen (2004) among logistics managers of mechanical, electronic, and medical equipment companies in Denmark in
2001 (46 usable questionnaires, response rate: 10 %) the number of suppliers, production
facilities and warehouses has not been changed in the last three to five years in Europe, but
has been increased or will be increased outside Europe.
Bandy (2005) conducts an anonymous survey among 24 students that shows that a simple spreadsheet in-class simulation helps students understand the impact of pooling safety
stock.
Reviewing literature and interviewing Belgian companies, Naesens et al. (2007) find
that companies are reluctant to implement inventory pooling in a horizontal collaboration.
Nonetheless, companies seem to have conducted inventory pooling within companies to
a broad extent.
Twenty-seven percent of North American and 29.1 % of non-North American worldclass companies consider substitution flexibility (“[t]he ability to substitute product or
service offerings in the event of a delay or stockout versus backorder or line cancellation”)
less or least important, 46.2 % or 25 % respectively more or most important. Responsibility for substitution flexibility rests 49.9 % with logistics, 35.63 % with marketing according
to North American, or 48.41 % or 42.95 % respectively according to non-North American
world-class companies. 44.2 % of North American and 37.5 % of non-North American
world-class companies believe they perform better or much better than their competitors in
terms of substitution flexibility.836
Only few surveys provide information on how many companies apply the respective
risk pooling method.
Nearly 50 % of more than 350 companies from all over the world have not implemented
postponement strategies.837 Hence, about half of these companies use postponement.
More than 40 % of the companies surveyed by Kisperska-Moroñ (2003: 131) gear total
production towards customer orders. Surveyed companies manufacture on average 16 % to
835
836
837
Modern Materials Handling (2002).
Workbook Section 3: Relative Performance Competencies, Question 29, “Electronic Appendix” Disk to
CLM (1995).
Oracle (2004).
139
Appendix A
stock and 84 % to order, engineering 97 %, metal 74 %, plastic products 83 %, and electrotechnical companies 77 % to order. Thus one could infer that about 40 % of the surveyed
companies in Upper Silesia, Poland apply manufacturing postponement.
From 1988 to 1993 inventory was centralized or pooled by 68.31 % of the European
companies surveyed by the CLM.838
Virtual pooling is applied by 33.3 % of the U.S. e-tailers that Randall et al. (2006) interviewed.
None of the surveys gives detailed information on Germany, although Germany is the
fourth largest economy in the world according to its nominal GDP in USD in 2008839 and
is very progressive, advanced, and sophisticated in logistics, especially in “operating efficiency and cost” and customer service, and, like other European countries, in the “functional integration of logistics work within the firm” and “environmental issues” like “reverse logistics”840. European countries have opportunities for improvement in “the external
integration of logistics systems and development of supply chain relationships throughout
Europe”841.
1.2
Objective
We would like to determine to what extent the different risk pooling concepts are known and
applied by 102 German manufacturing and trading companies and examine for our sample the
following remarks, suggestions, and demands:
Van Hoek (1998b) finds that postponement is extensively applied in electronics and automotive and less extensively applied in food and clothing. We would like to find out
whether this applies to our sample as well.
Alfaro and Corbett (2003: 12f., 15) observe that “several approaches to the widely recognized challenge of managing product variety rely on the pooling effect. Pooling can be
accomplished through the reduction of the number of products or stock-keeping units
(SKUs), through postponement of differentiation, or in other ways [component commonality and inventory pooling]. These approaches are well known and becoming widely
applied in practice”. However, there are no studies yet whether product pooling and component commonality really are widely applied in practice.
838
839
840
841
Logistics Practices Results, Question 7, “Electronic Appendix” Disk to CLM (1995).
IMF (2009).
CLM (1995: 365).
CLM (1995: 366).
140
Appendix A
Herer et al. (2006) remark “Transshipments are not widely adopted in practice because
the IT infrastructure is inadequate and there are no realistic models to take advantage of
transshipment benefits”. However, there are no studies yet whether transshipments really
are not widely used in practice.
Thomas and Tyworth (2006) demand a survey to determine whether order splitting is
employed in practice842.
Boone et al. (2007) review postponement literature published from 1999 to 2006 and
conclude research should be extended to non-manufacturing postponement and investigate
the slow rate of postponement adoption among practitioners.
Huang and Li (2008b: 12) only surveyed large electronic/information technology, clothing, and electric appliances companies. They remark large companies may apply postponement more than small ones, since they may be better able to afford the redesign of
products and/or processes usually required by postponement843. “Hence, further studies
could compare the differences of postponement application between large-scale and small
and medium companies”844.
842
843
844
“Yet, despite the impressive amount of past and present work on pooling lead-time risk by order splitting,
it is difficult to find any substantive evidence of successful applications in academic or practitioner literature” (Thomas and Tyworth 2006: 246). “Although studies in both tracks provide hypothetical evidence
that pooling lead-time risk by splitting orders simultaneously may be worthwhile, it is difficult, if not impossible, to find substantive empirical validation of the proposition” (Thomas and Tyworth 2006: 254).
“Collectively, these limitations make the value proposition rather dubious. Thus future research in this
area should include case studies, simulations, and surveys to determine whether companies use such order
splitting methods and the business setting where successful applications appear” (Thomas and Tyworth
2006: 254f.).
Ernst and Kamrad (2000), Aviv and Federgruen (2001b).
Huang and Li (2008b: 19).
141
2
The Survey
There has not been a survey on how many companies know and apply the various risk pooling
methods yet, especially not in Germany. In order to respond to the aforementioned demands
and remarks, we conducted a survey among German manufacturing and trading companies
from September 2008 to August 2009 and obtained 102 completed questionnaires (response
rate: 21.3 %) from logistics or supply chain management professionals. Since an earlier sixpage survey that was e-mailed to 3,600 companies had a response rate of only 0.3 %, we asked
478 manufacturing and trading company representatives in person to complete the one-page
questionnaire in figure A.4 or forward it to the appropriate person mainly on company and job
fairs in various German cities.
Respondents were promised a summary of the survey results as an incentive.845 Our experience supports that face-to-face methods usually achieve higher response rates846.
2.1
Research Design
The respondents worked for companies from the following branches of economic activity according to the German Classification of Economic Activities Edition 2003 of the German Federal Statistical Office (Statistisches Bundesamt Deutschland):
845
846
Cf. Yang et al. (2005b: 996).
Kisperska-Moroñ (2003: 130), Groves et al. (2004: 165).
142
Appendix A
The whole
Responding
companies
a
population
Classification
Description
Number
%
Number
%
Variance (%)
11
Extraction of crude petroleum and natural gas;
service activities incidental to oil and gas extraction,
excluding surveying
17
0.01
1
0.98
0.97
15
Manufacture of food products and beverages
5,189
4.46
4
3.92
-0.54
16
Manufacture of tobacco products
24
0.02
1
0.98
0.96
18
Manufacture of wearing apparel; dressing and
dyeing of fur
378
0.32
1
0.98
0.66
21
Manufacture of pulp, paper and paper products
817
0.70
2
1.96
1.26
22
Publishing, printing and reproduction of recorded
media
2,456
2.11
2
1.96
-0.15
24
Manufacture of chemicals and chemical products
1,405
1.21
3
2.94
1.73
25
Manufacture of rubber and plastic products
2,635
2.26
2
1.96
-0.30
26
Manufacture of other non-metallic mineral products
1,677
1.44
1
0.98
-0.46
27
Manufacture of basic metals
897
0.77
1
0.98
0.21
28
Manufacture of fabricated metal products, except
machinery and equipment
6,175
5.31
4
3.92
-1.38
29
Manufacture of machinery and equipment n.e.c.
5,990
5.15
13 12.75
7.60
30
Manufacture of office machinery and computers
164
0.14
1
0.98
0.84
1,922
1.65
7
6.86
5.21
542
0.47
5
4.90
4.44
2,067
1.78
2
1.96
0.18
1,001
0.86
14 13.73
12.87
314
0.27
3
2.94
2.67
1,484
1.27
2
1.96
0.69
168
0.14
3
2.94
2.80
31
32
33
34
Manufacture of electrical machinery and apparatus
n.e.c.
Manufacture of radio, television and communication
equipment and apparatus
Manufacture of medical, precision and optical
instruments, watches and clocks
Manufacture of motor vehicles, trailers and semitrailers
35
Manufacture of other transport equipment
36
Manufacture of furniture; manufacturing n.e.c.
37
Recycling
40
Electricity, gas, steam and hot water supply
1,196
1.03
2
1.96
0.93
45.2
Building of complete constructions or parts thereof;
civil engineering
6,352
5.46
1
0.98
-4.48
51.46
Wholesale of pharmaceutical goods
3,148
2.70
2
1.96
-0.74
51.47.8
Wholesale of paper and paperboard, stationery,
books, newspapers, journals and periodicals
2,259
1.94
3
2.94
1.00
1,254
1.08
2
1.96
0.88
1,333
1.15
1
0.98
-0.16
24,790
21.30
7
6.86
-14.44
51.53.1
51.88
52.11
Non-specialized wholesale of wood, construction
materials and sanitary equipment
Wholesale of agricultural machinery and
accessories and implements, including tractors
Retail sale in non-specialized stores with food,
beverages or tobacco predominating
52.42
Retail sale of clothing
25,896
22.25
10
9.80
-12.44
52.46
Retail sale of hardware, paints and glass
11,279
9.69
1
0.98
-8.71
52.48.6
Retail sale of games and toys
3,564
3.06
1
0.98
-2.08
116,393
100
102
100
Total
Table A.1: Comparing Respondents with the Total Population of Manufacturing and Trading
Companies in Germany
a
Source: Statistisches Bundesamt Deutschland (2009i: 371, 408f.). Companies with in general 20
employees and more. Status of 09/30/2006 (trade), 09/30/2007 (manufacturing).
143
Appendix A
As 78.7 % of the sampling frame population did not respond and the sample is small, it is not
too representative of neither the whole population in the different branches of economic activity the respondents' companies belong to in table A.1 nor of the target population of German
manufacturing and trading companies.847 Not all areas of domestic production and trade are
covered. Our sample consists of too many manufacturing companies, especially from vehicle
construction (34, 35), although this is an important industry in Germany, manufacture of machinery (29, 31, 32), and recycling (37) and too few trading companies, particularly in food
(52.11), clothing (52.42), and hardware retail (52.46) as the variance in the last column shows.
Deviations of responding companies from the whole population in Huang and Li
(2008b: 13) are of similar magnitude. In contrast, the responding companies in Yang et al.
(2005b: 997) closely reflect the whole population. Of the 28 mentioned surveys in this section848 only Huang and Li (2008b) and Yang et al. (2005b) (7.14 %) compare the responding companies' characteristics to the whole population (retrospective quota sampling).
We have to highlight that the whole population in table A.1 only consists of companies
with 20 or more employees, while our sample encompasses three companies (respondents
2, 65, and 100 from industrial sectors 52.42, 27, and 51.47.8) with less than 20 employees.
If we omitted them, the variance would increase and the representativeness decrease even
more. A detailed classification of the branches of economic activity with all German companies with any number of employees is not publicly available. The German Federal Statistical Office told us we could apply for a special query with charges. A retrospective quota
sampling with more detailed subgroups of industrial economic activity than in table A.1
and all German companies, which cannot be conducted due to lacking data, might reveal
that our sample is more representative of these subgroups.
