A Diagnostic Analysis of Retail Out-of-Stocks
by
Yong Ning Foo
B.Eng., Electrical Engineering, National University of Singapore (2006)
Submitted to the School of Engineering
in Partial Fulfillment of the Requirements for the Degree of
Master of Science in Computation for Design and Optimization
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
September 2007
©Massachusetts Institute of Technology 2007. All rights reserved.
A
Author....................................
.....................
School of Engineering
August 16 2007
Certified by.....................
.....
.
..................
Stephen C. Graves
Abraham J. Siegel Professor of Management Science
Thesis Supervisor
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A/i
Accepted by..............
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CF TECHNOLOGY
SEP 7 7 2007
LIB RAR IE S
Jaime
Peraire
Professor of Aeronautics and Astronautics
Codirector, Computation for Design and Optimization Program
BARKER
2
A Diagnostic Analysis of Retail Out-of-Stocks
by
Yong Ning Foo
Submitted to the School of Engineering
on August 16, 2007, in partial fulfillment of the
requirements for the degree of
Master of Science in Computation for Design and Optimization
Abstract
In the highly competitive retail industry, merchandize out-of-stock (OOS) is a significant
and pertinent problem. This thesis performs a diagnostic analysis on retail out-of-stocks
using empirical data from a major retailer.
In this thesis, we establish the empirical relationship of OOS rate with the amount of safety
stock carried, the time between orders and the forecast error, providing insights to the
effects of these three factors on the probability of OOS occurrences.
The root causes of OOS are also examined in the thesis. We find that up to 34% of OOS
can be attributed to forecast error while up to 22% can be attributed to delay in order
replenishment. For the OOSs that were associated with order delay, we can trace 60% of
these to out-of-stock at the store's distribution center (DC).
The thesis also examines a peculiarity in the occurrence of OOSs. We found that the OOS
rate of Class C items is significantly higher in stores with higher sales volume. We can
attribute much of this phenomenon to three factors: stores with higher sales volume hold
less safety stock for Class C items, have a shorter time between orders and have relatively
larger forecast errors.
Thesis Supervisor: Stephen C. Graves
Title: Abraham J. Siegel Professor of Management Science
3
Acknowledgement
I am deeply grateful to Professor Stephen C. Graves for the great opportunity to work with
him. His clarity in thoughts, analytical insights and attention to details is inspirational. I will
also never forget his willingness to address my academic and personal concerns during the
course of the project.
I am thankful to the collaborators from Beta for making this project possible. I would love
to name these wonderful individuals but I guess that would render the idea of anonymous
reference pointless.
My gratitude extends to Xin, who took the time to attend all the meetings and provide
valuable suggestions and comments.
I would also like to show my appreciation to the Singapore-MIT Alliance for awarding me
the Graduate Fellowship. The experience, like many others, has been invaluable.
I must thank my Mom, Dad and my brother, Don for everything that they have given me
all these years. To Candice, who takes such an important place in my heart, I thank her for
the unconditional love and support she has shown for the last 5 years.
I would also like to thank my friends Zhengyi, Fabian, Joline, Rebecca, Xu Song, Jia
Chuan, Heidi and Fang Fang for making my stay in MIT much more fun and enjoyable; my
roommate, Vinay, who has graciously allowed his table to be a part of my extended
workspace; Jocelyn and John from SMA office for the awesome trips and dinners; and
every person who should be here but whom my memory betrays.
5
Contents
List of Figures............................................................................................................10
List of Tables.............................................................................................................12
Chapter 1
Introduction ......................................................................................
15
1.1 Company Background......................................................................................................
15
1.2 Company's Inventory Policies........................................................................................
1.2.1 The Order-Up-To-Level (R, S) Control System ...................................................
1.2.2 Replenishment Frequency and Constraints..........................................................
1.2.3 Classification of SKUs............................................................................................
15
16
17
17
1.3 Project Motivation and Description..............................................................................
18
1.4 Literature Review .................................................................................................................
1.4.1 Factors influencing Out-of-Stock Rates ................................................................
1.4.2 Root Causes of Out-of-Stocks ..............................................................................
19
19
20
1.5 Thesis Overview...................................................................................................................
20
Chapter 2
Data Description and Definitions
2.1 Description of Data Set
.............................
...................................................................
2.1.1 Inventory Data .. e ................................................................................................
2.1.2 Store D ata
..............................................................................................................
2.1.3 Merchandize Data........................................................................................................
2.2 Preprocessing of Data .....................................................................................................
2.2.1 Removing Excess Data...........................................................................................
....
2.2.2 Removing Inaccurate Data.........................................................................................
2.2.3 Dealing wZ......................................
ih ccrateD at ..............................................
2..3 Dei inw
th. Zer.F. reca.................................................................
21
21
22
24
24
25
25
25
25
26
2.3 D efinitio ns ............................................................................................................................ 2 6
2 .3.1 O u t-o f-Sto ck .................................................................................................................
2.3.2 Out-of-Stock Rate ...................................................................................................
7
26
26
Empirical Model of OOS Rate .........................................................
29
3.1 Out-of-Stock Rate and Safety Stock .............................................................................
29
3.2 Out-of-Stock Rate and Time Between Orders............................................................
33
3.3 Out-of-Stock Rate and Normalized Forecast Error...................................................
36
Chapter 3
Out-of-Stock Causes and Conditions ...............................................
39
4.1 General OOS Causes in Retail Stores...........................................................................
39
4.2 Algorithm to Determine OOS Causes..............................................................................
4.2.1 Description of Algorithm.......................................................................................
4.2.2 Discussion on Algorithm Accuracy...........................................................................
40
40
44
Chapter 4
4 .3 R esults............................................................................................................
Chapter 5
................. 45
Examining a Peculiarity ...................................................................
51
5.1 T he P eculiarity .............................................................................................................---......
51
5.2 Peculiarity is not by Chance ..........................................................................................
5.2 .1 A N O V A ........................................................................................................................
5.2.2 Multiple Hypothesis Tests ......................................................................................
53
53
55
5.3 Three Causes of the Peculiarity Identified ...................................................................
5.3.1 Differences in Weeks of Safety Stock Carried.....................................................
5.3.2 Differences in Time Between Orders ...................................................................
5.3.3 Differences in Normalized Forecast Error ..........................................................
56
56
59
62
5.4 Other Hypothesized Causes that are not True............................................................
64
Chapter 6
Conclusion ...................................................................................
.. 67
Appendix A Data for Exchange Curve of OOS Rate and WEEKS.SS ..................... 69
Appendix B Data for Exchange Curve of OOS Rate and TBO ............................
73
Appendix C Data for Exchange Curve of OOS Rate and NFE ...........................
77
Appendix D Data on OOS Causes ............................................................................
83
Appendix E Data on OOS Rate of CLASS C SKUs By Stores.................85
Appendix F Data on Relative Frequency of WEEKS.SS of CLASS C SKUs in RANK
... 87
A Stores .................................................................
Appendix G Data on Relative Frequency of TBO of CLASS C SKUs in RANK A
........ 89
Stores.................................................................
8
Appendix H Data on Relative Frequency of NFE of CLASS C SKUs in RANK A
Stores..................................................................................................
91
Appendix I Distribution of Stores by OOS Rate of CLASS C SKUs ...................
Appendix
J
95
Analysis to Reject the Hypothesis that RANK A Stores Carry more
SKUs that have Higher OOS Rate.....................................................97
R eferences: ..............................................................................................................
9
101
List of Figures
Figure 3.1: Plot of OOS rate against WEEKS.SS for CLASS A items ...................
31
Figure 3.2: Plot of OOS rate against WEEKS.SS for CLASS B items.......................
31
Figure 3.3: Plot of OOS rate against WEEKS.SS for CLASS C items...................32
Figure 3.4: Plot of OOS rate against WEEKS.SS for New items ..........................
32
Figure 3.5: Plot of OOS rate against TBO for CLASS A items .............................
34
Figure 3.6: Plot of OOS rate against TBO for CLASS B items .............................
34
Figure 3.7: Plot of OOS rate against TBO for CLASS C items .............................
35
Figure 3.8: Plot of OOS rate against TBO for New items .....................................
35
Figure 3.9: Plot of OOS rate against NFE for CLASS A items .............................
37
Figure 3.10: Plot of OOS rate against NFE for CLASS B items ...........................
37
Figure 3.11: Plot of OOS rate against NFE for CLASS C items.............................38
Figure 3.12: Plot of OOS rate against NFE for New items...................................38
Figure 4.1: Summary of distribution of OOS causes at retail stores in general [6] ..40
Figure 4.2: Plot of percentage occurrence of OOS causes and conditions............46
Figure 4.3: Plot of percentage occurrence of OOS causes and conditions, split by
46
SKU CLA SS ..........................................................................................
Figure 4.4: Plot of percentage occurrence of major OOS. ....................................
47
Figure 4.5: Plot of percentage occurrence of major OOS causes normalized to 100%
for each forecast error type....................................................................-47
Figure 4.6: Key OOS Causes.............................................-49
Figure 5.1: OOS rate aggregated by SKU CLASS and STORE RANK....................52
Figure 5.2: OOS rate of CLASS C SKUs aggregated by SKU.DIV and RANK........52
Figure 5.3: OOS Rate of CLASS C SKUs aggregated by PF and RANK...............53
Figure 5.4: Box Plot of the OOS Rate of the Stores.........
10
.................
54
Figure 5.5: Relative frequency of safety stock in weeks in RANK A Stores ............. 57
Figure 5.6: Relative frequency of safety stock in weeks in RANK E Stores ............. 57
Figure 5.7: Relative frequency of time between orders in RANK A Stores ...........