The size of the responding companies ranges from 5 to 182,739 employees. 2 % have
less than 10, 9 % less than 50, 31 % less than 250, 32 % less than 500, and 68 % have 500
847
848
There were 52,362 manufacturing (9.94 % of manufacturing and trading companies) and 474,065
(90.06 %) trading companies with in general 20 or more employees in Germany in 2007 or 2006 respectively (Statistisches Bundesamt Deutschland 2009i: 409, 371). In our sample there are 75 (73.53 %) manufacturers and 27 (26.47 %) trading companies.
Jackson (1985), CLM (1995), Morehouse and Bowersox (1995), Van Hoek (1998b, 2000b), McKinnon
and Forster (2000), Van Hoek and Van Dierdonck (2000), Dubelaar (2001), Chiou et al. (2002), Griffis et
al. (2003), Kisperska-Moroñ (2003, two surveys), Rabinovich and Evers (2003b), Lemoine and SkjoettLarsen (2004), Oracle (2004), Bagchi and Skjoett-Larsen (2005), Nair (2005), White (2005), Yang et al.
(2005a, 2005b), Himola and Szekely (2006), Johnson (2006), Randall et al. (2006), Shao and Ji (2006),
Naesens et al. (2007), Böhnlein and Lünemann (2008), Huang and Li (2008b), and Chikán (2009).
144
Appendix A
or more employees. The majority of the sample consists of larger companies, while the
majority of the whole population comprises small ones.849
Nevertheless our survey can at least show the risk pooling knowledge and activities of
the surveyed companies for a given moment in time. They are relatively heterogeneous in
terms of industry membership and number of employees (size), so that risk pooling knowledge and activities of a wide company spectrum and size specific specialties can be detected.850 Besides, the respondents do not deviate from the overall population extremely
regarding the branches of activity. Therefore, the absence of data from the nonrespondents may not contaminate the conclusions drawn from the sample too much.851
The questionnaire was scrutinized by three academics and three logistics managers,
pretested among eleven companies, and adjusted according to the suggestions and detected problems before the final distribution to insure content validity.852 Validity measures whether the questions capture what they are intended to capture.853 Of the 28 surveys
mentioned previously 28.57 % deal with their validity. Reliability measures “whether respondents are consistent or stable in their answers”854. Only 17.86 % of the 28 surveys mentioned address their reliability. We did not measure reliability as respondents usually are
not willing to be interviewed twice or to answer a questionnaire enlarged by asking for the
same construct twice.855 We could not check for “systematic reporting errors”856 (response
bias), as external data, which the survey responses could be compared to, are not available857. None of the 28 surveys mentioned refers to their response bias.
We did not check for non-response bias, because we could not collect the nonrespondents' characteristics858. Non-response bias is the distortion of the sample and therefore the
basic population because some people do not respond or do not answer certain questions.
The answers of respondents may differ from the ones of nonrespondents. There is no consensus on when nonresponse reduces survey quality and therefore on appropriate response
849
850
851
852
853
854
855
856
857
858
In 2006 there were 4,307 (0.63 %) active industrial and 1,362 (0.18 %) trading companies with 250 and
more, 680,561 (99.37 %) or 735,820 (99.81 %) ones respectively with less than 250 employees subject to
social security (Statistisches Bundesamt Deutschland 2009i: 493). In our sample 74.67 % of the industrial
and 51.85 % of the trading companies have 250 and more employees.
Cf. Böhnlein and Lünemann (2008: 6).
Cf. Vockell and Asher (1995: ch. 8).
Cf. Yang et al. (2005b: 995, 998), Huang and Li (2008b: 13).
Groves et al. (2004: 254).
Groves et al. (2004: 261).
Groves et al. (2004: 266), Yang et al. (2005b: 998).
Groves et al. (2004: 259).
Cf. Groves et al. (2004: 266).
Cf. Groves et al. (2004: 169-196), Schneekloth and Leven (2003).
145
Appendix A
rates.859 Nevertheless, our response rate is above the unfavorable response rates below
20 %860, within the 10 % to 30 % of the past mean861 and the 4 % to 32.7 % of large samples in the Journal of Business Logistics from 1997 to 2001862, and higher than a lot of the
mentioned surveys' ones863.
Nonresponse rates often are ignored, because it is assumed that the reason for the nonresponse is not associated with the measured statistical values and therefore it does not
affect the quality of the survey's results.864 Of the 28 surveys we mentioned ten (35.71 %)
deal with their non-response bias. Most of these determine the nonresponse bias, checking
whether the answers of first respondents and late respondents differ, although late respondents may not be an appropriate estimate for nonrespondents.
Nonetheless, the answers of our 51 first and 51 last respondents are independent (the
null hypothesis that there is no significant relationship between the answers cannot be rejected) in Pearson's and Yates' chi-square and Fisher's exact test at the 5 % level, except for
the question about their risk pooling knowledge865 and centralization in the past866. In all
other cases the distribution of the answers within the two groups does not differ significantly: The two-sided asymptotic significance of the respective test statistic is greater than
0.05 in each case, so that it is safe to say that any differences are due to chance variation,
which implies that the two groups answered equally.
With our sample size of 102 the confidence interval or margin of error is 9.7 on the
95 % confidence level for an estimated percentage of 50 %, i. e. one can be 95 % certain
that if 50 % of the sample picks an answer between 40.3 % (50-9.7) and 59.7 % (50+9.7)
of the whole population would have also picked that answer. However, the true percentage
of the population only is the sample's percentage plus/minus the confidence interval, if a
genuine simple random sample of the relevant population was drawn. This cannot be confirmed for our sample, so that this confidence interval is an underestimate. No errors and
“biases of coverage, sampling, nonresponse, or measurement […] are included in the margin of error”867. When random sampling is not used, one has to depend on logic apart from
859
860
861
862
863
864
865
866
867
Fowler (1993), Schneekloth and Leven (2003), Groves et al. (2004: 169-196).
Yu and Cooper (1983).
Flynn et al. (1990).
Griffis et al. (2003: 242).
Cf. Yang et al. (2005b: 998).
Groves et al. (2004: 169-196), Schneekloth and Leven (2003).
In this case Pearson's chi-square test gives χ2 = 9.046 with df = 1 and p = 0.00263, Yates' correction for
continuity χY
= 7.880 with df = 1 and p = 0.004998, and Fisher's exact test p (two-tailed) = 0.004728.
In this case χ2 = 4.752 with df = 1 and p = 0.029264, χY
= 3.928 with df = 1 and p = 0.047432, and
p = 0.046973 in Fisher's exact test.
Groves et al (2004: 382).
146
Appendix A
mathematical probability to assess to what extent the sample deviates from the population
it was drawn from.868
2.2
Data Analysis and Findings
2.2.1
Risk Pooling Knowledge and Utilization in the German Sample
Companies
Percent of Responding Companies
100
90
66
70
58
70
54
50
40
30
20
79
76
80
60
91
88
84
49
66
54
45
28
64
46
40
25
64
66
55
47
48
41
35
34
28
79
35
22
17
16
7
6
10
0
Knowledge
Utilization
Figure A.1: Risk Pooling Knowledge and Utilization in the German Sample Companies
The most known concepts related to risk pooling in the whole sample are central ordering,
product substitution, selective stocking, transshipments, and order splitting, followed by product pooling, commonality, virtual pooling, capacity pooling, “risk pooling”, postponement,
demand reshape, the portfolio effect (PE), inventory turnover curve, and square root law (SRL)
in order of descending percentage of respondents that know these concepts.
Surprisingly, the SRL (28 %) is less known than the PE (54 %), although it is the simpler concept and there are more and earlier publications on it in business logistics. Perhaps
the PE is more popular, as it is a generalization of the SRL and originated in finance.
868
Vockell and Asher (1995: ch. 8).
147
Appendix A
A lot of respondents obviously did not realize that risk pooling may comprise all these
different concepts. Otherwise they would have noted that they know and apply risk pooling, whenever they checked to know or apply any of these concepts. Risk pooling is a
hypernym and not a risk pooling concept itself.
The most applied risk pooling concepts in the whole sample are selective stocking,
transshipments, central ordering, commonality869, and centralization, followed by product
substitution, virtual pooling, capacity pooling, product pooling, postponement, order splitting, “risk pooling”, the PE, inventory turnover curve, demand reshape, decentralization,
and the SRL in order of descending percentage of surveyed companies applying these concepts.
While the knowledge of the different risk pooling concepts is fairly good870 (only the
SRL and the inventory turnover curve are known by less than 50 %), they are not widely
applied. Only the well established concepts selective stocking, transshipments, and central
ordering show application rates over 50 %, namely 66 %. This disagrees with Herer et al.
(2006), who remark “Transshipments are not widely adopted in practice because the IT
infrastructure is inadequate and there are no realistic models to take advantage of transshipment benefits”. Some companies which do not employ central ordering remarked it
increased transportation and delivery costs too much. This could be counteracted with a
centralized ordering system like the one we designed for Papierco earlier. Transportation
costs do not increase (substantially) or the supplier incurs them.
Postponement is only applied by 35 % of the companies. Thus we cannot conclude
“that firms are rapidly adopting both form and time postponement”871 and widely apply
it872 in Germany as CLM (1995: 209) reports for North America and Europe, McKinnon
and Forster (2000: 5) for Europe, and Chiou et al. (2002) and Huang and Li (2008b) for
China. More sample companies in Germany (65 %) have not implemented postponement
strategies than suggested by Oracle (2004) (nearly half of 358 mainly manufacturing companies from all over the world). We agree with Van Hoek et al. (1998), Bowersox et al.
(1999), Battezzati and Magnani (2000), Brown et al. (2000: 78), Oracle (2004), Yang et al.
869
870
871
872
Wazed et al. (2009: 70) find “Although the benefits of commonality are widely known, many companies
are still not taking full advantage of it when developing new products or re-designing the existing ones”.
We can agree with them for our sample.
Alfaro and Corbett (2003: 12f., 15) already remark that risk pooling approaches such as product pooling,
postponement, component commonality, and inventory pooling “are well known […] in practice”.
CLM (1995: 213).
Alfaro and Corbett (2003: 12).
148
Appendix A
(2004, 2005a, 2005b, 2007), and Boone et al. (2007) that postponement is not applied as
much (as expected).
Some respondents told us they did not use postponement as it entailed completely different production and storage concepts and therefore usually was uneconomical. Research
has to determine more clearly the changes necessary for postponement, methods for calculating the costs of postponement, and conditions that render postponement economical.
Practice seems to lack the knowledge to implement postponement economically. Perhaps
more concepts have to be developed that may make postponement less expensive, such as
operations reversal. This is in line with Oracle (2004: 7f.). Our survey suggests that the
reason for the low application may not lie in the basic knowledge of this concept (55 %
know it), but it is less known than most of the other concepts except for demand reshape,
the PE, inventory turnover curve, and SRL.
Component commonality is well known and applied by nearly every second surveyed
company. Thus, we can support Kim and Chhajed (2001: 219), who remark “The use of
commonality in product line extensions is a growing practice in many industries”, and Alfaro and Corbett (2003: 12, 15), who observe it is “becoming widely applied in practice”.
Nevertheless some companies who do not use it pointed out it was too expensive. This
confirms that the cost of common components can be high873.
Location flexibility achieved by transshipments and virtual pooling seems to be more
important in the sample companies in Germany than suggested by CLM874 for North
American and non-North American world class companies. McKinnon and Forster (2000:
9, 17) predicted virtual pooling in the form of drop-shipping to increase. Randall et al.
(2006) found that 33.3 % of the 56 interviewed U.S. e-tailers relied on virtual pooling.
More generally we find that 46 % of the surveyed manufacturers and traders apply virtual
pooling in Germany. Our sample only contains a single toy e-tailer.