60
Figure 5.8: Relative frequency of time between orders in RANK E Stores ........... 61
Figure 5.9: Relative frequency of normalized forecast error in RANK A Stores.......63
Figure 5.10: Relative frequency of normalized forecast error in RANK E Stores.....63
Figure 1.1: Distribution of RANK A stores by OOS of CLASS C SKUs................95
Figure 1.2: Distribution of RANK B stores by OOS of CLASS C SKUs ...............
95
Figure 1.3: Distribution of RANK C stores by OOS of CLASS C SKUs ...............
96
Figure 1.4: Distribution of RANK D stores by OOS of CLASS C SKUs...............96
Figure 1.5: Distribution of RANK E stores by OOS of CLASS C SKUs ...............
96
Figure J.1: OOS Rate of CLASS C items grouped by difference in relative frequency
in RANK A and RANK E stores ..........................................................
98
11
List of Tables
Table 4.1: Distribution of OOS Causes ................................................................
48
Table 5.1: P values of the hypothesis tests ............................................................
55
Table 5.2: Degrees of freedom of the hypothesis tests..............................................56
Table 5.3: WEEKS.SS Model and Actual OOS Rate.............................................59
Table 5.4: Percentage Responsibility of WEEKS.SS...............................................59
Table 5.5: TBO Model and Actual OOS Rate.......................................................
61
Table 5.6: Percentage Responsibility of TBO.......................................................62
Table 5.7: NFE Model and Actual OOS Rate.......................................................64
Table 5.8: Percentage Responsibility of NFE.......................................................64
Table A.1: Data for OOS Rate versus WEEKS.SS, all SKUs.................................69
Table A.2: Data for OOS Rate versus WEEKS.SS, CLASS A SKUs only..............70
Table A.3: Data for OOS Rate versus WEEKS.SS, CLASS B SKUs only ................. 70
Table A.4: Data for OOS Rate versus WEEKS.SS, CLASS C SKUs only .............. 71
Table A.5: Data for OOS Rate versus WEEKS.SS, New SKUs only.........................72
Table B.1: Data for OOS Rate versus TBO, all SKUs...........................................73
Table B.2: Data for OOS Rate versus TBO, CLASS A SKUs only........................74
Table B.3: Data for OOS Rate versus TBO, CLASS B SKUs only .......................
74
Table B.4: Data for OOS Rate versus TBO, CLASS C SKUs only .......................
75
Table B.5: Data for OOS Rate versus TBO, New SKUs only...................................76
Table C.1: Data for OOS Rate versus NFE, All SKUs ...........................................
77
Table C.2: Data for OOS Rate versus NFE, CLASS A SKUs ...............................
78
Table C.3: Data for OOS Rate versus NFE, CLASS B SKUs only .......................
79
Table C.4: Data for OOS Rate versus NFE, CLASS C SKUs only .......................
80
12
Table C.5: Data for OOS Rate versus NFE, New SKUs only...............................
81
Table D.1: Data on frequency of occurrence of OOS conditions ..........................
83
Table D.2: Data on frequency of occurrence of OOS conditions, split by CLASS... 83
Table E.1: Data on the OOS rate of CLASS C SKUs by stores .............................
85
Table F.1: Data on relative frequency of SS of CLASS C SKUs in A Stores...........87
Table F.2: Data on relative frequency of SS of CLASS C SKUs in E Stores ............. 88
Table G.1: Data on relative frequency of TBO of CLASS C SKUs in A Stores ......... 89
Table G.2: Data on relative frequency of TBO of CLASS C SKUs in E Stores ........ 90
Table H.1: Data on relative frequency of NFE of CLASS C SKUs in A Stores ........ 91
Table H.2: Data on relative frequency of NFE of CLASS C SKUs in E Stores........92
Table J.1: Data on OOS Rate of CLASS C items grouped by difference in relative
frequency in RANK A and RANK E stores ........................................
13
98
Chapter 1
Introduction
In the highly competitive retail industry, merchandize out-of-stock has been recognized as
a significant problem. Using real data from a major retailer, we examine in this thesis the
interdependencies of out-of-stock rate with various factors and we identify the root causes
for out-of-stocks. We also look in depth into a peculiarity in the out-of-stock rate of the
company, which serves to provide insights into the factors affecting the out-of-stock rate.
1.1 Company Background
The company is a United States based major retailer with over 1,000 retail stores and
10,000 SKUs. Due to confidentiality, we will refer to the company by the disguised name
of Beta.
1.2 Company's Inventory Policies
Beta carries approximately 6,300 SKUs per store, which are replenished either from the
DC or directly from the supplier (or distributor) by a flow through policy. About 70% of
the SKUs are replenished from the DC while the remaining items are replenished by the
flow through policy.
15
Each store is replenished on a regular replenishment cycle based on its pick frequency,
which specifies the number of times the store is replenished per week. For example, a pick
frequency of 2 would mean that the store is replenished twice a week.
Beta manages the inventory in its retail stores primarily with a periodic-review, order-up-tolevel (R, S) control system [9] with replenishment constraints. The review period is one day
with review at the end of each day.
1.2.1 The Order-Up-To-Level (R, S) Control System
For each item (or SKU) and each retail store, the inventory control system generates a
seasonalized weekly forecast using past sales performance. For each item and each retail
store, the inventory control system computes the amount of safety stock required, based
on the forecast, the service level, the replenishment lead time and the pick frequency for
the store. We term this safety stock as "system generated safety stock" and denote it as
SYS.SS. The system allows managers to set for each item and store, the minimum
presentation stock, MIN.P; this is the minimum number of units the manager wishes the
item to have on the shelf at all time.
As shown by equation 1.1, the greater of the safety stock and minimum presentation, gives
the amount of safety stock that the system uses to calculate the re-order point and the
order up to level.
SS = max(SYS.SS , MIN.P).
(1.1)
Thus, the minimum presentation can be viewed as a restricted form of override for the
system generated safety stock; the minimum presentation can be used to increase the
amount carried but never to decrease it. In order to compute the re-order point, we first
need to compute the vendor order point (VOP), which is given as,
VOP = max(SYS.SS , MIN.P) + LT.UNITS + VCS,
16
(1.2)
where SYS.SS, MIN.P, LT.UNITS and VCS are the safety stock, minimum presentation,
lead time demand in units and the vendor cycle stock in units. Managerial control over the
re-order point is provided by the parameter, Buyer Minimum, which we denote by
BUYR.MIN. The reorder point, ROP is given by
ROP = max(VOP, BUYR.MIN )-1.
(1.3)
Items are re-ordered when their inventory position (inventory on hand plus inventory on
order) is equal to or lower than the reorder point.
The system computes an order-up-to-level, which we denote as SYS.OUTL, by adding the
item cycle stock to the reorder point given by equation (1.3). Managerial control over the
order-up-to-level is provided by two adjustable parameters: the buyer maximum and the
hard maximum denoted by BUYR.MAX and HARD.MAX respectively. These parameters
allow the manager to decrease the order-up-to-level. The BUYR.MAX is a soft stop in the
sense that the system would ignore it if the service level goal cannot be achieved. The
HARD.MAX however is a hard stop. We use OUTL to denote the final order-up-to-level
after considering BUYR.MAX and HARD.MAX.
1.2.2 Replenishment Frequency and Constraints
The pick frequency of a store depends on its sales volume. It goes as high as 5 times per
week for high volume stores and as low as once per week for low volume stores. Stores do
not replenish on Sunday.
1.2.3 Classification of SKUs
Beta categorizes their SKUs into five divisions based on their intrinsic properties. In this
study, we examine SKUs from all five divisions.
Within each division, the SKUs are classified into priority ratings of CLASS A, CLASS B
and CLASS C that correspond to the
2 0 th
3 0 th
and
5 0 th
percentile of the SKUs' sales
performance. In other words, the top 20% of SKUs in terms of sales performance are
17
classified as CLASS A, the next 30% as CLASS B and the final 50% as CLASS C. This
classification is done at the store level, which means that the same SKU may have a
different priority rating at different stores. SKUs that are new and thus have no prior sales
information are simply classified as New.
Beta uses a different service level target (percent in stock) for each product class, with
CLASS A having the highest target and CLASS C having the lowest.
1.3 Project Motivation and Description
In the highly competitive retail industry, merchandize in-stock has been recognized as an
important factor in sales growth. A higher level of merchandize in-stock is associated with
increased sales and greater customer satisfaction, and thus is an important competitive
advantage. The problem of OOS is compounded by the ever increasing number of SKUs
carried by retailers. It has been found that a larger assortment may lead to an increased risk
of OOS occurrence [2][3], making it much more challenging to keep products in stock and
available at all time.
In the recent years, two key developments had led to the urgency and significance of the
OOS issues. The first development is the increasing consumers' intolerance of OOS
situations [6]. With more purchasing channels, alternative outlets and information,
consumers are increasingly likely to make their purchases elsewhere when encountered
with an OOS.
The second development is the advent of technologies that allow retailers new ways to
manage OOS issues [6] without incurring the huge costs in increased labor or greater
inventory safety stock associated with traditional recommendations.
This thesis will examine the root causes of out-of-stocks and establish the interdependencies between out-of-stock rate and various factors.
18
1.4 Literature Review
While the significance of out-of-stock (OOS) issues in retail has been pointed out as early
as the 60s by practitioners and researchers [7], recent advances in Category Management
and Electronic Data Interchange have led to a renewed interest in the causes, extent and
impact of out-of-stocks [3] [4].