Fewer German sample companies (48 %) have centralized their stockholding than European ones overall (68.31 %)875. Our findings agree with McKinnon and Forster (2000:
6f.), Modern Materials Handling (2002), and Alfaro and Corbett (2003: 12f.) that inventory
centralization is an important trend. However, we can also confirm the minority opinion
of 15 % of the panelists in McKinnon and Forster (2000: 6f.) that there will be a slight net
decentralization of inventory in Germany in the future. Thirty-five percent of the German
873
874
875
Van Mieghem (2004: 419).
Workbook Section 3: Relative Performance Competencies, Question 20, “Electronic Appendix” Disk to
CLM (1995).
Logistics Practices Results, Question 7, “Electronic Appendix” Disk to CLM (1995).
149
Appendix A
sample companies have not changed the number of warehouses or production facilities in
the past. Lemoine and Skjoett-Larsen (2004) reached a similar result in Denmark. Some of
the companies that did not or will not centralize declared it increased transportation costs
too much.
Most companies have already centralized or to a lesser extent decentralized their warehouse or logistics system in the past. Only six percent intend to centralize their logistics
system in the future. Merely seven percent plan to increase the number of warehouse or
production locations in the future. This is in opposition to the expectation that the increasing fuel and transportation costs induce companies to decentralize their warehouse or logistics systems. The risk pooling advantages derived from physical inventory pooling may
outweigh the increased transportation costs.
Product substitution flexibility seems to be more important in Germany than suggested
by CLM876 for North American and non-North American world class companies. Companies applying demand reshape mostly indicated they persuaded customers to buy another
substitute product even though the original customer wish was available to increase the
profit margin and not for risk pooling reasons as intended by Eynan and Fouque (2003,
2005).
We have to disagree with Alfaro and Corbett (2003: 12) who observe “the reduction of
the number of products or stock-keeping units (SKUs)”, also known as product pooling877, and “postponement of differentiation” are “becoming widely applied in practice”.
Product pooling is applied by 40 % and postponement by 35 % of the companies in our
sample.
We can answer the call of Thomas and Tyworth (2006: 254f.) for empirical research “to
determine whether companies use such order splitting methods”, pointing out that only
35 % of German companies in our sample do apply them. However, our survey does not
inform about the conditions and success of these order splitting applications.
Some interviewees said they did not know when and how it was favorable to apply the
various risk pooling concepts. Research needs to address these issues further. More research is needed to convey to practice when and how the different risk pooling concepts
may be implemented successfully. Our research constitutes one step in this direction.
876
877
Workbook Section 3: Relative Performance Competencies, Question 29, “Electronic Appendix” Disk to
CLM (1995)
Cachon and Terwiesch (2009: 330, 467).
150
Appendix A
2.2.2
Association between the Knowledge of Different Risk Pooling
Concepts
The knowledge of risk pooling is significantly associated with the knowledge of postponement
(Goodman and Kruskal's Tau (τ) = 0.147, approximative significance based on chi-square approximation (p) = 0.000), product pooling (τ = 0.104, p = 0.001), transshipments (τ = 0.091,
p = 0.002), the turnover curve (τ = 0.087, p = 0.003), commonality (τ = 0.066, p = 0.010), demand reshape (τ = 0.061, p = 0.013), and virtual pooling (τ = 0.050, p = 0.025) in order of descending significance.
Goodman and Kruskal's Tau was chosen, as it offers advantages over all other measures of association for nominal variables. It can be interpreted easily, its maximum is one,
it takes the value 0, if the variables are independent, and it is suitable, if the number k of
the independent variable x's categories is not equal to the number m of the dependent variable y's categories. Its only disadvantage is its complicated calculation, which is remedied
with modern statistics software.878 Goodman and Kruskal's Tau measures the association
of two categorical variables in terms of an improvement of prediction relative to a random
distribution of people (or responding companies in this case) based on the marginal distribution.879 It is a measure of proportional reduction of error (PRE).880
The above Tau of 0.147, for instance, means that the postponement knowledge of
14.7 % more of responding companies is predicted correctly, if we predict the postponement knowledge of a company not only according to the general distribution of postponement knowledge, but according to the conditional distribution of postponement knowledge
that is distinguished by the risk pooling knowledge.881 Postponement might be the most
popular type of risk pooling, as its recognition shows the highest correlation with the
knowledge of risk pooling. Forty-two of the 59 responding companies who know risk pooling also know postponement. Twenty-nine of the 43 logistics professionals not knowing
risk pooling do not know postponement either. The knowledge of risk pooling is also highly significantly associated with knowing product pooling (τ = 0.104, p = 0.001) and transshipments (τ = 0.091, p = 0.002).
Further significant correlations at least at the 5 % level between the knowledge of the
different risk pooling concepts can be read from table A.2 at the end of this section.
878
879
880
881
Müller-Benedict (2007: 203, 206).
Müller-Benedict (2007: 203).
Müller-Benedict (2007: 200).
Cf. Müller-Benedict (2007: 204).
151
Appendix A
Most significantly correlated is the knowledge of product pooling and transshipments
(τ = 0.163, p = 0.000), risk pooling and postponement (τ = 0.147, p = 0.000), transshipments
and capacity pooling (τ = 0.139, p = 0.000), as well as transshipments and postponement
(τ = 0.135, p = 0.000) and vice versa in order of descending strength of correlation.
In this sample the knowledge of postponement and capacity pooling (τ = 0.116,
p = 0.001), product substitution and demand reshape (τ = 0.112, p = 0.001), product pooling and demand reshape (τ = 0.104, p = 0.001), postponement and order splitting
(τ = 0.101, p = 0.001), selective stocking and transshipments (τ = 0.098, p = 0.002), as well
as demand reshape and transshipments (τ = 0.095, p = 0.002) is relatively strongly correlated. These concepts seem to be related and therefore to be known together: Postponement
and capacity pooling are popular and applied together e. g. in the auto industry. Both in
product substitution and demand reshape goods are substituted. One can offer a limited
number of products by product pooling or offer a variety of products (but not store all of
them) and apply demand reshape or transshipments. In order splitting certain steps in the
order and supplier delivery process may be postponed. If SKUs are only stocked at certain
locations (selective stocking), transshipments may be necessary between these locations.
Usually, we call a correlation in the social and economic sciences strong, if the measure
of correlation is > 0.5. In social and economic sciences any two characteristics are in general only weakly connected, i. e. the measure of correlation is < 0.3 for a lot of bivariate
distributions of socio-scientific data, because social and economic interrelations are not
transparent at first glance, but multidimensional, flexible, and versatile.882 Furthermore, the
other nominally scaled measures of correlation show much higher values than Tau, but are
difficult to interpret except for Lambda. However, Lambda has the disadvantage of taking
the value 0, even if both variables are not independent.883 In our research the Tau values
are one half to one third of the other measures' ones.
A statistical correlation does not necessarily mean that there is a real cause and effect
relationship between two variables: First of all, with a 95 % confidence interval there is
still a 5 % chance that a measured correlation is coincidental. Secondly, without a theory
one cannot determine the cause and the effect. Thirdly, there might be a spurious causation, i. e. two characteristics change in the same way, although they are not connected.
They both are connected to and influenced by a third characteristic. In order to elucidate
these effects also statistically one has to analyze more than two variables collectively by
882
883
Müller-Benedict (2007: 197f.).
Müller-Benedict (2007: 203ff.).
152
Appendix A
multivariate data analysis.884 Multivariate analysis methods for only nominal data seem
less powerful and clear than the ones for metric data885 and are not widely available in
software packages886. If all variables are nominal, contingency table, configuration frequency, log-linear, latent structure (if additional latent variables are used), and cluster
analysis can be employed. Most multivariate analysis methods require higher scales of
measurement.887 They should not be used without understanding them, their assumptions,
controversies, and theoretical foundations as modern software facilitate and some researchers do.888
Knowledge of a risk pooling concept certainly is not only connected to the knowledge
of other risk pooling concepts and a company's industrial sector and size (number of employees), but also to other factors. Likewise, the application of a risk pooling concept
might be correlated to additional factors besides the awareness of this and other concepts,
the application of other concepts, and a company's sector of economic activity and size.
These other factors remain subject to further research.
884
885
886
887
888
Reynolds (1984: 72ff.), Müller-Benedict (2007: 267ff.).
Reynolds (1984: 78), Holtmann (2007).
Breakwell (2007: 441).
Holtmann (2007).
Breakwell (2007: 441f.).
153
Appendix A
Risk SRL
Pooling
Risk Pooling
Selective Commo‐ Turnover Product Product Demand Transship‐ Postpone‐ Virtual Capacity Central Order Stocking nality
Curve
Pooling Substi‐ Reshape ments
ment
Pooling Pooling Ordering Splitting
tution
a 0.066
1
SRL
b
(0.010 )
0.087 (0.003)
0.104 (0.001)
0.061 (0.013)
0.091 0.147 0.050 (0.002)
(0.000) (0.025)
0.046 (0.031)
1
PE
Selective Stocking
Commo‐
nality
Turnover Curve
Product Pooling
Product Substitu‐
tion
Demand Reshape
Trans‐
ship‐
ments
Post‐
pone‐
ment
Virtual Pooling
Capacity Pooling
Central Ordering
Order Splitting
PE
1
1
0.066 (0.010)
0.087 0.046 (0.003) (0.031)
0.104 (0.001)
0.059 (0.015)
0.059 (0.015)
1
1
0.056 (0.017)
0.070 0.042 0.042 0.046 0.046 (0.008) (0.040) (0.040) (0.032) (0.032)
0.067 (0.009)
0.038 0.098 0.042 (0.049)
(0.002)
(0.039)
0.056 0.046 (0.017)
(0.031)
0.042 0.052 0.054 (0.039)
(0.022) (0.019)
0.052 0.104 0.163 0.058 1
(0.022) (0.001)
(0.000)
(0.016)
0.052 (0.022)
0.061 (0.013)
0.038 (0.049)
0.091 (0.002)
0.067 0.098 (0.009) (0.002)
0.147 0.070 (0.000) (0.008)
0.050 0.042 (0.025) (0.040)
0.042 (0.040)
0.046 (0.032)
1
0.112 (0.001)
0.042 0.104 0.112 (0.039) (0.001) (0.001)
1
0.163 (0.000)
0.095 (0.002)
0.042 0.046 0.052 0.058 (0.039) (0.031) (0.022) (0.016)
0.044 0.088 (0.034)
(0.003)
0.054 0.045 0.071 (0.019) (0.033) (0.007)
0.054 (0.020)
0.087 (0.003)
0.095 (0.002)
1
0.135 (0.000)
0.071 0.044 (0.007) (0.035)
0.135 (0.000)
0.139 (0.000)
0.116 0.042 0.101 (0.001) (0.040) (0.001)
1
0.054 0.087 (0.019)
(0.003)
0.044 0.054 0.139 0.116 (0.034) (0.019)
(0.000)
(0.001)
0.045 0.071 0.042 (0.033)
(0.007)
(0.040)
0.088 0.071 0.054 0.044 0.101 (0.003) (0.007) (0.020)
(0.035)
(0.001)
1
1
1
0.072 (0.007)
0.072 (0.007)
1
Table A.2: Significant Correlations at the 5 % Level of the Knowledge of Risk Pooling Concepts
a. Goodman and Kruskal’s Tau
b. Approximative significance based on chi-square approximation.