A rather extensive research on the extent and causes of retail out-of-stocks is reported in
[6]. The report examines the extent and magnitude of out-of-stocks in the fast moving
consumer goods (FMCG) industry worldwide and identifies the root causes of out-ofstocks. Other empirical studies on the factors affecting out-of-stocks can be found in
[1][3][5]. Due to the large number of factors that can impact out-of-stocks, we will review
only factors that are of most relevance.
1.4.1 Factors influencing Out-of-Stock Rates
The intuitive reasoning that higher inventory levels correspond to lower out-of-stock rates
is rejected by [6]. It shows, using data from a few studies that there is a positive correlation
between out-of-stock rates and the amount of safety stock carried. It argues that excessive
backroom inventory may impede shelf replenishment and may indicate the presence of
ineffective in-store inventory management and ordering systems.
It is suggested in [6] that out-of-stock rates are higher on promoted items. The conclusion
is based on the fact that among the studies examined, all those that report promotional
effects find substantially greater out-of-stock rates on promoted items than everyday items.
We would like to note here the possibility of self-selection bias in the reports - studies that
did not find a relationship between out-of-stock rates and promotion are less likely to
report it.
[1] [3] [5] suggest that larger SKU assortments may lead to an increased risk of out-of-stock
occurrence by virtue of the fact that there is less shelf space per SKU in larger assortments,
19
which impacts faster moving items more severely due to constraints on minimum ship
pack.
1.4.2 Root Causes of Out-of-Stocks
[6] attributes up to 50% responsibility for out-of-stocks to retail store ordering and
forecasting, 25% to execution issues and 25% to upstream causes. The findings suggest
that most of the direct causes of out-of-stocks lie at the retail store level.
1.5 Thesis Overview
In Chapter 2 we present a detailed description of the dataset used in our analysis, describe
the pre-processing procedures and state several definitions that will be used throughout the
thesis. In Chapter 3 we establish the empirical relationship of out-of-stock (OOS) rate with
safety stock and forecast error while in Chapter 4 we examine the root causes of OOS. In
Chapter 5 we look in detail at a peculiarity whereby the out-of-stock rate of CLASS C items
is higher in RANK A (highest volume) stores than in RANK E (lowest volume) stores.
Chapter 6 concludes the thesis and provides some suggestions on further work.
20
Chapter 2
Data Description and Definitions
In this chapter, we provide a detailed description on the data set used in our analysis,
describe the pre-processing procedures and state several definitions that we use throughout
the thesis. We do not describe fields that were captured by the database but were not used
in our analysis.
2.1 Description of Data Set
The data was collected from 233 stores located in the Northeastern region of United States
over a period of 11 weeks. All stores are replenished from a common DC (distribution
center) and carry a similar range of merchandize. Only active SKUs are included in the data
set. By active SKUs we include all SKUs that were physically available on the store shelves
at any time during the 11-week period.
There are three types of data that were collected: inventory data, store data and
merchandize data. Inventory data provides detailed weekly information on the inventory
status for all SKUs at each of the stores; store data provides information on the physical
size, location, inventory policy and last quarter's revenue; merchandize data provides
information on the categorization of the SKUs by their intrinsic properties.
21
2.1.1 Inventory Data
Inventory data was collected from Beta's information system on the stores' inventory
status for each Saturday in the 11 week period. We obtained detailed information on the
inventory status of each and every SKU in all 233 stores over 11 weeks. For simplicity, we
refer to a Store-SKU-Week triple as an observation and if needed use subscript i to
denote stores which range from 1 to 233, subscript k to denote SKUs and subscript t to
denote time periods from 1 to 11. Throughout the thesis, we will use OBS to denote
observation. In total the data base consists of 16,842,783 observations.
SLG denotes the service level goal (or target) which takes on value of 99.8, 99.5, 99.0 or
99.2. CLASS is used to denote the priority ratings [8] of the SKUs: A (most volume), B
(intermediate) and C (least volume), which correspond to SLG of 99.8, 99.5 and 99.0
respectively. SLG of 99.2 is reserved for new items. Throughout the thesis, we will use
SLG and CLASS interchangeably depending on the situation. SLG is observation specific the same SKU may have a different SLG at different stores and the same store-SKU pair
may take on different SLG at different weeks. The latter case however is rather rare.
SRC.CODE is used to indicate the replenishment policy for that particular SKU at a
particular store. It takes on two possible values: 'D' and 'V' corresponding to
replenishment from DC and replenishment via a flow through policy respectively. The
same SKU may have different SRC.CODE at different stores and may also differ from
week to week. However, given an SKU-store pair, it is very rare for its SRC.CODE to
change over a short period of time.
STORE.BASE.FORECAST
and STORE.SEASONAL.INDICES
of an observation
denote the base weekly forecast in units (de-seasonalized) and week seasonal index of the
corresponding SKU in that particular Store for that week. Note that in the raw data, the
weekly forecast and seasonal index information provided in the current week's record for a
particular SKU-Store pair in fact corresponds to the observation of the same SKU-Store
pair in the next week; that is, the forecast we obtain in week t is the forecast for the
demand in week t+1. However, to avoid confusion in this thesis, we will not explicitly
22
denote this fact in our formulations or equations. The number of weeks of data, which is
given as 11, has already taken this fact into account. For further convenience, we will use
FC to denote the seasonalized weekly forecast which we compute by multiplying
STORE.BASE.FORECAST by STORE.SEASONAL.INDICE for a given observation.
IOH, UNITS.SOLD and INV.ADJ denote the number of units of inventory available on
hand at the store, the net units sold in that week and the net weekly inventory adjustment.
IH
is always non-negative, while UNITS.SOLD and INV.ADJ can take on any integer
value. A negative value in UNITS.SOLD would correspond to there being more
merchandize returned than sold in the given week. The inventory adjustment reflects a
correction of the inventory records; a store will make an inventory adjustment whenever it
discovers a discrepancy between its actual on hand inventory and the recorded amount in
Beta's information system. A negative value in INV.ADJ would correspond to a downward
adjustment in inventory, which occurs when the actual inventory on the store's shelf is less
than the IOH in the information system.
OUT.POINT, VOP, SYS.OUTL, MIN.P, SYS.SS, SHIP.PACK and LEAD.TIME denote
the out-of-stock point, vendor order point in units, system generated order up to level in
units, minimum presentation in units, system generated safety stock in units, unit of
measure the warehouse ships in and the item lead time in days, respectively. The out-ofstock point indicates the inventory level at which the item is considered out-of-stock. For
example, an item with out-of-stock point of one would be considered out-of-stock if its
inventory on hand is equal or lower than one. An out-of-stock point of one occurs when
the store requires a demo unit, which is not intended for sale. Nevertheless, most items will
have an out-of-stock point of zero. The vendor order point is used to determine the reorder point. As described in detail in section 1.2.1, the greater of MIN.P and SYS.SS gives
SS, which denotes safety stock in units. Approximately 85%, 50% and 25% of the
observations from CLASS C, B, and A respectively have a MIN.P that is greater than the
SYS.SS.
BUYR.MIN, BUYR.MAX and HARD.MAX denote the lower limit in units on the vendor
order point, an upper limit in units on the order up to level and the inventory cap in units,
23
respectively. In the raw data, BUYR.MIN and BUYR.MAX can in fact be given in terms of
days of demand. In this thesis, however, their uses are always in terms of units.
DIOH denotes the amount of on hand inventory in units at the DC. Since all the stores in
our study have a common DC, all observations corresponding to the same SKU-Week pair
have the same DIOH value.
All of the above mentioned fields other than DIOH may take on different values across
different stores, SKUs or weeks. DIOH is the only field whose value would remain the
same across all stores for a given SKU-week pair.
2.1.2 Store Data
Store data provides us with information on the stores' physical location, physical size, past
sales performance and pick frequency.
RANK and PF denote the store rank and the store pick frequency respectively. RANK can
be A, B, C, D or E and is determined by the store's fourth quarter sales in year 2006, with
RANK A corresponding to stores with the highest sales volume. Each rank corresponds to
roughly one fifth of the stores in the region. PF can take on integer values of 1 to 5 and is
determined by the store's performance, size and location. Most stores are replenished 2 or
3 times each week. The store pick frequency simply tells us the number of times a store is
replenished on a weekly basis. Furthermore, a store will be replenished on the same days
each week, given its pick frequency.
2.1.3 Merchandize Data
The merchandize data provides a classification of the SKUs based on their intrinsic
properties. SKUs are first classified into product classes, which are classified by product
department, which finally are classified by product divisions.
24
SKU.DIV
and SKU.DEPT denote the division and department respectively. The
information on the classification into classes by their intrinsic properties is not used in this
thesis and thus is not denoted. This is also to avoid confusion with CLASS which, as
defined in section 2.1.1 is used to denote the classification of the SKUs by their relative
demand volume. There are 5 SKU divisions and within each division there are between 10
and 18 departments.
2.2 Preprocessing of Data
We preprocessed the raw data to remove inaccurate, incomplete and/or questionable
observations, and to correct rounding errors that result in zero forecasts. The intent is to
create a dataset that is consistent and accurate for the purposes of the study.
2.2.1 Removing Excess Data
We removed any data that falls outside the set of stores or products that were specified as
part of the study. More specifically, we discarded observations corresponding to: stores
that do not match our set of 233 stores, service targets that do not match one of the four
product classes and SKUs that are not from one of the five SKU divisions. Also, we
removed inactive SKUs that were out-of-stock at all stores and all weeks.
2.2.2 Removing Inaccurate Data
All observations that have negative FC (forecast) or which FC information is unavailable
were removed. Less than 1,000 observations were removed under this rule.