2.2.3
Association between Knowledge and Utilization of Risk Pooling
Concepts
There is a strong highly significant correlation between the knowledge of a risk pooling concept and its application as the diagonal in the correlation matrix in Table A.3 at the end of this
section shows. This suggests that increasing practitioners' knowledge and understanding of risk
pooling by praxis-oriented research may increase its application. The strongest correlation exists between the knowledge and the application of virtual pooling (τ = 0.431, p = 0.000). That
means the error of predicting the variable utilization of virtual pooling can be reduced by
43.1 %, if the distribution of the variable knowledge of virtual pooling is known. Forty-six of
the 65 respondents who know virtual pooling also apply it. Of the 37 respondents who do not
know virtual pooling 36 also do not apply it. Consequently, one professional did not recognize
the concept perhaps by its name, but when reading the explanation he came to realize that his
154
Appendix A
company applies this concept. There are a few cases like that pertaining to the other risk pooling concepts as well.
The next highest correlations exist between the knowledge and application of the SRL
(τ = 0.319, p = 0.000) and of commonality (τ = 0.317, p = 0.000).
The recognition of transshipments is significantly correlated with both the application
of selective stocking (τ = 0.088, p = 0.003) and risk pooling (τ = 0.071, p = 0.008), the
knowledge of postponement with the use of risk pooling (τ = 0.079, p = 0.005). This
highlights again that the respondents seem to mainly associate the popular concepts of
postponement and transshipments with risk pooling. The knowledge of transshipments
might favor the implementation of selective stocking, since products have to be exchanged
between locations as they are only stored at few locations for economical reasons.
Utilization Risk Pooling
Utilization Knowledge SRL
PE
Selective Commo‐ Turnover Product Product Demand Trans‐ Post‐ Virtual Capacity Central Order Centra‐ Centra‐ Decentra‐ Decentra‐
Stocking nality
Curve Pooling Substitu‐ Reshape ship‐ pone‐ Pooling Pooling Ordering Splitting lization lization lization lization future
past
past future
ments ment
tion
a Risk Pooling
0.202
b
(0.000 )
0.319 (0.000)
SRL
0.047 (0.029)
0.291 (0.000)
PE
Selective Stocking
0.292 (0.000)
0.317 (0.000)
Commonality
Turnover Curve
Product Pooling
Product Substitution
Demand Reshape
Transship‐
ments
0.288 (0.000)
0.053 (0.021)
0.039 (0.048)
0.098 (0.002)
0.119 (0.001)
0.041 (0.043)
0.071 (0.008)
0.079 Postponement
(0.005)
Virtual Pooling
0.058 (0.016)
0.088 (0.003)
0.037 (0.054)
0.151 (0.000)
0.041 (0.042)
0.304 (0.000)
0.178 (0.000)
0.045 (0.032)
Capacity Pooling
Central Ordering
0.039 (0.047)
0.431 (0.000)
0.301 (0.000)
Order Splitting
0.128 (0.000)
0.141 (0.000)
Table A.3: Significant Correlations at the 5 % Level (except in the case Product Substitution/Demand Reshape) between Knowledge and Utilization of Risk Pooling Concepts
a. Goodman and Kruskal’s Tau
b. Approximative significance based on chi-square approximation.
155
Appendix A
2.2.4
Association of the Utilization of Different Risk Pooling Concepts
Most significantly and strongly associated is past decentralization with future decentralization
(τ = 0.253, p = 0.000), the utilization of product substitution and demand reshape (τ = 0.212,
p = 0.000), past centralization and decentralization (τ = 0.185, p = 0.000), the application of the
inventory turnover curve and transshipments (τ = 0.132, p = 0.000), commonality and product
pooling (τ = 0.127, p = 0.000), risk pooling and transshipments (τ = 0.121, p = 0.000), the
turnover curve and order splitting (τ = 0.117, p = 0.001), selective stocking and virtual pooling
(τ = 0.113, p = 0.001), transshipments and virtual pooling (τ = 0.113, p = 0.001), risk pooling
and postponement (τ = 0.109, p = 0.001), product substitution and transshipments (τ = 0.096,
p = 0.002), as well as product substitution and virtual pooling (τ = 0.096, p = 0.002) and vice
versa as shown in Table A.4 at the end of this section.
Eighty-four (99 %) of the 85 companies which did not decentralize in the past do not
intend to decentralize in the future. Eleven of the 17 companies which did decentralize will
continue to decentralize in the future. Eighty-four (88 %) of the 95 companies which do
not intend to decentralize their warehouse or logistics system, did not decentralize in the
past either. Six (86 %) of the seven companies planning to decentralize in the future, already decentralized in the past. It seems that these companies follow their warehouse or
logistics system strategy of decentralization or no decentralization consistently over time.
Fifty-one (94 %) of the 54 respondents who do not apply product substitution do not
apply demand reshape either. Twenty of the 48 respondents using product substitution
use demand reshape as well. Fifty-two of the 80 companies which do not reshape demand
do not substitute products in case of a stockout either. Twenty of the 22 demand reshaping
companies also use product substitution. It seems that companies which do not persuade
customers to buy a substitute product in case of a stockout mostly do not do so either, if the
desired product is available. This might occur, if a company does not sell substitute products. Ninety-one percent of demand reshapers also apply product substitution, perhaps because both strategies are similar in that they both substitute products.
If a company centralized in the past (49 companies), there was absolutely no decentralization in the past. If a company conducted no centralization in the past, there was mostly no decentralization either: Of the 53 companies which did not centralize in the past only
17 decentralized in the past, 36 ones (68 %) did not. Past centralization and decentralization thus show a rather negative correlation as the Phi value of -0.430 (p = 0.000) sug-
156
Appendix A
gests889. Forty-nine (58 %) of the 85 companies which did not decentralize centralized in
the past and none of the 17 companies which decentralized centralized in the past. It appears that decentralization excludes centralization and vice versa. The strategy of decentralization, centralization, or no change is followed fairly consistently over time.
Thirty-four (97 %) of the 35 companies which do not transship do not use the inventory
turnover curve. Forty-three of the 67 transshipping companies utilize the turnover curve.
Thirty-four of the 77 responding companies which do not use the inventory turnover curve
do not take advantage of transshipments either. Twenty-four (96 %) of the 25 companies
using the turnover curve transship. One could assume that companies using the inventory
turnover curve attach great importance to inventory turnover. If therefore they tend to
mainly store fast movers at every location, this might explain why they also use transshipments to exchange e. g. slow movers between locations.
Forty (77 %) of the 52 companies which have not implemented component commonality do not use product pooling. Twenty-nine of the 50 companies using common components also use product pooling. Forty of the 61 companies which have not implemented
product pooling have not implemented component commonality either. Twenty-nine
(71 %) of the 41 product pooling companies use common components as well. This comes
as no surprise as product pooling may rely on common components to satisfy customers
that were previously offered their own product variant with a single common product890.
Furthermore, both methods take advantage of standardization. “[S]tandardization enables
risk pooling across products, leading to lower inventories, and allows firms to use the information contained in aggregate forecasts more effectively”891.
Thirty-one (89 %) of the 35 companies not relying on transshipments likewise declared that they did not apply risk pooling. Thirty-one of the 67 companies using transshipments also use risk pooling. Thirty-six of the 67 companies which indicated that they
are not using risk pooling do not use transshipments either. Thirty-one (89 %) of the 35
ones using risk pooling do use transshipments as well. This highlights again that the responding professionals strongly associate risk pooling with transshipments.
Fifty-seven (74 %) of the 77 companies which do not use the turnover curve do not
apply order splitting either. Sixteen of the 25 companies employing the turnover curve
split orders as well. Fifty-seven (86 %) of the 66 companies not splitting orders do not use
889
890
891
Although we deal with nominal variables, we can exceptionally refer to a negative correlation here (cf.
Schulze 2007: 127).
Cachon and Terwiesch (2009: 330, 335).
Simchi-Levi et al. (2008: 357), cf. Reiner (2005: 434), Sheffi (2006, 2007: 186-193).
157
Appendix A
the turnover curve. Sixteen of the 36 companies that utilize order splitting use the inventory turnover curve as well. Splitting an order into multiple orders or goods receipts may not
only decrease supplier lead time variability but also reduce average inventory and therefore
increase inventory turnover. The inventory turnover is reflected in the inventory turnover
curve. Inventory policies, which may be determined and controlled with the inventory
turnover curve, might lead to order splitting.
Twenty-seven of the 55 not virtually pooling companies do not store SKUs selectively
at warehouses. Thirty-nine (83 %) of the 47 companies which apply virtual pooling also
apply selective stocking. Twenty-five (71 %) of the 35 logistics professionals indicating
that their company does not rely on selective stocking do not pool virtually either. Thirtynine of the 67 companies using selective stock-keeping also apply virtual pooling. Virtual
pooling may entail selective stocking and vice versa: On the one hand, access to other locations' inventories via virtual pooling may favor a specialization in stock holding. On the
other hand, stocking products only at few locations due to cost considerations may necessitate that these locations can access each other's inventories. For instance, a company may
choose to stock only fast movers at all regional warehouses and have slow movers dropshipped to customers or cross-filled. Thus inventories and demands at different locations
are pooled virtually.
Seventy-seven percent (27) of the companies not using transshipments (35), do not pool
virtually either. Fifty-eight percent (39) of the companies transshipping (67) use virtual
pooling in addition. Twenty-seven of the 55 responding companies which do not use virtual pooling do not use transshipments either. However, thirty-nine (83 %) of the 47 virtually pooling companies rely on transshipments. Extending a company's warehouse or
warehouses beyond its or their physical inventory to the inventory of other own locations
or of other companies' locations via information technology and the internet (virtual pooling) often entails stock transfers between locations (transshipments). Virtual pooling resembles transshipments, if it comprises drop-shipping892 or cross-filling893.
Of the 67 respondents who indicated not having implemented risk pooling 51 ones
(76 %) have not implemented postponement either. Twenty (57 %) of the 35 ones who
use risk pooling also use postponement. Fifty-one (77 %) of the 66 survey participants indicating no postponement utilization also denied the use of risk pooling. Twenty (56 %) of
the 36 companies having implemented postponement also confirm the usage of risk pool892
893
Netessine and Rudi (2006: 845).
Ballou and Burnetas (2000, 2003), Ballou (2004b: 385-389).
158
Appendix A
ing. Consequently, the responding logisticians strongly associate risk pooling with postponement.
Twenty-six (74 %) of the 35 companies that do not use transshipments do not substitute products either. Thirty-nine of the 67 transshipping companies also use product substitution. Twenty-six of the 54 companies not substituting products do not use transshipments either. Thirty-nine (81 %) of the 48 product substitutionists use transshipments in
addition. This shows that product substitution and transshipments can be applied side by
side just like in the case of Papierco. For this company product substitution is the cheaper
option, so that it should only use transshipments as an alternative, if it is not possible to
substitute products in case of a stockout.
The same applies to virtual pooling: Thirty of the 48 companies which rely on product
substitution pool virtually as well. Thirty-seven (69 %) of the 54 ones not substituting
products, do not apply virtual pooling either. Thirty-seven (67 %) of the 55 companies not
pooling virtually do not use product substitution either. Thirty of the 47 ones pooling virtually also substitute products.
We can support Rabinovich and Evers' (2003b) finding that time postponement (emergency transshipments and inventory centralization) contributes to the implementation of
form postponement at best only weakly for our sample: Postponement is only weakly and
at the 5 % level just not statistically significantly associated anymore with transshipments
(τ = 0.035, p = 0.059) and selective stocking (τ = 0.035, p = 0.059). Twenty-eight (42 %)
of the 67 companies stocking selectively thereby centralizing inventory also apply postponement. Twenty-seven (77 %) of the 35 ones not using selective stocking do not use
postponement either. The same applies to transshipments.