2.2.3 Dealing with Zero Forecast
The STORE.BASE.FORECAST and STORE.SEASONAL.INDICE in the raw data are
accurate to two decimal places. Any value that falls below 0.005 gets rounded off to zero,
which creates a problem when computing the percentage or normalized forecast errors. To
resolve this problem, we replaced any zero values in STORE.BASE.FORECAST and
25
STORE.SEASONAL.INDICE
STORE.BASE.FORECAST
with 0.005.
FC is then computed
by STORE.SEASONAL.INDICE.
by multiplying
Approximate 390,000
observations, which constitute less than 2.5% of all the observations were adjusted based
on this processing rule.
2.3 Definitions
There are many ways to define out-of-stock (OOS) and to compute the OOS rate. Here,
we provide the definitions that we use throughout the thesis.
2.3.1 Out-of-Stock
We declare an SKU at a particular store to be out-of-stock (OOS) if its on-hand inventory
is equal to or lower than the out-of-stock point. The out-of-stock point takes a value of
one if there is a display set and a value of zero if there is no display set. The definition
remains the same even if the SKU has multiple facings (exists in multiple locations in the
store). We will use
Vi,
to represent the OOS status that correspond to the observation of
SKU i in Store k at week t, (i.e. OBSIk). We define Vi,
Vikt
1
fok~
as,
(2.1)
IOH,,, OUT.POINT
,
otherwise
2.3.2 Out-of-Stock Rate
We measure the out-of-stock (OOS) rate as a fraction of active SKUs that are out of stock
at the retail store at a particular moment in time, which is the most accepted approach [6].
We will want to compute the OOS rate for various combinations of stores and SKUs, over
various periods of time. For any specification of stores, SKUs, and time, we will compute
the OOS rate as the ratio of the number of out-of-stock observations to the total number
of observations. That is, we define the aggregate OOS rate,
26
rIKT
as
i,k,t
rI,K,T
SI,K,T
IiE I
(2.2)
ic-K iET
where I, K and T correspond to the set of SKUs, stores and weeks under consideration
respectively; SI,K,T is the corresponding set of observations; and ISI,K,TI is the cardinality
of
SI,K,T -
For example, the OOS rate of CLASS C items in store i over all weeks is
computed by dividing the total number of OOS occurrences of CLASS C items seen in
store i by the total number of observations of CLASS C items in store i.
27
Chapter 3
Empirical Model of OOS Rate
In this chapter, we establish the empirical relationship of out-of-stock (OOS) rate with
safety stock, time between orders and forecast. We will see in this chapter that the OOS
rate decreases as safety stock increases, decreases as time between orders increases and
increases as forecast error increases.
3.1 Out-of-Stock Rate and Safety Stock
We use WEEKS.SS to denote safety stock expressed in weeks of demand, which we will
refer to as "safety stock in weeks" or "weeks of safety stock". It is computed as
WE EKS .SS
SS
FORECAST
max(SYS.SS, MIN.P)
.
FORECAST
(3.1)
To obtain the empirical relationship between the OOS rate and safety stock in weeks, we
first compute the WEEKS.SS for each and every observation. Then we group observations
with similar WEEKS.SS together and finally compute the OOS rate of each group by
dividing the number of out-of-stocks by the number of observation, i.e., by using equation
(2.2).
Figure 3.1, Figure 3.2, Figure 3.3 and Figure 3.4 show the exchange curves between OOS
rate and safety stock in weeks for CLASS A, CLASS B, CLASS C and New SKUs
29
respectively. Note that the weights are not the same for all points since the number of
corresponding observations varies from point to point. Refer to Appendix A for the data.
In general, the OOS rate decreases as the amount of safety stock increases, which is not a
surprise. The "smoothness" of the curves, however, is rather remarkable.
There are three interesting results. The first is that for CLASS B and CLASS C SKUs, the
curves flatten off at out-of-stock rates that correspond to their respective service level
targets. CLASS B has a service level target of 99.5%, which corresponds to an OOS rate of
0.005; CLASS C has a service level target of 99.0%, which corresponds to an OOS rate of
0.010.
The second is that for CLASS B and CLASS C SKUs, the out-of-stock rate that
corresponds to zero weeks of safety stock is exceptionally low. The number of
observations with zero weeks of safety stock is small but not insignificant - about 12,000
and 160,000 for CLASS B and CLASS C respectively, which translates to approximately 5
and 62 SKU equivalents respectively. (In the data base, for each SKU we have
approximately 2500 observations as we have one observation for each of 11 weeks for each
of 233 stores.) Also most of these observations have exactly zero safety stock (i.e. zero
SYS.SS and zero MP) - about 9,400 and 159,000 for CLASS B and CLASS C respectively.
Though we do not know for sure the reason for this exception, it is possible that these
observations correspond to items that are being discontinued; their safety stocks have been
cut to zero but still have some inventory on hand.
The third is that for a given amount of safety stock in weeks, the OOS rate for CLASS A is
lower than that of CLASS B, which in turn is lower than that of CLASS C. This might be
because CLASS C items have a smaller demand rate than CLASS B and as such, its
demand is relatively more variable. The same comparison can be made between CLASS B
and CLASS A items
30
* 99.8 (Al) (NI)
Plot of Out-of-Stock Rate against Safety Stock In Weeks (of Denand)
(Considering CLASS A SKUs only)
0.018
0.016
0.014
e0.012
0.01
0.008
0
0.006
0.004
0.004
0.002
0
0
10
20
30
40
50
Safety Stock In Weeks of DeMnand
60
70
80
90
Figure 3.1: Plot of OOS rate against WEEKS.SS for CLASS A items
+
Plot of Out-of-Stock Rate against Safety Stock in Weeks (of Denand)
(Considering CLASS B SKUs only)
()()
0.025
0.02
0.015
0.01
0
0.005
0
0
10
20
30
40
50
Safety Stock in Weeks of Denand
60
70
80
Figure 3.2: Plot of OOS rate against WEEKS.SS for CLASS B items
31
90
Plot of Out-of-Stock Rate against Safety Stock In Weeks (of Demand)
(Considering CLASS C SKUs only)
S99 (All) (Al)
0.035
0.03
0.025
0.02
0.015
0.01
0
0.005
0
0
30
20
10
50
40
Safety Stock in Weeks of Demand
70
60
80
90
Figure 3.3: Plot of OOS rate against WEEKS.SS for CLASS C items
* 99.2 (AM) (AI)
Plot of Out-of-Stock Rate against Safety Stock in Weeks (of Demand)
(Considering New SKUs only)
0.035
0.03
0 0.025
0.02-
0.015
0
0.01
0.005
0
0
10
20
60
50
40
Safety Stock in Weeks of Demand
30
Figure 3.4: Plot of
70
80
90
100
OOS rate against WEEKS.SS for New items
Figure 3.1 which gives the plot for CLASS A SKUs is relatively more scattered because of
the smaller number of CLASS A SKUs. CLASS A SKUs constitute approximately 20% of
all SKUs while CLASS B and CLASS C items constitute about 30% and 50% respectively.
The rather scattered plot we see in Figure 3.4 is due to the small number of observations
available for new products. We have less than 600,000 observations which translate to
approximately 230 SKU equivalents.
32
3.2 Out-of-Stock Rate and Time Between Orders
We denote the time between orders by TBO and compute it as
TBO = OUTL-ROP
FC
(3.2)
where OUTL, ROP and FC are the final order-up-to-level, re-order point and seasonalized
forecast as given in section 1.2.1. However, because computing the OUTL is rather
complex, we estimate equation (3.2) using
TBO = SYS.OUTL -VOP+1
FC
(3.3)
Since the number of observations with active BUYR.MIN, BUYR.MAX and HARD.MAX
is small, equation (3.3) provides a good enough estimate for the purpose of our work in
this section.
We establish the relationship between time between orders and OOS rate in a similar
manner as outlined in section 3.1. Specifically, we first compute the TBO for each and
every observation; group observations with similar TBO together; and finally compute the
OOS rate of each group by dividing the number of OOSs by the number of observations,
i.e. by using equation (2.2).
Figure 3.5, Figure 3.6, Figure 3.7 and Figure 3.8 show the exchange curves between the
OOS rate and time between orders in weeks for CLASS A, CLASS B, CLASS C and New
SKUs respectively. Note that the weights are not the same for all points since the number
of corresponding observations varies from point to point. Refer to Appendix B for the
data.
We can see from the figures that for the same time between orders, CLASS A items have a
lower OOS rate than CLASS B items, which in turn have a lower OOS rate than CLASS C
items. Like in the case of safety stock, this is presumably because the demand for CLASS C
and B items is relatively more variable than that for CLASS B and A items, respectively.
33
S(All) (All) 99.8
Plot of Out-of-Stock Rate against Time Between Ordering
(Considering Class A SKUs only)
0.01600.0140 -
0.0120
+
0.0100
c
0.0080
0.0060
0
0.0040
0.0020
0.0000
10
0
20
30
50
40
Time Between Ordering in Weeks
60
70
80
90
80
90
Figure 3.5: Plot of OOS rate against TBO for CLASS A items
* (All) (Al) 99.5
Plot of Out-of-Stock Rate against Time Between Ordering
(Considering Class B SKUs only)
- -7-
0.0200
0.0180
0.0160
S0.0140
Ix
0.0120
0.0100
0.0080
O 0.0060
0.0040
0.0020-
-
0.0000
0
10
20
30
50
40
Time Between Ordering in Weeks
60
70
Figure 3.6: Plot of OOS rate against TBO for CLASS B items
34
* (RI) (RI)
99
Plot of Out-of-Stock Rate against Tine Between Ordering
(Considering Class C SKUs only)
0.03000.0250
1i 0.0200-
_
*
ra0.01500.0100
0.05
0.0050
-
0
20
10
30
50
40
Time Between Ordering In Weeks
60
80
70
90
Figure 3.7: Plot of OOS rate against TBO for CLASS C items
* (All) (AMI) 99.2
Plot of Out-of-Stock Rate against Time Between Ordering
(Considering New SKUs only)
0.0"0
0.0250
T
aR
0.0200
0.0150
0 0.0100
Y
0.0050
0.0000
0
20
40
60
Tirne Between Ordering in Weeks
80
100
120
Figure 3.8: Plot of OOS rate against TBO for New items
Like before, the scattering we see in Figure 3.8 is due to the small number of observations
we have for new products, which is approximately only 230 SKU equivalents. On the same
ground, the points on Figure 3.5 are relatively more scattered than the points in Figure 3.6
and Figure 3.7.
35
3.3 Out-of-Stock Rate and Normalized Forecast Error
We denote the normalized forecast error by NFE, and define it as
(34)
NFE = UNITS.SOLD - FC
FC
where FC as defined earlier is the seasonalized weekly forecast. We note here that (3.4) is
not the most widely
accepted
definition
of normalized
forecast error.
Having
UNITS.SOLD instead of FC as the denominator in (3.4) will give us the more common
definition. However, since many observations have zero UNITS.SOLD, the more accepted
definition would face the problem of division by zero.
The relationship between out-of-stock rate and normalized forecast error is established in a
similar fashion as outlined in section 3.1. We note that since UNITS.SOLD is rarely
negative, then effectively a lower bound on NFE is -1, which corresponds to zero
UNITS.SOLD.
However, the NFE often take on a large positive values as many items
have weekly forecasts of less than one unit; for instance, if the weekly forecast were 0.25,
and we sell one unit, then NFE = 3.
Figure 3.9 to Figure 3.12 show the exchange curves between OOS rate and normalized
forecast error for CLASS A, B, C and New items respectively. The results, which show that
in general OOS rate increases as normalized forecast error increases is just as we would
expect. The data for the plots can be found in Appendix C.
Figure 3.9 shows that the OOS rate corresponding to -1 normalized forecast error is higher
than when the normalized forecast error is close to zero. Though at first glance it seems to
contradict the general pattern that OOS rate increases as normalized forecast error
increases, it is perfectly explainable; a large number of the observations that have -1
normalized forecast error have zero UNITS.SOLD and thus have zero sales because they
were out-of-stock and not because there was no demand. The fact that (actual) demand for
CLASS C SKUs is smaller than that of CLASS A SKUs suggests that most of the zero
UNITS.SOLD observed for CLASS C SKUs are legitimate, thus explaining why this
36
pattern is not observed in Figure 3.11. This clearly illustrates the limitation of estimating
actual demand using observed demand.
Plot of Out-of-Stock Rate against Normalized Forecast Error
(CLASS A SKUs)
0.08
0.07
0.06
W 0.05
0.04
0.03
0
0.02
0.01
0
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
18
19
20
21
Nornulized Forecast Error
+ (All) (All) 99.8 - (All) (All) 99.8
Figure 3.9: Plot of OOS rate against NFE for CLASS A items
Plot of Out-of-Stock Rate against Normalized Forecast Error
(CLASS B SKUs)
0.12
0.1
0.08
0.06
0.04
0.02
0
-3
-2
-1
0
1
+ (All) (All) 99.5 0 (All) (A) 99.5
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Normalized Forecast Error
Figure 3.10: Plot of OOS rate against NFE for CLASS B items
37
Plot of Out-of-Stock Rate against Normalized Forecast Error
(CLASS C SKUs)
0.120.1
0.08
0.06
0 0.04
0.02
0
-3
-2
0
-1
1
2
3
4
5
6
* (Al) (Al) 99 * (Ail) (m) 99
10 11 12
7
8
9
Normalized Forecast Error
13
14
15
16
17
18
19
20
21
18
19
20
21
Figure 3.11: Plot of OOS rate against NFE for CLASS C items
Plot of Out-of-Stock Rate against Normalized Forecast Error
(New SKUs)
0.16
0.14
0.12
aR
1
0.1
0.08
0.06
0.04
0.02
0
-3
-2
-1
0
1
* (All) (All) 99.2 * (AlI) (Al) 99.2
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Normalized Forecast Error
Figure 3.12: Plot of OOS rate against NFE for New items
Again, like before, the rather scattered plot we see in Figure 3.12 is caused by the small
number of observations available, which we already mentioned in section 3.1 is less than
600,000.
38
Chapter 4
Out-of-Stock Causes and
Conditions
In this chapter, we will first look at the causes of out-of-stocks in retail stores in general.
Following this, we will develop an algorithm to identify the causes behind the out-of-stocks
we see in our data. The algorithm also identifies certain conditions under which the out-ofstocks have occurred. By conditions, we are referring to inventory status or information
which may provide insights to the out-of-stock but cannot be defined as being responsible
for it. Finally we will show the results of our algorithm on our dataset.
4.1 General OOS Causes in Retail Stores
[6] reports that between two-third to three-quarter of OOS are caused by problems at the
store level while the remaining are caused by problems upstream in the supply chain. For
the out-of-stocks that are caused by problems at the store, almost half of them can be
attributed to bad forecasting. Figure 4.1 shows the summary of the various OOS causes in
general as given by [6].
39
Summary of Findings of OOS Causes
Other Causes
4%
Retail HQ or
Manufacturer
14%
Store Ordering
13%
Distribution C;enter
10%
Store Forecasting
34%
Store Shelving
25%
Figure 4.1: Summary of distribution of OOS causes at retail stores in general [6]
As noted in [6], the distribution of OOS causes varies significantly between studies. The
results shown in Figure 4.1 simply provide an overall picture on the causes.
4.2 Algorithm to Determine OOS Causes
We have developed an algorithm to determine the possible OOS causes using only the
information from the dataset. This section will describe the algorithm and provide a
discussion on its accuracy and possible pitfalls.
4.2.1 Description of Algorithm
Recall that our dataset is a weekly snapshot of the inventory status of all active SKUs at
233 selected stores over a period of 11 weeks. Because the dataset consists of weekly
snapshots, we are limited in our ability to identify the reasons for any particular out-ofstock occurrence. From the data we have, we can identify the following possible causesout-of-stock at the DC, out-of-stock at the DC in the prior week, order delayed and
40
insufficient replenishment. We also keep track of three conditions under which the OOS
has occurred. The first is whether any replenishment occurred during the week; the second
is the type and extent of forecast error; and the third is on the existence of an inventory
adjustment.
In this section, we denote the store, SKU and week using the first, second and third
subscripts respectively. Thus an observation in store i of SKU k at the end of week t is
denoted by OBSk . All of the notations we use here have been declared in section 2.1.1.
Out-of-Stock
Given OBSk,,,
we declare that it corresponds to an out-of-stock if
IOH , : OUT.POINTIj.
(4.1)
OOS at DC
For SKUs that are replenished from the DC, an OOS at a store might be due to the fact
that the DC was previously out of stock and a replenishment order has thus been delayed.
We have the data on the inventory status of the DC; to determine if the DC was out-ofstock at week t and/or at the prior week, we check this directly from the data as shown by,
DIOHij
0
DIOH , 1 5 0.
(4.2)
(4.3)
SKUs that are replenished directly by the suppliers via the flow through policy do not hold
any stock at the DC; hence, for these SKUs, their OOSs are precluded from the above
checks. Another way to look at it is that OOSs that are not flagged as being OOS at DC
either have stocks available at the DC or are flow through items.
No Replenishment in Week t
We can identify that no replenishment was received during week t if the number of units
sold in the week is less than or equal to the net change in on hand inventory from the prior
41
week. That is, we conclude that there was no replenishment in week t if the following
condition is true:
UNITS.SOLDijt
IOHi,,
- IOHj, + INV.ADJijt
(4.4)
Order Delayed
We can infer from the data that an order was delayed if there was no replenishment in
week t, the inventory on hand in the prior week was lower or equal to the re-order point
and the lead time was less than 6 days. In order words, we assert that an order was suppose
to arrive in week t, but did not, if the following conditions are satisfied:
UNITS.SOLDjt
IOH,3 ~1
IOH1 ,
-
IOHj + INV.ADJjt
(4.5)
! ROi,jt
(4.6)
LEAD.TIMEi,_11 < 6
In using the above criteria to identify an order delay, we are making two assumptions. The
first assumption is that an order was placed in the prior week, given that the inventory on
hand was at or below its reorder point. The second assumption is that if the lead time is
less than 6 days, then any order placed in the prior week should have arrived at the store by
the end of the current week; our understanding of Beta's operations indicate that this
should be true even if a store has a pick frequency of 1 or 2 times a week.
Inventory Adjustment
We can use the occurrence of an inventory adjustment as an indicator of the store
execution performance. An OOS might be due to inventory inaccuracy; an inventory
adjustment occurs whenever the store finds an inventory inaccuracy, namely a discrepancy
between its on-shelf inventory and the inventory records.
Since the data provides
information on the net inventory adjustment for the week, determining if an inventory
adjustment has occurred is straight forward.
Negative Inventory Adjustment
if
INV.ADJJt <0,
(4.7)
Positive Inventory Adjustment
if
INV.ADJjt >0,
(4.8)
42
Insufficient Replenishment
We declare that there was insufficient replenishment if an order was received and the order
received was less than the expected order quantity. This event occurs if the following two
equations are satisfied.