Postponement is statistically significantly independent of past (τ = 0.000, p = 0.903)
and future centralization (τ = 0.009, p = 0.350). The contrary is true for its association with
risk pooling (τ = 0.109, p = 0.001) and component commonality (τ = 0.068, p = 0.009).
Forty of the 66 not postponing companies do not use component commonality. Twentyfour (67 %) of the 36 postponing companies also employ common components. Forty
(77 %) of the 52 companies not applying component commonality do not apply postponement either. Twenty-four of the 50 users of common components also rely on postponement. This shows that the implementation of postponement and commonality may go hand
159
Appendix A
in hand894 as we already highlighted describing the Risk Pooling Decision Support Tool.
The implementation of postponement may even require component commonality.895
Risk SRL
Pooling
Risk Pooling
SRL
Selective Commo‐ Turnover Product Product Demand Trans‐ Post‐ Virtual Capacity Central Order Centra‐ Centra‐ Decentra‐ Decentra‐
Stocking nality
Curve
Pooling Substi‐ Reshape ship‐ pone‐ Pooling Pooling Ordering Splitting lization lization lization lization future
tution
ments ment
past
future past
PE
a 1
0.066 (0.010)
PE
0.068 (0.009)
0.066
b
(0.010 )
0.052 (0.022)
1
0.077 (0.005)
0.051 (0.023)
1
Selective Stocking
Commo‐
nality
Turnover Curve
Product Pooling
Product Substi‐
tution
Demand Reshape
Transship‐
ments
Postpone‐
ment
Virtual Pooling
Capacity Pooling
Central Ordering
Order Splitting
Centra‐
lization past
Centra‐
lization future
Decentra‐
lization past
Decentra‐
lization future
1
0.068 (0.009)
0.127 (0.000)
0.121 (0.000)
0.109 (0.001)
0.059 (0.014)
0.069 (0.008)
0.113 (0.001)
0.04 0.132 (0.045) (0.000)
0.038 (0.049)
0.117 (0.001)
0.05 (0.025)
1
0.04 (0.045)
0.132 (0.000)
0.212 (0.000)
0.096 (0.002)
0.088 (0.003)
0.096 (0.002)
0.212 0.096 (0.000) (0.002)
0.096 (0.002)
0.079 (0.005)
0.113 (0.001)
1
1
0.068 (0.009)
0.069 (0.008)
0.088 (0.003)
1
0.077 0.051 (0.005) (0.023)
0.113 (0.001)
0.045 (0.033)
0.068 (0.009)
1
0.039 (0.047)
0.074 0.068 (0.006) (0.009)
0.039 0.074 (0.047) (0.006)
0.068 (0.009)
0.127 (0.000)
1
0.052 (0.022)
0.121 0.109 0.059 (0.000) (0.001) (0.014)
0.077 (0.005)
1
0.079 0.113 (0.005) (0.001)
0.117 (0.001)
0.079 (0.008)
1
1
0.052 (0.022)
0.052 (0.022)
1
0.079 (0.008)
0.058 (0.016)
1
0.058 (0.016)
0.185 (0.000)
1
1
0.045 (0.033)
0.05 (0.025)
0.077 (0.005)
0.038 (0.049)
0.185 (0.000)
1
0.253 (0.000)
0.253 (0.000)
1
Table A.4: Significant Correlations at the 5 % Level between the Utilization of Risk Pooling
Concepts
a. Goodman and Kruskal’s Tau
b. Approximative significance based on chi-square approximation.
894
895
Zinn and Bowersox (1988: 124f.), Lee (1996, 1998), Van Hoek (1998b, 2001: 173), Van Hoek et al.
(1998), Feitzinger and Lee (1997), Pagh and Cooper (1998), Swaminathan and Tayur (1998), Aviv and
Federgruen (2001a, 2001b: 579), Swaminathan (2001), Yang et al. (2005b: 993), Simchi-Levi et al.
(2008: 345).
Swaminathan (2001: 132), Simchi-Levi et al. (2008: 347).
160
Appendix A
2.2.5
Risk
Pooling
Knowledge
and
Utilization
in
the
Responding
Manufacturing and Trading Companies
Figure A.2: Risk Pooling Knowledge and Utilization in the Sample Manufacturing and
Trading Companies
161
Appendix A
When we subdivide the original sample for subanalyses in this section, we decrease our sample
size and therefore enlarge our confidence intervals896.
At the 5 % level Pearson's and Yates' chi-square and Fisher's exact test revealed significant differences between manufacturing and trading companies in employing product substitution (Pearson's chi-square χ2 = 8.01, degrees of freedom df = 1, p = 0.004652), commonality (χ2 = 7.84, df = 1, p = 0.00511), and transshipments (χ2 = 6.19, df = 1,
p = 0.012847), in the knowledge of commonality (χ2 = 5.47, df = 1, p = 0.019346), and in
the utilization of postponement (χ2 = 4.52, df = 1, p = 0.033501897) in descending order of
asymptotic significance (two-sided).
The 75 manufacturing companies surveyed know central ordering, product substitution,
selective stocking, and order splitting the most, followed by transshipments, product pooling, commonality, capacity pooling, virtual pooling, risk pooling, postponement, demand
reshape, the PE, inventory turnover curve, and SRL.
The 27 trading companies recognize central ordering, product substitution, selective
stocking, transshipments, order splitting, product pooling, the PE, virtual pooling, capacity
pooling, demand reshape, commonality, risk pooling, the inventory turnover curve, postponement, and the SRL in decreasing order of awareness.
The manufacturing and trading companies do not differ statistically significantly at the
5 % level in their knowledge of the various risk pooling concepts, except for commonality.
Seventy-six percent of the manufacturing and 52 % of the trading companies are aware of
this concept.
Selective stocking (63 %), central ordering (61 %), transshipments (59 %), and commonality (57 %) are the concepts most frequently applied by the manufacturers. Capacity
pooling (47 %), centralization, virtual pooling, product pooling, postponement, product
substitution, order splitting, risk pooling, the PE, inventory turnover curve, demand reshape, the SRL, and decentralization follow in order of descending employment.
Trading companies apply transshipments (85 %), central ordering (78 %), selective
stocking (74 %), and product substitution (74 %) the most, followed by centralization
(63 %), virtual pooling, order splitting, risk pooling, the PE, product pooling, demand reshape, commonality, capacity pooling, the inventory turnover curve, postponement, decentralization, and the SRL.
896
897
Vockell and Asher (1995: ch. 8).
However, in this case χY
= 3.58 with df = 1 and p = 0.058479, but p = 0.037049 in Fisher's exact test.
162
Appendix A
All concepts are more widely used in the trading companies than in the manufacturing
companies, except for the SRL, commonality, the inventory turnover curve, product pooling, postponement, and capacity pooling. As already mentioned above, this relationship is
statistically significant only for product substitution, commonality, transshipments, and
postponement at the 5 % level. This supports our hypothesis from the Risk Pooling Decision Support Tool that component commonality, postponement, and capacity pooling
are rather applied by manufacturers and might be more suitable in a manufacturing environment. However, the utilization of capacity pooling in manufacturing and trading
companies is just not statistically significantly different at the 5 % level anymore
(χ2 = 3.53, df = 1, p = 0.060268).
Forty-one percent of the manufacturing companies apply postponement. This matches
the more than 40 % of the manufacturers surveyed by Kisperska-Moroñ (2003: 131) in
Upper Silesia, Poland that gear total production towards customer orders.
Thirty-seven percent of the 27 electronics (classification numbers 30, 31, and 32) and
automotive (34) and 40 % of the five food (15) and clothing (18) manufacturers employ
postponement. Consequently, with our sample we cannot support at the 5 % level Van
Hoek (1998b), who finds that postponement is extensively applied in electronics and automotive and less extensively applied in food and clothing. The utilization of postponement by electronics and automotive and food and clothing manufacturers in our sample is
independent in the Fisher Exact Probability Test898 (p (two-tailed) = 1). It differs neither in
these two nor in the four groups significantly at the 5 % level. However, Van Hoek's
(1998b) observation may apply to the whole population, as the confidence interval for the
aforementioned conditions is very broad with 18.86 for electronics and automotive and
43.83 for food and clothing. For the same reasons as given earlier this confidence interval
can only serve as a crude estimate here. Only five answers from food and clothing manufacturers are probably not enough to compare postponement application between different
industrial sectors.
898
The Fisher Exact Probability Test is used, because some contingency table (crosstab) cells have expected
counts less than 5. Nevertheless, Pearson's and Yates' chi-square test led to the same conclusion.
163
Appendix A
2.2.6
Knowledge and Utilization of the Different Risk Pooling Concepts in
Small and Large Responding Companies
Figure A.3: Knowledge and Utilization of the Different Risk Pooling Concepts in Small and
Large Responding Companies
164
Appendix A
The answers of the 33 small (having less than 500 employees) and 69 large companies (having
500 or more employees according to the Deutsches Institut für Mittelstandsforschung (German
Institute for Midium-sized Businesses Research)) are independent (the null hypothesis that
there is no significant relationship between the answers cannot be rejected) in Pearson's and
Yates' chi-square and Fisher's exact test at the 5 % level, except for the usage of risk pooling
(χ2 = 5.63, df = 1, p = 0.017656), centralization in the past (χ2 = 4.75, df = 1, p = 0.029298),
and postponement (χ2 = 4.24, df = 1, p = 0.039482899). This means only for these last three
variables the distribution in the two groups of small and large companies differs statistically
significantly900, most significantly for risk pooling.
The small companies tend to have more knowledge of selective stocking, demand reshape, central ordering, product pooling, and order splitting, while a higher percentage of
large ones know the SRL and postponement. The large companies apply all concepts more
than small companies (especially risk pooling, postponement, transshipments, capacity
pooling, the PE, and product pooling) except for centralization in the past, demand reshape, commonality, product substitution, and central ordering in order of descending percentage difference of companies applying the respective concept. Hence, we can agree
with Huang and Li (2008b: 12) that large companies may apply postponement more than
small ones, since they may be better able to afford the redesign of products and/or
processes usually required by postponement901.
899
900
901
However, in this case χY
= 3.37 with df = 1 and p = 0.066394, but p = 0.047623 in Fisher's exact test.
This means that one can be certain that this statistic is dependable, the difference is genuine and not by
coincidence. It does not mean that the difference is large, important, or useful (Walonick 2009).
Ernst and Kamrad (2000), Aviv and Federgruen (2001b).
165
3
Critical Appraisal
We need to point out that the assumption of the significance test of random sample data may
be violated. For population data any crosstable differences are real and thus significant. With
non-random sample data we cannot establish significance.902 However, significance tests are
sometimes used as rough approximations.903 For criticism of significance testing you may e. g.
refer to Carver (1978), Cohen (1994), and Thompson (1996). Statistical significance does not
tell if a research's results will reoccur904 or the strength and generalizability of relationships in a
sample and hence may divert attention from more crucial concerns905.
Although a thorough research process was followed, the limited representativeness of
this survey has to be acknowledged. This should be remedied in another survey by a higher
response rate. However, this might be difficult, as response rates for academic studies are
low906 and have been declining over the last years907. Perhaps there are so few surveys in
logistical research, since it is very difficult to obtain a random or at least representative
sample because of low response rates as we experienced. A lot of companies are swamped
with surveys and/or have a policy of not answering surveys. Some researchers pay companies to take part in surveys or give them other perquisites, which might also lead to a response bias. Practitioners should not criticize business research as too theoretical on the
one hand and not take part in surveys on the other hand.
As it is laborious to design and administer surveys, the usually low response rates disappoint the researcher and “imperil the strength of the research findings”908, and survey
research is prone to so many biases and errors909, one perhaps should consider other empirical research. Netessine (2005: 6), for instance, suggests using university research database, publicly available, consulting company, or industry journal data. Still for a Ph.D.
student with little funds it is difficult to access some of these data sources that are subject
to charges.