UNITS.SOLDJ , > IOH,4 1 - IOHij~ + INV.ADJiJ,
UNITS.SOLDj
<
''-,j x SP,,-1 + NET.CHANGEI,
where SP denotes the Ship Pack for the SKU,
[.]
(4.9)
(4.10)
represents rounding to the nearest
integer and NET.CHANGE denotes the net change in on hand inventory, which is given
as
NET.CHANGEj
= IOH,,, - IOH,+ INV.ADJ ,
(4.11)
Thus, equation (4.9) signifies that a replenishment was received in week t while (4.10)
indicates that the amount received was less than what was expected. The term in brackets
is the number of ship packs that would need to be ordered to bring the inventory up to the
order -up-to level.
Forecast Error
An OOS might be due to a forecast error, especially when demand exceeds the forecast.
We characterize the types and extent of the forecast error in week t as follows,
Non-positive error
if
FEi,
Small positive error
if
0 < FEi,, 5
Medium positive error if
Large positive error
FC,1
if
5 0,
(4.12)
FC,,
< FE,'' 5 2 FC,,
FE , > 2FCI,, ,
(4.13)
(4.14)
(4.15)
where FC is defined in section 2.1.1, and denotes the seasonalized weekly forecast, and FE
denotes the forecast error, which is computed as
43
SELt
UNITS.SOLD
, - FC(4
(4.16)
We categorize the positive forecast errors into small, medium and large based on the
relative size of the error. In particular we use the square root of the weekly forecast as the
basic unit for scaling the forecast error. This choice of scale is arbitrary.
4.2.2 Discussion on Algorithm Accuracy
Given that the dataset we have provides us with only snapshots of the weekly inventory
status, the accuracy of our algorithm is thus limited. Here, we discuss two errors that our
algorithm might make when checking for order delay.
False Positives on Detecting Order Delayed
By false positives, we refer to OOS that were not caused by a delay in the order but yet this
condition was flagged otherwise by our algorithm. For our algorithm, we assume that if a
store places an order on Saturday, then this order will normally arrive by the following
Saturday. It is possible that this might not be true. For instance, if the store has a pick
frequency of once a week, it is conceivable that the replenishment lead time is such that the
order placed on Saturday cannot be shipped as part of the one weekly replenishment for
the store. Technically, an order which fails to arrive at the store after its lead time has
lapsed because it has legitimately missed the replenishment day of the store cannot be
classified as being caused by an order delay. However, given that over 70% of the
observations have a lead time of two days or less and that more than 80% of the stores are
replenished at least twice a week, we expect the number of false positive to be small.
False Negatives on Detecting Order Delayed
There are three ways for false negatives to occur. By false negatives we refer to OOS that
were caused by a delay in the order and we were not able to detect this order delay this
with our algorithm.
The first case happens when the lead time is greater than 6 days. By default all OOSs for
SKUs with a lead time of 6 days or more would not be flagged as being caused by an order
44
delay. Approximately 28% of the observations have a lead time of 6 days or more, of which
more than 85% corresponds to SKUs that are on flow-through replenishment from the
supplier.
The second case occurs when the inventory position hits the reorder point after Saturday
of week t-1 but before Saturday of week t and the time between reordering and Saturday of
week t is less than the lead time. By making the assumption that demand is Poisson, then
with the information on the total demand of the week we will have a conditional Poisson
distribution, which essentially is the same as having the observed demand uniformly
distributed over the week. Thus, for a given OOS observation, we might observe that an
order was delayed if the order had been placed (say) by Monday of week t; given the
observed demand for the week and the assumption of Poisson demand, we could find the
probability that an order was delayed in arriving by the end of week t.
The third case occurs when there are multiple replenishment orders outstanding and one
or more of these are received in week t.
According to our specification, because a
replenishment was received during week t, we do not associate an order delay to this
OS;
however, the fact that an order was received in week t need not rule out the possibility that
there is an outstanding delayed replenishment order.
4.3 Results
Figure 4.2 gives the overall picture of the conditions and causes surrounding the out-ofstocks. We note that for each OOS we associate all of the conditions and causes that are
satisfied. Thus each OOS might have several conditions or causes. We see that for 86% of
the OOSs, either there was inventory at the DC in week t or they are flow through items;
for
83%
of the OOSs, either there was inventory at the DC in week t-1 or they are flow
through items. The percentages corresponding to the four types of forecast error sum up
to a hundred. Figure 4.3 shows the same picture but with a breakdown by SKU CLASS.
Refer to Appendix D for the data.
45
Percentage Occurrence of OOS Causes and Conditions
Percentage Occurrence of OOS Causes and Conditions
(All SKUs, All Stores)
(All)
(All) (All)
* (All) (All)
m
50.00%'6
45.00%
40.00%
35.0006
30.00%
25.00%
20.00%/
15.00%
10.00%/0
5.00%
0.00%
110
0
0
Z
J
de'Al
x re-
.
.40
440
(<0
<0 40
40
P0
'0
q4b
se
4I
0
09
Figure 4.2: Plot of percentage occurrence of OOS causes and conditions
Percentage Occurrence of OOS Causes and Conditions
(Split by SKU Class, All Stores)
70.00%
5000CLASS
C
40.00%/
40.0
mCLASS
H
B
o CLASS A
30.00 !
New
20.
10.000/0
0
00
NO'~
40
40
.40
40
40
0
.10
.40
N,
.00
0~
Figure 4.3: Plot of percentage occurrence of OOS causes and conditions, split by SKU
CLASS
To get a consolidated view of the OOS causes and conditions, we selected a few
combinations of OOS conditions and causes that are most pertinent and compare their
relative frequencies. The results are shown in Figure 4.4 and Figure 4.5. Out-of-stocks are
classified as "No Other" if the only condition that we could identify for the OOS was that
of the forecast error. "Only Neg Adj" and "Only Order Delay" correspond to the OOS for
which we could detect only "negative
inventory adjustment" and "order delayed"
46
respectively. "Order Delay and DC problem" corresponds to an order that was delayed
and at the same time the DC was OOS at week t or t-1. Anything that does not fall under
the above would go under "others".
Stockout Conditions
(Bar Chart)
50.00%
45.00%
40.00%
35.00%
flOthers
& 30.00%
a
Order Delay and DC Problem
25.00%
Only Order Delay
20.00%
m Only Negative Adjustment
15.00%
* No Other
10.00%
5.00%
0.00%
Non Positive Error
Small Error
Medium Error
Large Error
Forecast Error
Figure 4.4: Plot of percentage occurrence of major
OOS.
Stockout Conditions
(100% Stacked Bar Chart)
100%
80%
mOthers
&
60%
Order Delay and DC Problem
A
Only Order Delay
m Only Negative Adjustment
aNo Other
40%
20%
0% Non Positive Error
Small Error
Medium Error
Large Error
Forecast Error
Figure 4.5: Plot of percentage occurrence of major OOS causes normalized to 100% for
each forecast error type.
47
Table 4.1: Distribution of OOS Causes
No Other
Only Neg Adj
Only Order Delay
Order Delay & DC Problem
Others
Total
Non
Positive
Error
18.47%
7.81%
6.79%
10.95%
2.69%
46.71%
Small
Error
12.78%
5.80%
2.36%
2.52%
2.35%
25.81%
Medium
Error
6.86%
0.92%
0.16%
0.10%
1.21%
9.25%
Large
Error
14.38%
1.38%
0.19%
0.08%
2.20%
18.23%
Total
52.50%
15.90%
9.50%
13.65%
8.45%
100.00%
Table 4.1 shows the percentages for Figure 4.4 and Figure 4.5. From this table we can see
that about 34% of the OOS have a positive forecast error with no other causes. Thus, we
may view these as normal out-of-stocks that are caused by a greater than expected demand.
Approximately 16% of OOSs have negative inventory adjustment of which 85% occur
when there was negative or small positive forecast error. This suggests that negative
inventory adjustment was the key reason that we could identify for nearly 14% of OOSs .
For over 22% of OOSs there is an order delay along with having a negative forecast error
or small positive forecast error. This suggests that the order delay is probably the key
driver in these OOSs. Out of these OOSs, close to 60% have the DC being OOS, which
might reasonably be the cause for the order delay.
There are also 11 % of OOSs which are attributed to multiple causes and thus are difficult
to separate out one key driving factor. And finally, some 18% of OOSs occur with a
negative forecast error with no other causes being identified; we can postulate no
explanation for these OOSs.
Figure 4.6 provides us with an overview of the key driving factors of the out-of-stocks as
we have earlier described.
48
Key OOS Causes
Multiple Reasons,
11.28%
Unknown,
18.47%
Order Delay
22.62%
Negative Adjustment,
13.61%
DC Problem
59.54%
'A
Forecast Error,
34.02%
No DC Problem
40.56%
Figure 4.6: Key
OOS Causes
Thus, we see that there is much room for improving the OOS rate. Although improving
forecast accuracy is generally agreed to be difficult, we see from the Figure 4.6 that it is not
the sole cause of OOS. Other causes contribute up to 66% of the OOSs we see and thus
certainly present opportunities for improvement.
49
Chapter 5
Examining a Peculiarity
Beta's managers had found an odd phenomenon, which we will conveniently refer to as the
"peculiarity" whereby the out-of-stock rate of CLASS C items is higher in RANK A stores
than in RANK E stores. In this chapter, we will examine the "peculiarity", show that it is
unlikely to have been due to chance, review a list of likely causes and report on the three
major causes that we have found.
5.1 The Peculiarity
Figure 5.1 illustrates the "peculiarity", which in fact suggests that higher ranked stores have
a higher OOS rate for CLASS C products. Though there seems to be a hint of this
peculiarity for CLASS B SKUs as well, it is not as distinct as that of CLASS C SKUs.
Figure 5.2 shows how the peculiarity persists across different SKU divisions while Figure
5.3 shows how the peculiarity persists across stores with different pick frequencies. We can
interpret Figure 5.3 in the sense that if given a handful of stores with the same pick
frequency, stores with higher rank still tend to have a higher OOS rate. We note that the
OOS rate of RANK E stores with pick frequency 3 is higher than that of RANK A stores,
contradicting the peculiarity. This however is because there are only 3 RANK E stores with
pick frequency of 3.
51
Out-of-Stock Rate Aggregated By CLASS and Store RANK
0.0250
-
0.0200
0.0150
0.0100
0
0.0050
0.0000
A
B
C
SKU CLASS, Store RANK
Figure 5.1: OOS rate aggregated by SKU CLASS (A, B, C) and STORE RANK (A, B, C, D,
E)
Out-of-Stock Rate of CLASS C SKUs - Aggregated By SKU Division and Store Rank
-
0.08
0.07
.
EU
0.06
.g 0.05
S0.04
0.03
0 0.02
0.01
0
-
A
B
A
1
B
C
D
E
A
B
CD
EA
3
2
B C
5
D
E
A
B
C
D
E
7
SKU Division, Store Rank
Figure 5.2: OOS rate of CLASS C SKUs aggregated by SKU DIVISION (1, 2, 3, 5, 7) and
STORE RANK (A, B, C, D, E)
52
Out-of-Stock Rate of CLASS C SKUs Aggregated by Store Pick Frequency and Rank
0.03
0.025
0.02
0.015
0.01
0
0.005
0
C
D
A
E
B
C
D
E
A
B
C
D
E
3
2
1
A
B
4
E
A
B
C
D
E
5
Pick Frequency, Store Rank
Figure 5.3: OOS Rate of CLASS C SKUs aggregated by Pick Frequency (1, 2, 3, 4, 5) and
Store RANK (A, B, C, D, E)
5.2 Peculiarity is not by Chance
Though Figure 5.1 by itself already paints a rather convincing picture that there is
something systematic underlying the out-of-stocks, we will still provide a quantitative
analysis of it. Here we will use ANOVA and hypothesis tests to show that the peculiarity is
unlikely to have occurred by chance alone. Refer to Appendix E for the data on the OOS
rates.
5.2.1 ANOVA
We will use ANOVA to test the null hypothesis that the mean OOS rates of stores of
different ranks are the same against the alternate hypothesis that not all the mean OOS
rates are equal.
Let JUA, p1 B , plc ,
1
D
and PE be the mean OOS rate of CLASS C items in RANK A, B,
C, D and E stores respectively. We have a sample of 28, 37, 45, 52 and 71 RANK A, B, C,
D and E stores respectively. The OOS rate of CLASS C items in a particular store is
53
calculated by dividing the total number of OOS of CLASS C items in that store by the total
number of observations that correspond to CLASS C items.
The null hypothesis is given as,
H0
:
=
C
ID
(5.1)
,E
while the alternate hypothesis is
(5.2)
H : Not all the p are equal.
The result of ANOVA is to reject the null hypothesis with a type I error probability of less
than
X 10
14
. Type I error is the error of rejecting the null hypothesis when the null
hypothesis is true. Figure 5.4 shows the box plot of the OOS rate of the stores grouped by
their RANK.
Box Plot
0.04
-
+
-
0.035
-
+
0.03
(n
a)
0.025
T
+
0.02
0.015f
-
-
0.01
Rank A
Rank B
Rank C
Rank D
Figure 5.4: Box Plot of the OOS Rate of the Stores
54
Rank E
We note here that in applying ANOVA, two rather strict assumptions are made by default.
The first is that the OOS rate of the stores within each RANK is normally distributed and
the second is that the standard deviations of the OOS rates of stores within a particular
RANK are the same across the RANKS.
5.2.2 Multiple Hypothesis Tests
The alternate hypothesis in section 5.2.1 fails to provide us with much information since it
only tells us that the mean OOS rates of the stores are not equal. Here we will perform
multiple hypothesis tests in attempt to show that plA > pB
>C
ID >E
We let the null hypothesis be
HO :pt =U,,
where, x, y e
{A,
(5.3)
B, C, D, E} and x < y. And let the alternate hypothesis be
HI : P, > P,,1
(5.4)
Since for each hypothesis test, the two samples are of unequal size, have combined size of
at least 65 and have unequal variances, we apply the 2-sample unpooled T-test. Table 5.1
and Table 5.2 show the p values and degrees of freedom of the hypothesis tests
respectively.
Table 5.1: P values of the hypothesis tests
A
A
B
x
B
0.058221
C
C
0.024394
0.276019
D
0.000012
0.000201
E
0.000000
0.000000
0.003513
0.000000
0.001620
D
E
55
Table 5.2: Degrees of freedom of the hypothesis tests
A
B
C
60.37
79.75
B
51.87
A
DY
xC
D
51.65
82.27
E
42.39
73.03
87.54
76.81
102.91
D
E
We can see from Table 5.1 that at 5% level, we would accept the alternate hypotheses of
A > pc > AD > AE and AB
A
=
AR and that
D
E
We cannot reject the null hypotheses that
B =C
5.3 Three Causes of the Peculiarity Identified
We have found that differences in safety stock carried, the time between orders and the
forecast error are three contributors to the peculiarity. In this section, we will report on
these three causes and estimate the extent to which they are responsible for the difference
between the OOS rates for Class C items at rank A and rank E stores.
5.3.1 Differences in Weeks of Safety Stock Carried
In section 3.1, we have seen how OOS rate decreases as the amount of safety stock
increases. Here, we will see that RANK E stores carry more safety stock (on a relative
basis) than RANK A stores and thus RANK E stores have a lower OOS rate. Though not
quantified in our analysis, the integrality effect seems to play a role in creating this
difference in the relative amount of safety stock carried. CLASS C items in RANK E stores
usually have FC that is quite small, and typically is smaller than one. Rounding to nearest
integer in computing the re-order point and order quantity results in a relative increase in
the safety stock carried for these items.
56
RANK E Stores carry more weeks of safety stock than RANK A Stores
Figure 5.5 and Figure 5.6 show the relative frequency of the weeks of safety stock in
RANK A and RANK E stores respectively. To obtain Figure 5.5, we first compute the
WEEK.SS for each and every observation of CLASS C items in RANK A stores and then
develop a frequency chart. Figure 5.6 is obtained in similar fashion but considering CLASS
C items in RANK E stores only.
Visually, it is clear that RANK E stores have more weeks of safety stock than RANK A
stores. Refer to Appendix F for the data.
* 99 (Al) A
Relative Frequency of Final Safety Stock In Rank AStores
(Considering Class C SKUs only
12.0%
10.0%
8.0%
6.0%.9 4.0%/
2.0%
0.0%0
1
2
3
4
567
8
9
10
11
12
13
14
15
16
17
18
19
20
30
40
50
60
70
100
>
21
31
41
51
61
71
101
Final Safety Stock (expreIed Inweeka of denund)
Figure 5.5: Relative frequency of safety stock in weeks in RANK A Stores
*99 (AI) E
Relative Frequency of Final Safety Stock In Rank E Stores
(Considering Class C SKUs only
12.0%
210.0%8.0%/k
6.0%/6
aA.
0%
24.0%
2.0%0.00%/030
S 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
1
2021
40
50
60
70
100
>
31
41
51
61
71
101
Final Safety Stock (expre-sed In weeks of derwand)
Figure 5.6: Relative frequency of safety stock in weeks in RANK E Stores
57
Approximately 60% Responsible
We use the empirical model for the relationship between OOS rate and weeks of safety
stock as shown in Figure 3.3 to determine the extent to which the difference in amount of
safety stock carried is responsible for the "peculiarity". In particular, we suppose that the
relationship shown in Figure 3.3 is exactly true for both rank A and Rank E stores. Then
rate
given the safety stock profiles shown in Figures 5.5 and 5.6, we can estimate the 00S
for each rank of store.
We let the empirical model of OOS rate and weeks of safety stock be given as,
),
r =f
(5.5)
where P is the OGS rate and x is the safety stock in weeks. We predict the OOS rate of
CLASS C items in stores of an arbitrary RANK k by the model:
rk =
where wek
w, j
(xi),
(5.6)
is the relative fraction of observations of CLASS C SKUs in the RANK k
stores that have xi weeks of safety stock. In particular, these weights are given in Figure
5.5 and Figure 5.6 for rank A and E stores, respectively.
From equation (5.6) we find that i^ = 0.0 1977 and iE = 0.01493.
Thus, we see that
there is a difference in OOS rate of 0.005 that seems to be due to the differences in safety
stocks between RANK A and RANK E stores.
There are two ways to evaluate the extent to which safety stock differences are responsible
for the differences in the OOS rate. The first method uses the ratio of the OOS rate and is
given by,
58
% responsibility = rE
X100% ,
(5.7)
rA
rE
The second method makes use of the difference in the OOS rates and is given as
% responsibility = rA
r-
E
rE
x 100%,
(5.8)
Table 5.3 shows the results of the model and actual OOS rates while Table 5.4 shows the
percentage responsibility computed using the two different methods. We see that the two
methods give relatively comparable results.