Besides, some specific data are not available at all or insufficient. For example, we
could not obtain any information about the number of warehouses from business and logis902
903
904
905
906
907
908
909
Garson (2009).
Dorofeev and Grant (2006: 253f.), Garson (2009).
Carver (1978).
Thompson (1994).
Bickard and Schmittlein (1999), Goldsby and Stank (2000).
Baruch (1999).
Griffis et al. (2003: 237).
Groves et al. (2004: 39ff., 377f., 380).
166
Appendix A
tics associations and federal statistical offices in Germany and the U.S. to derive how inventories changed in dependence of the number of warehouses compared to SRL predictions or how the number of warehouses changed over time. Some researchers expected the
number of warehouses to increase with increasing fuel costs.
Furthermore, the number of companies in the industrial sectors in different publications
of the German Federal Statistical Office differs, as it receives its information from different
data sources. If the industrial sectors are broken down further, only companies with 20 or
more employees are considered.910 If all companies with any number of employees are
considered, they are not subdivided into detailed industrial sectors.911 This impaired our
retrospective quota sampling.
Another survey could also shed light onto the companies' reasons for and against as well
as the manner, degree, benefits, and costs of applying the risk pooling concepts, as we intended in the six-page version of this survey that yielded a uselessly low response rate. As
risk pooling can affect the whole supply chain, another survey could consider a supply
chain wide perspective rather than single companies.
A lot of respondents do not perceive all the questioned concepts as risk pooling ones. It
appears that mainly transshipments and postponement are associated with risk pooling.
Although at least in our sample the risk pooling concepts are known fairly well (central
ordering, product substitution, and selective stocking the most), only selective stocking,
transshipments, and central ordering are widely applied. Transshipments912 are more important and applied, postponement913 and product pooling914 less than suggested by some
publications mostly for other regions.
Nearly half the sample centralized its warehouse or logistics system in the past. This is
less than overall in Europe915. In contrast to the expected trend to decentralize due to increasing transportation costs, only seven percent will increase, six percent even decrease
the number of warehouse or production locations in the future. It seems that the companies
are very consistent in their strategy of centralization, decentralization, or no change over
time.
910
911
912
913
914
915
For example Statistisches Bundesamt Deutschland (2009i: 371).
For example Statistisches Bundesamt Deutschland (2009i: 378).
CLM (1995), Herer et al. (2006).
CLM (1995: 209), McKinnon and Forster (2000: 5), Chiou et al. (2002), Alfaro and Corbett (2003: 12),
Oracle (2004), Huang and Li (2008b).
Alfaro and Corbett (2003: 12).
CLM (1995).
167
Appendix A
The utilization and knowledge of a risk pooling concept are correlated. This suggests
that improving the knowledge about risk pooling may increase its application. Research
needs to convey to practitioners under what conditions and how the different risk pooling
concepts can be applied successfully. This research constitutes one step in this direction.
Prominently associated is past decentralization with future decentralization, the utilization of product substitution and demand reshape, past centralization and decentralization
(the only negative correlation), the application of the inventory turnover curve and transshipments, commonality and product pooling, risk pooling and transshipments, the inventory turnover curve and order splitting, selective stocking and virtual pooling, transshipments and virtual pooling, risk pooling and postponement, product substitution and transshipments, product substitution and virtual pooling, as well as postponement and commonality and vice versa.
We can support Rabinovich and Evers' (2003b) finding that time postponement (emergency transshipments and inventory centralization) contributes to the implementation of
form postponement at best only weakly for our sample.
Trading companies seem to apply transshipments and product substitution more than
manufacturing companies. The opposite is true for commonality and postponement. In
contrast to Van Hoek (1998b) our sample shows no significant difference in the application
of postponement by electronics, automotive, food, and clothing manufacturers.
More large companies appear to use risk pooling and postponement than smaller ones,
perhaps because they can afford to invest in expensive risk pooling strategies as suggested
by Huang and Li (2008b: 12). More small companies have centralized their warehouse or
logistics system in the past than large ones in our sample.
Our survey shows that different risk pooling methods are and can be applied together as
we already suggested in the Risk Pooling Decision Support Tool and the Papierco example.
168
4
Questionnaire
Survey on Risk Pooling in Business LogLVWLFV
by Dipl.-Kfm. Gerald Oeser
1 Line of business
2 Number of employees in Germany
3 Your position (e. g. logistics manager)
Do you know the following concepts? Does your company use them?
Known?
4 Risk Pooling (Demand and/or lead time variability is reduced, if one aggregates demands and/ Yes
No
or lead times e. g. across locations, because it becomes more likely that higher-than-average demands and/or lead times will be offset by lower-than-average ones. This reduction in variability allows
to reduce safety stock and therefore reduces average inventor y without reducing the service level.)
5 Square Root Law (Total (safety) stock in n warehouses = (safet y) stock in 1 centralized
Yes
warehouse * square root of the number of warehouses n.)
No
6 The Portfolio Effect shows the reduction in aggregate safety stock by consolidating several ware- Yes
houses' inventories in one warehouse in percent.
No
7 Selective Stock Keeping/Specialization (Reducin g inventory carr ying cost treating products
Yes
differently without reducing the service level substant ially. For example, products with a low turnNo
RYHU PLJKWRQO\EHVWRFNHGDW IHZORFDWLRQVGXH WRFRVWFRQV LGHUDWLRQV
8 Component Commonality (Products are designed sharing com ponents. This reduces the va- Yes
riability of demand.)
No
9 The Inventory Turnover Curve shows average inventory in dependence of the inventory Yes
throughput for a specific company. It can be used to estimate the average inventory for any
No
(planned) warehouse throughput (shipments from the warehouse or sa les).
10 Product Pooling (Unification of several prod uct designs to a single generic or universal design Yes
or reducing the number of products thereby serving dem ands that were previously served by their No
own product version with fewer products.)
11 Product Substitution (One tries to make custom ers buy another alternative product, becauseYes
the original customer wish is out of stock
No
12 RU DOWKRXJKWKHRULJLQDOFXVWRPHUZLVKLVDYDLODEOH'HPDQG 5HVKDSH 7KLV UHGXFHV YDULDELOL Yes
No
ty of demand and inventory costs .)
13 Transshipments/Inventory Sharing Inventor y transfers among locations (e. g. between Yes
warehouses or stores) for example in case of a stock out.
No
14 Delayed Product Differentiation and Postpon ement 3RVWSRQHPHQWRIHJPDQXIDFWXULQJ
DVVHPEO\SDFNDJLQJODEHOLQJRUGHOLYHU\3URGXFWFXVWRPL]DWLRQVKRXOGEHGHOD\HGDVORQJDVSRVVLYes
EOH 7KLV DOORZV WR VKLS D VLQJOH JHQHULF SURGXFW IXUWKHU GRZQ WKH VXSSO\FKDLQDQGWRFKDQJHLW No
ODWHULQWRLQGLYLGXDOSURGXFWV DFFRUGLQJ WR UHFHQW GHP DQG LQIRUP DWLRQ 'HP DQG IRU LQGLYLGXDOSUR
GXFWV LV DJJUHJDWHG WRWKH GHPDQG IRU WKH JHQHULF SURGXFWRQSUHFHGLQJVXSSO\FKDLQVWDJHV
$JJUHJDWHGGHPDQGIRUWKHJHQHULFSURGXFWIOXFWXDWHVOHVV VLQFHVWRFKDVWLFIOXFWXDWLRQVRIWKHLQGL
YLGXDOGHPDQGVDUHRIIVHWWRDFHUWDLQH[WHQW,QYHQWRU\FDUU\LQJFRVWVDQGVWRFNRXWVFDQEHUHGXFHG
15 Virtual Inventory/Warehouse/Pooling: $ FRPSDQ\ H[WHQGV LWVZDUHKRXVHVEH\RQGWKH
Yes
SK\VLFDO LQYHQWRU\ WR WKH LQYHQWRU\ RI RWKHU RZQ ORFDWLRQV RU RI RWKHU FRP SDQLHV
ORFDWLRQVXVLQJ No
LQIRUPDWLRQDQGFRPPXQLFDWLRQWHFKQRORJ LHVGURSVKLSSLQJDQGFURVVILOOLQJ
16 Capacity Pooling &RQVROLGDWLRQRISURGXFWLRQVHUYLFHRUZDUHKRXVHFDSDFLWLHVRIVHYHUDO
Yes
No
IDFLOLWLHV:LWKRXW SRROLQJ HYHU\ IDFLOLW\ IXOILOOV GHP DQG MXVW ZLWK LWV RZQ FDSDFLW\:LWKSRROLQJ
GHPDQGLVDJJUHJDWHGDQG IXOILOOHG E\ D VLQJOH SHUKDSV YLUWXDOO\ MRLQW IDFLOLW\$KLJKHUVHUYLFH
OHYHOFDQEHDWWDLQHGZLWKWKHVDPHFDSDFLW\RU WKH VDP H VHUYLFH OHYHO FDQ EH RIIHUHGZLWKOHVV
FDSDFLW\
17 Central Ordering for several locations and later allocation of the orders (perhaps by a depot) Yes
No
to the distribution points or requisitioners according to recent demand inform ation.
18 Order 6plitting LVSDUWLWLRQLQJDUHSOHQLVKPHQWRUGHULQWRPXOWLSOHRUGHUVZLWKPXOWLSOHVXSSOLHUVRU Yes
LQWRPXOWLSOHGHOLYHULHV
No
19 a) Did you centralize your warehouse/logistics system (reduce the number of warehouse or
production locations)?
b) Do you intend to centralize your warehouse/logistics system?
20 a) Did you decentralize your warehouse/logistics system (increase the number of warehouse
or production locations)?
b) Do you intend to decentralize your warehouse/logistics system?
In
use?
Yes
No
Yes
No
Yes
No
Yes
No
Yes
No
Yes
No
Yes
No
Yes
No
Yes
No
Yes
No
Yes
No
Yes
No
Yes
No
Yes
No
Yes
No
Yes
No
Yes
Yes
No
Yes
No
No
Please push to send answers
Figure A.4: Questionnaire
169
Answers
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1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Order Splitting
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
Central Ordering
0
1
0
1
0
1
0
1
0
0
0
1
1
1
1
1
0
1
1
0
1
0
0
1
1
0
1
0
1
1
1
1
0
0
1
1
0
0
1
1
1
1
0
1
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
1
1
1
0
0
0
1
0
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
Virtual Pooling
1
1
1
1
0
1
0
1
0
1
1
0
1
1
1
0
0
1
1
1
0
0
0
1
1
0
1
1
1
1
1
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
1
1
1
1
1
0
1
1
1
0
1
1
0
0
1
0
1
1
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
1
0
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
Capacity Pooling
Postponement
1
0
1
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
1
0
1
0
1
1
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
1
1
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
1
0
1
1
1
1
1
0
0
0
1
1
1
1
1
1
0
1
1
1
1
1
Transshipments
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
0
0
0
1
0
0
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
0
1
1
0
1
0
0
1
1
1
1
1
1
0
0
1
1
1
1
1
0
1
1
1
0
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Demand Reshape
1
1
1
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
1
1
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
0
1
1
0
1
0
1
0
1
1
0
1
1
1
1
0
1
0
1
1
1
1
1
0
1
1
0
0
1
1
0
0
1
1
0
1
1
0
0
1
1
0
1
1
Product Substitution
Postponement
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Product Pooling
Transshipments
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
0
0
0
0
1
0
1
1
0
1
1
1
1
0
1
1
0
1
1
1
1
0
1
1
0
1
1
1
1
0
0
1
0
1
0
0
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
Turnover Curve
Demand Reshape
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
1
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
1
1
0
0
1
0
0
1
1
1
1
0
0
1
0
1
1
0
1
Commonality
Product Substitution
0
1
1
1
1
1
1
1
1
1
0
0
1
1
1
0
1
0
0
0
1
0
0
1
1
0
1
1
1
1
1
1
0
0
1
0
0
1
1
1
0
1
1
1
1
1
0
0
1
1
0
0
0
1
0
1
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
1
0
1
0
1
1
Selective Stocking
Product Pooling
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
1
1
0
1
1
0
1
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
PE
Turnover Curve
1
1
1
1
1
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
1
0
0
1
1
1
0
0
1
1
1
1
1
1
0
1
1
0
0
1
1
0
1
0
1
1
1
0
1
1
0
1
0
1
SRL
Commonality
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
Risk Pooling
Selective Stocking
1
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
1
0
0
1
1
1
1
1
1
1
0
0
1
1
0
1
0
1
1
0
0
1
0
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
Order Splitting
PE
16,000
5
2,000
3,000
100
60
190
2,000
50
120
133,000
78,000
500
150
100
1,600
13,000
9,000
121,000
30
120
143
1,500
47,296
1,000
170,000
20
150
65
346
2,500
500
2,000
600
12,000
22
20
114,000
800
100
7,000
10,000
25,103
500
120
12,000
2,000
36,000
12,600
15,000
200
550
5,000
2,000
73,000
8,000
95,500
10,000
3,000
14,000
100
50
900
66,000
10
150
150
27,000
37,000
29,000
850
1,000
20
1,200
7,000
50,000
9,500
110
60,000
50
850
12,800
1,980
3,000
10,767
6,342
242
107
40
65
5,700
3,200
956
1,000
60,000
1,850
60,000
6,000
4,500
9
182,739
1,652
Central Ordering
SRL
52.42
52.42
29
29
29
34
25
31
31
37
33
34
32
29
52.42
30
34
37
52.11 51.46
45.2
25
35
29
31
52.11 52.42
52.11 52.11 28
16
15
34
29
52.42
51.53.1
51.46
29
15
21
52.42
34
34
37
36
34
15
29
32
52.11 31
31
34
34
52.11 35
34
52.42
35
52.46
33
24
28
40
27
31
28
34
34
52.42
22
26
31
28
11
29
51.53.1
52.48.6 24
52.11 29
29
18
15
24
52.42
36
29
51.88
51.47.8
21
22
52.42
29
34
40
32
32
32
51.47.8
34
51.47.8
Virtual Pooling
Risk Pooling
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
Capacity Pooling
Employees
UTILIZATION
Industry classification
KNOWLEDGE
Respondent
5
1
1
1
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
1
1
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
0
0
1
1
1
1
1
1
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
1
1
0
1
1
0
1
1
1
1
0
0
1
0
1
0
1
1
0
1
1
1
1
1
0
1
1
1
1
0
0
0
1
1
1
0
0
1
1
1
1
1
0
1
1
1
0
1
0
0
0
0
1
1
1
1
0
1
0
1
1
0
0
0
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
0
0
1
1
0
0
1
1
1
0
1
1
1
0
1
1
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
1
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
1
0
1
0
0
0
1
0
0
1
1
1
1
1
0
1
0
1
1
1
0
1
0
0
1
0
0
1
0
1
1
1
1
0
1
1
1
1
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1 = Yes, 0 = No
170
Appendix A
Industry Classification Description
11
Extraction of crude petroleum and natural gas; service activities incidental to oil and gas extraction, excluding surveying
15
Manufacture of food products and beverages 16
Manufacture of tobacco products 18
Manufacture of wearing apparel; dressing and dyeing of fur
21
Manufacture of pulp, paper and paper products 22
Publishing, printing and reproduction of recorded media 24
Manufacture of chemicals and chemical products 25
Manufacture of rubber and plastic products 26
Manufacture of other non‐metallic mineral products 27
Manufacture of basic metals 28
Manufacture of fabricated metal products, except machinery and equipment 29
Manufacture of machinery and equipment n.e.c. 30
Manufacture of office machinery and computers
31
Manufacture of electrical machinery and apparatus n.e.c. 32
Manufacture of radio, television and communication equipment and apparatus 33
Manufacture of medical, precision and optical instruments, watches and clocks 34
Manufacture of motor vehicles, trailers and semi‐trailers 35
Manufacture of other transport equipment 36
Manufacture of furniture; manufacturing n.e.c. 37
Recycling
40
Electricity, gas, steam and hot water supply 45.2
Building of complete constructions or parts thereof; civil engineering 51.46
Wholesale of pharmaceutical goods 51.47.8
Wholesale of paper and paperboard, stationery, books, newspapers, journals and periodicals 51.53.1
Non‐specialized wholesale of wood, construction materials and sanitary equipment 51.88
Wholesale of agricultural machinery and accessories and implements, including tractors 52.11 Retail sale in non‐specialized stores with food, beverages or tobacco predominating 52.42
Retail sale of clothing 52.46
Retail sale of hardware, paints and glass 52.48.6 Retail sale of games and toys Table A.5: Survey Participants' Answers to the Questionnaire
171
Appendix B: Proof of the Square Root Law for Regular,
Safety, and Total Stock
Based on a numerical example in Ballou (2004b: 379f.) and in a manner different from the
flawed916 one in Maister (1976), we formally prove that under certain assumptions the SRL
applies to regular, safety, and total stock.
Let average regular stock at location i be the economic order quantity (EOQ) Qi divided
by two:
(B1)
,
where di is demand at warehouse i, S the fixed order cost, I the inventory carrying cost rate and
C the product value per unit. Regular system inventory for n decentralized warehouses equals
∑
∑
(B2)
.
Regular stock in one centralized warehouse is
916
Das (1978: 334) correctly remarks “But Maister's proof is incorrect due to a combination of faulty algebra
and possible misprints” without pointing out the mistakes. Indeed, we found e. g. that it is supposed to be
∑
∑
...
instead of
...
(Maister 1976: 129) and
∑
∑
∑
instead of ∑
(Maister 1976: 130). The expression
∑
∑
∑
(Maister 1976: 130) is also in-
correct. Furthermore, it has to be 0.2
0.005 instead of 0.02
0.005 (Maister 1976: 129).
Changing a three-location to a one-location system reduces inventory by 42 (not 43) % and changing a
ten-location to a four-location system reduces inventory by 37 (not 38) % according to the SRL (Maister
1976: 131). Maister (1976: 132) wrongly states
∑
∑
√ , although he ear-
1 (Maister 1976: 127). He also explains “If the original decentralised system had 16
lier notes that ∑
locations, and inventory costs account for one-half of total costs in this system, then inventory savings
from centralisation equal
1
. But transportation must represent 1
, or
√
in the decentralised system. Hence, we can afford to almost double transportation expenses and still retain
a system cost less than in the original system” (Maister 1976: 133). However, we can only afford 1.75
times and not almost double the transportation cost or, in other words, we could only increase transportation cost by 75 % at the most. But if all inventory savings were spent on increased transportation costs,
we would not retain a system cost less than in the original system. The centralized and decentralized system costs would be equal and we would be indifferent between them.
1 and incorrectly uses the equality instead of the apNevertheless, Das (1978: 333) also misprinted
proximation sign, although the power (square root) function cannot equal a linear one. Furthermore,
, ,...,
should be , , . . . , and ∑
should be ∑
(Das 1978: 334). Das (1978: 332) also
refers to a proof to his solution in the appendix, but the journal does not contain it. Professor emeritus
Chandrasekhar Das, College of Business Administration, University of Northern Iowa, Department of
Management, agreed with us and kindly rewrote the proof, as it was not available at the publisher anymore in 2009 (personal correspondence on February 27, 2009).
172
Appendix B
∑
∑
(B3)
.
Regular stock in one centralized warehouse times a factor α equals regular system stock
in n decentralized warehouses:
∑
·
∑
∑
·
∑
(B4)
∑
·
∑
∑
.
∑
If demand at each warehouse is equal (d), the regular system inventory for n decentralized warehouses equals the one in one centralized warehouse times the square root of the
number of warehouses n:
·
∑
√
·
∑
√
·
√
·√
√ √ √
√ √
(B5)
.
This means the SRL applies to regular stock, if an EOQ order policy is followed, the
fixed cost per order and the per unit stock holding cost (inventory carrying cost rate times
the product value per unit), demand at every location, and total system demand is the same
both before and after centralization.917 However, according to Maister (1976: 128f.) the
SRL can also be “a good approximation when demand rates at all the field locations are not
equal”.
If regular inventory in each of n locations in the decentralized system (RSs) is considered the following relationship holds:
·√
·√
√ √
√ .
√
This corresponds to equation 9-28 in Ballou (2004b: 380):
(B6)
√ .
Safety stock in warehouse i is
√
(B7)
,
where z is the same safety factor for every warehouse, sdi the standard deviation of demand at
warehouse i, and LT the constant replenishment lead time for every warehouse.
System safety stock in n decentralized warehouses is
√
917
∑
.
(B8)
Cf. Maister (1976: 125, 127, 131).
173
Appendix B
If the demands are uncorrelated, safety stock in the centralized warehouse is
√
∑
(B9)
.
Safety stock in one centralized warehouse times a factor α equals systemwide safety
stock in n decentralized warehouses:
·
∑
√
√
√
∑
∑
∑
∑
·
∑
√
·
∑
.
∑
(B10)
If the standard deviation of demand at each warehouse is equal (sd), the systemwide
safety stock in n decentralized warehouses is equal to the safety stock in one centralized
warehouse times the square root of the number of warehouses n:
·
∑
·
∑
·
√ √
√
·
·√
√
(B11)
.
This means the SRL applies to safety stock, if demands at the decentralized locations
are uncorrelated918, the variability (standard deviation) of demand at each decentralized
location919, the safety factor (safety stock multiple)920 and average lead time are the same
at all locations both before and after consolidation, average total system demand remains
the same after consolidation921, no transshipments occur922, lead times and demands are
independent and identically distributed random variables and independent of each other923,
the variances of lead time are zero924, and the safety-factor (kσ) approach is used to set
safety stock for all facilities both before and after consolidation925.
If demands at the warehouses are correlated, the SRL does not even yield an approximation. The safety stock savings through centralization decrease with increasing correlation
between demands at the warehouses and become zero with perfectly positive correlation.926
Total inventory is the sum of regular and safety stock.927 Therefore total inventory in the
decentralized system TId with n warehouses equals total inventory in one centralized warehouse TIc times the square root of the number of warehouses n:
918
919
920
921
922
923
924
925
926
Maister (1976: 132).
Maister (1976: 130).
Maister (1976: 132).
Evers and Beier (1993: 110), Evers (1995: 4).
Zinn et al. (1989: 2), Evers and Beier (1993: 110), Evers (1995: 4).
Evers and Beier (1993: 110), Evers (1995: 4).
Zinn et al. (1989: 2), Evers and Beier (1993: 110), Evers (1995: 4).
Maister (1976: 129).
Maister (1976: 130).
174
Appendix B
·√
·√
·√
·√ .
(B12)
The SRL applies to total inventory, if the assumptions stated above of the SRL both as
applied to regular and safety stock hold. For a critical review of these assumptions please
refer to Maister (1976: 125, 132f.), Das (1978: 331f.), McKinnon (1989: 102ff.), and Evers
(1995: 2, 14f.).
It should be checked whether the conditions or assumptions necessary for the SRL to hold
(necessary conditions) are also sufficient conditions, i. e. whether, if the SRL holds, these conditions also automatically apply. This analysis, however, is beyond the scope of this thesis.
Ballou (2004b: 380) incorrectly states “The square-root rule […] measures only the
regular stock reduction, not both regular and safety stock effects […]. Assuming that an
inventory control policy based on the EOQ formula is being followed and that all stocking
points carry the same amount of inventory, the square-root rule can be stated as follows:
√ […]
where
AILT = the optimal amount of inventory to stock, if consolidated into one location in dollars,
pounds, cases, or other units
AILi = the amount of inventory in each of n locations in the same units as AILT
n = the number of stocking locations before consolidation”.
Traditionally the SRL has been mainly applied to safety stock, but as proven above it is also
valid for regular stock or both regular and safety stock, if the respective necessary assumptions
stated above hold. If it is only applied to regular stock as in Ballou's case, all the assumptions of
the SRL as applied to regular stock enumerated above must apply, not only the two mentioned
by Ballou here. Ballou's formulation of the second assumption may confuse, as Maister (1976:
125) assumes “the demand rates at all the field locations are equal”.928
927
Ballou (2004b: 380). Total inventory might also include pipeline, speculative, and obsolete stock (Ballou
2004b: 330f.), which is neglected here.
928
Professor emeritus Ronald H. Ballou, Weatherhead School of Management, Case Western Reserve University, agreed with us in a personal correspondence on May 15, 2007.
175
Appendix C: What Causes the Savings in Regular Stock
through Centralization Measured by the SRL?
The total EOQ in the decentralized system is
∑
.
(C1)
.
(C2)
The EOQ in the centralized system is
∑
Due to the subadditive property of the square root, the sum of the square root of the demands at the locations i is greater than or equal to the square root of the sum of these demands:
∑
∑
(C3)
.
Therefore, the total EOQ in the decentralized system (the sum of the EOQs of the locations i) is greater than or equal to the EOQ in the centralized system:
∑
∑
(C4)
.
However, the total EOQ in the decentralized and centralized system are only equal, if
demands or demand forecasts at at least n-1 locations are zero929, which is unusual: ∑
∑
∑
2∑
∑
∑
∑
∑
∑
∑
0.
(C5)
If n-1 di equal zero, (C4) becomes
(C6)
for this single non-zero di. If all di are zero, (C4) becomes
0
.
(C7)
Therefore, if demands (at at least two locations) are larger than zero, the EOQ and
therefore the average regular inventory and thus the inventory holding costs are lower in
the centralized system. However, under the above condition the EOQ per decentralized
location i is less than the one for the centralized one, as n > 1:
929
This theoretically questions Wanke and Saliby's (2009: 680) general statement that “[t]he cycle stock
savings are based on the fact that the square-root of the aggregate demand is always smaller than the sum
of the square roots of individual demands”.
176
Appendix C
∑
∑
∑
.
(C8)
The total number of orders in the decentralized system is
∑
∑
∑
∑
.
(C9)
The number of orders in the centralized system is
∑
∑
∑
.
∑
(C10)
Due to the subadditive property of the square root, the total number (the sum of the
numbers) of replenishment orders in the decentralized system is greater than or equal to the
number of orders in the centralized one:
∑
∑
∑
∑
.
(C11)
In analogy to (C5)-(C7), if demands (at at least two locations) are larger than zero930,
the total number of replenishment orders in the decentralized system is greater than the
number of orders in the centralized one resulting in lower total order fixed costs in the centralized system. However, in this case the number of orders (lead times) per decentralized
location i is smaller than the number of orders for the centralized one931, as n > 1:
∑
∑
∑
∑
∑
∑
∑
(C12)
.
The savings in regular stock stem from the assumption of an EOQ order policy, constant
fixed costs per order, holding costs (inventory carrying cost rate times product value per
unit), and total demand for all locations before and after centralization. In the centralized
system, usually the total order fixed cost is lower because of less orders and the inventory
holding cost is lower due to a smaller EOQ than in the decentralized system.932
930
931
932
Ronen (1990), Zinn et al. (1990), and Evers (1995) neglect this.
Cf. Ronen (1990: 132). Zinn et al. (1990: 139) state that “inventory centralization will increase the number of lead times per year if an EOQ ordering quantity is used”. “[A]n increase in the number of lead
times with the same expected annual demand decreases the average base stock” (Zinn et al. 1990: 141).
This is true for the centralized warehouse compared to each decentralized one.
Evers (1995: 5).
177
Appendix D: Tables
Table D.1: Fulfillment of the SRL's Assumptions by Eleven Surveyed Companies
Survey respondents Number
Country
Industry
Employees
Position
1
2
3
4
5
6
7
8
9
10
11
Denmark Germany Germany
France
Sweden
U.S.
U.S.
Italy
U.S.
U.S.
Germany
Paper Paper Paper Reusable Paper Semicon‐ Wireless Paper Automotive Utilities Electronics
wholesale production production packaging
wholesale ductors telecom wholesale
200
10,000
60,000
1,850
60,000
9
4,500
6,000
1,652
65
40,000
Supply Vice‐
Director of Functional Chain Supply Logistics Logistics Marketing Materials Adminis‐ president Director of Logistics & Integrator Optimiza‐
Chain Manager
Analyst
Manager
Manager
trator
Supply Logistics
IT
Lead
tion Manager
Chain
Manager
Central warehouses
Regional warehouses
Assumptions of the SRL when applied to
Safety Stock
Demands iid (are indepen‐
dent and identically distributed random variables)
Locations' demands uncorrelated
Locations' demand variance the same
Zero supplier lead time variance
Locations face same average lead time
Lead times iid
Lead times and demands independent of each other
Safety factor approach used
Locations use same safety factor
No transship‐
ments between locations
Safety Stock/ Average total Regular Stock
system demand remains the same after consolidation
Locations' Regular Stock
demands the same
EOQ Order Policy
Locations' fixed order cost the same
Locations' per unit holding cost the same
2
0
5
10
5
2
0
1
1
2
0
0
100
0
10
66
8
24
2
5
12
21
0
1
0
0
0
0
0
0
1
1
1
0
1
1
1
0
1
1
0
1
1
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
1
1
0
1=Yes, 0=No
178
Appendix D
Table D.2: Comparison of Important Inventory Consolidation Effect, Portfolio Effect, and
Square Root Law Models
179
Appendix D
Continuation of Table D.2
180
2
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1
!
Pioneers
Critics
Variable lead time
Transshipments
Optimal consolidation
Network design
Appendix D
Continuation of Table D.2
181
Appendix D
Continuation of Table D.2
182
Appendix D
Continuation of Table D.2
183
Appendix D
Table D.2 shows the different SRL and PE models and the assumptions they are based
upon. With the help of this table one can choose the model best fit for assessing inventory
changes from centralization or decentralization for given conditions. The corresponding
formulae for calculating the inventory savings achievable by inventory pooling can be
found on the respective publication's page noted in the first or second row of this table.
In order to facilitate readability the assumptions are grouped according to the rubrics
stock-, inventory-policy-, demand-, and lead-time-related. The columns or models are
arranged chronologically according to their year of publication, so that the development
and adding or dropping of assumptions over time can be retraced where possible.
The models are also grouped by colors according to their main contribution or focus,
although this is not too definite, as they are very different or overlapping and the terms
SRL and PE are sometimes used interchangeably.
Maister (1976) showed the SRL for the EOQ and the safety factor approach for both
cycle and safety stock, Eppen (1979) for the newsvendor model and expected costs, Zinn et
al. (1989) the PE as a generalization of the SRL, Mahmoud (1992) the Portfolio Quantity
and Portfolio Cost Effect, Evers (1995) the Consolidation Effect, Caron and Marchet
(1996) the impact of centralization on safety stock in a special two-echelon system, i. e. the
ratio of safety stock levels in a coupled system and an independent system, first (pioneers).
Das (1978) and Ronen (1990)933 (critics) critically review Maister's (1976) SRL and Zinn
et al.'s (1989) PE respectively. Evers and Beier (1993, 1998) and Tallon (1993) consider
variable lead times, Evers (1996, 1997) transshipments, Tyagi and Das (1998), Das and
Tyagi (1999), Wanke (2009), and Wanke and Saliby (2009) optimal consolidation
schemes, and Croxton and Zinn (2005) inventory pooling effects with the SRL in network
design.
Of course all researchers may be considered critical pioneers as they all contribute
something novel and critically review previous work, which is the essence of scientific
research. Mahmoud (1992: 198, 212) also considers the optimal consolidation scheme and
criticizes that the PE is not sufficient to define it. Evers and Beier (1993) and Evers (1995)
criticize Maister's (1976) SRL. Evers and Beier (1993) and Tyagi and Das (1998) consider
multiple consolidation points and the equal partitioning of demand assumption. Wanke and
Saliby (2009) also deal with regular transshipments. Important distinguishing assumptions
made or not made by the various models are highlighted in grey.
933
Ronen (1990) and Zinn et al. (1989, 1990) have a scientific dispute. For details please refer to the respective publications.
184
Appendix D
Table D.3: Conditions Favoring the Various Risk Pooling Methods
185
Appendix D
Continuation of Table D.3
186
Appendix D
Continuation of Table D.3
187
Appendix D
Continuation of Table D.3
188
Appendix D
Continuation of Table D.3
189
Appendix D
Continuation of Table D.3
190
Appendix D
Continuation of Table D.3
191
Appendix D
Continuation of Table D.3
192
Appendix D
Continuation of Table D.3
193
Appendix D
Continuation of Table D.3
194
Appendix D
Table D.4 The Risk Pooling Methods' Advantages, Disadvantages, Performance, and TradeOffs
195
Appendix D
Continuation of Table D.4
196
Appendix D
Continuation of Table D.4
197
Appendix D
Continuation of Table D.4
198
Appendix D
Continuation of Table D.4
199
Appendix D
Continuation of Table D.4
200
Appendix D
Continuation of Table D.4
201
Appendix E: Subadditivity Proof for the Order Quantity
Function (5.1)
The total system-wide order quantity in the centralized system is no greater than the one in
the decentralized system, because the order quantity function (5.1) is subadditive:
∑
∑
,
,
(5.4)
.
In order to prove this, we first resort to two warehouses with forecast demand minus
and
available inventory (net demand)
and seek to prove:
,
,
,
The order quantity function (5.1) is a compound function (E1)
.
consisting of an outer
maximum function and an inner ceiling function, which we henceforth denote by
respectively. The ceiling expression
Recall that a function
and ,
is a constant.
is called subadditive, if it obeys the inequality
(E2)
for any
,
from the function's domain.
We first show that
is subadditive,
i. e. that the following holds for any
,
:
(E3)
.
This can be verified by a case differentiation:
For
s d ,
s d
(E4)
,
s d , s d
for
s d ,s d
s d ,s d
,
(E5)
where notation a b stands for „a divides b“ or, equivalently, “b is a multiple of a” and
designates negation.
,
We now prove that
holds for any
,
is subadditive as well, i. e. that the following
:
,
g
For g
g
,g
,g
c, g
c
For g
c, g
c
,
,
,
,
(E6)
.
,
,
,
,
.
(E7)
.
(E8)
202
Appendix E
Then for the compound function
holds:
(E9)
,
since
,
where the first inequality is due to subadditivity of
and non-decreasing behavior of
(E10)
and
the second inequality is due to subadditivity of .
It is now straightforward to generalize (E9) to any number of summands. Given
, we by induction on n have:
,
(E11)
which hence gives
∑
∑
(E12)
and proves (5.4) to hold.
203
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