Table 5.3: WEEKS.SS Model and Actual OOS Rate
RANK A
0.01977
0.02052
WEEKS.SS Model OOS Rate, r
Actual OOS Rate, r
RANK E
0.01493
0.01306
Table 5.4: Percentage Responsibility of WEEKS.SS
Percentage Responsibility of WEEKS.SS
First Method
Second Method
(5.7)
56.80%
(5.8)
64.93%
The model predicts that the OOS rate for rank A would be 0.01977 and for rank E would
be 0.01493; thus, the model predicts a gap of about 0.005; as the actual gap is about 0.007,
we conclude that the difference in safety stock seems to be responsible for about 60% of
the difference in OOS, as shown in Table 5.4.
5.3.2 Differences in Time Between Orders
We have seen in section 3.2 that OOS rate decreases as the time between orders increases.
For each SKU, the time between orders depends on its order quantity; the larger is the
59
order quantity, the longer is the time between orders. From standard inventory theory, we
expect that the OOS rate would decline as the TBO or order quantity increase.
In this section, we will see that RANK A stores tend to have longer time between orders
than RANK E stores, partially explaining the peculiarity.
RANK A stores have longer time between orders than RANK E stores
Figure 5.7 and Figure 5.8 show the relative frequency of time between orders for RANK A
and RANK E stores respectively. We obtain the plots in similar manner as given in section
5.3.1, which is to first compute the time between orders (in weeks) for each and every
observation of CLASS C items and then develop the frequency charts for the respective
ranks. A visual inspection of the graphs clearly show that CLASS C items in RANK E
stores tend to have longer time between orders than CLASS C items in RANK A stores.
Refer to Appendix G for the data corresponding to the plots.
* A (A) 9
Distribution of Observations by Tin Between Ordering in Rank AStores
(Considering Class C SKUs only)
12.0%0/%
10.
.
%
0
.9
0%/
%
I
1
4.0%
2.0%
4
0.0%/6
01
2
3
4
5
6
3
7
8
---9
9
T 6
107 11
7 13
12 1
r1
1
14
1
1630
16 17
18] 19
20
21
40
50
31
41
60 70
51 61
Tine Between Ordering (in Weeks)
Figure 5.7: Relative frequency of time between orders in RANK A Stores
60
100
>
71
101
MOORE I
I
E (All) 99
Distribution of Observations by Tifnf Between Ordering in Rank E Stores
(Considering Class C SKUs only)
12.0%
S 10.0%
- -
- - --
---
-
-
6.7%
8.0
.9
%44%4.4%4
4
4.(O%
2.0%
0
1
2
3
4
5
6
7
8
9
10
11
Tine
12
13
14
15
16
17
18
19
20
30
40
50
60
70
100
>
21
31
41
51
61
71
101
Between Ordering (in Weeks)
Figure 5.8: Relative frequency of time between orders in RANK E Stores
Approximately 40% Responsible
We compute the extent to which the difference in TBO is responsible for the difference in
OOS in the same way as we did in section 5.3.1. Specifically, we suppose that the
relationship shown in Figure 3.7 is exactly true for both RANK A and RANK E stores.
Then given the TBO profiles shown in Figure 5.7 and Figure 5.8, we use equation (5.5) and
(5.6) to compute the OOS rate for each RANK. Finally, we use equation (5.7) and (5.8) to
compute the extent to which the difference TBO is responsible for the difference in OOS
rate.
From equation (5.6) we find that rA =0.01894 and rE =0.01562. Thus, we see that there
is a difference in OOS rate of 0.0033 that seems to be due to the differences in time
between orders between RANK A and RANK E stores.
Table 5.5 shows the results of the model and actual OOS rate while Table 5.6 shows the
percentage responsibility computed using the two methods.
Table 5.5: TBO Model and Actual
TBO Model OOS Rate, r
Actual OOS Rate, r
RANK A
0.01894
0.02052
61
OOS Rate
RANK E
0.01562
0.01306
-
Table 5.6: Percentage Responsibility of TBO
First Method
Percentage Responsibility of TBO
Second Method
(5.7)
(5.8)
37.26%
44.55%
Thus, the model predicts that the OOS rate for rank A would be 0.01894 and for rank E
would be 0.01562, which gives a gap of about 0.0033. Since the actual gap is about 0.0075,
we conclude that the difference in time between orders seems to be responsible for about
40% of the difference in OOS, as shown in Table 5.6.
5.3.3 Differences in Normalized Forecast Error
We have seen in section 3.3 that OOS rate increases as the normalized forecast error
increases. Here, we will see that RANK A stores tend to have greater normalized forecast
errors than RANK E stores, partly explaining the peculiarity.
RANK A stores have greater normalized forecast error than RANK E stores
Figure 5.9 and Figure 5.10 show the relative frequency of normalized forecast error for
RANK A and RANK E stores respectively. We obtain the plots in similar fashion as stated
in section 5.3.1, which is to first compute the normalized forecast error for each and every
observation of CLASS C items and then develop the frequency charts for the respective
ranks. Here we plot only the positive normalized forecast error. We note that the
percentage of observations with negative normalized forecast error is 69.7% and 84.3% for
RANK A and RANK E stores respectively. Appendix H contains the data used for the
plots. From these plots we see that the forecast errors for RANK A stores are larger than
that for RANK E, where much of this is due to the fact that RANK E stores have a much
higher percentage of negative forecast errors.
62
* A (AI) 99 A (AM) 99
Distribution of Observations by Normlized Forecast Error in Rank AStores
(Considering Class C SKUs only)
-
5.00%/
0.50%
-/
S3.0%
0
%
2.50%/
2.00%
4.00%
1.50%/
;
1.00%
0.%
.20.5 .75 1
2
.2
.5 .
235. 7
1l.2 1'.51.7
2
.202.5 .7
3.2.54
.2 1..5 .7
.2 0.7
8
567
.2
4
9
678
.5.
0
9
11
213 14 1516 17 18 19 20 >
10
12134151171192
Nornulized Forecast Error
Figure 5.9: Relative frequency of normalized forecast error in RANK A Stores
H E (All) 99 E (All) 99
Distribution of Observations by Nornulized Forecast Error In Rank E Stores
(Considering Class C SKUs only)
5.009%
4.50%/-S4.00%/4
3.50%Aa
3.00%
10% Reposil
-
.0%
.....
2 .50% -..........
.5%
&1.00%
a-0.50%/
0.001%
D.25-0.5 D.75 1 1.2!1.5 1.75 2
D .25 0.5 D.75 1 1.2- 1.5.7
.2-2.5'.72
3
.- 2.5 .7-
.2-3.5<.7-4
.2
3
4-2'45-7
.2- &. .-
.5.7
Normaie Fo
Figure
6
5
7
8
7
9
10
"7
1 12 13 14 15 16 1 7 18 19 20
0
112 1
14 15
61
>
18 19 20
-atError
5.10: Relative frequency of normalized forecast error in RANK E Stores
Approximately 10% Responsible
We compute the extent to which the difference in forecast error is responsible for the
difference in OOS in the same way as we did in section 5.3.1. Specifically, we suppose that
the relationship shown in Figure 3.11 is exactly true for both RANK A and RANK E
stores. Then given the normalized forecast error profiles shown in Figure 5.9 and Figure
5.10, we use equation (5.5) and (5.6) to compute the OOS rate for each RANK. Finally, we
use equation (5.7) and (5.8) to compute the extent to which the difference in forecast error
is responsible for the difference in OOS rate.
63
From equation (5.6) we find that ^ = 0.01726 and ^ =0.01624. Thus, we see that there
is a difference in OOS rate of 0.001 that seems to be due to the differences in forecast
error between RANK A and RANK E stores.
Table 5.7 shows the results of the model and actual OOS rate while Table 5.8 shows the
percentage responsibility computed using the two methods.
Table 5.7: NFE Model and Actual OOS Rate
NFE Model OOS Rate, r
Actual OOS Rate, r
RANK A
0.01726
0.02052
RANK E
0.01624
0.01306
Table 5.8: Percentage Responsibility of NFE
Percentage Responsibility of NFE
First Method
Second Method
(5.7)
11.02%
(5.8)
13.69%
Thus, the model predicts that the OOS rate for rank A would be 0.01726 and for rank E
would be 0.01624; thus, the model predicts a gap of about 0.001; as the actual gap is about
0.0075, we conclude that the difference in safety stock seems to be responsible for about
10% of the difference in OOS, as shown in Table 5.8.
5.4 Other Hypothesized Causes that are not True
Here, we will take a brief look at some other possible explanations that we had examined
but found unlikely to be true.
A Few Errant Stores
One hypothesis is that a few "bad" RANK A stores could be skewing the average OOS
rate of RANK A stores. However, a look at the distribution of the stores by their OOS rate
reveals that this is probably not the prime reason. A visual inspection of the distribution of
the stores by their OOS rate as shown in Appendix I indicates that instead of just a few
64
outliers, the entire distribution of RANK A stores is right shifted towards higher OOS
rates.
RANK A stores carry more SKUs that go OOS more frequently
It may be possible that certain SKUs have higher OOS rate and that RANK A stores just
happen to carry a greater proportion of these SKUs. To examine if the hypothesis is true,
we first group the SKUs based on the difference in their frequency of occurrences in
RANK A and RANK E stores. Then for each group of SKUs we compare the OOS rate
in RANK A and RANK E stores. We will see in Appendix J that within each SKU group,
RANK A stores still have higher OOS rate than RANK E stores.
More Advertising in RANK A Stores
Though not shown in this thesis, a plot of the advertising rate would reveal that advertising
rate is similar across the ranks. By making the assumption that advertising effects, if any, on
the OOS rate is the same across the ranks, we can conclude that advertising is not the
cause.
The relationship between promotion and OOS rate was also investigated. The result
however was inconclusive as we were unable to differentiate the effect of promotion from
the natural fluctuation in sales and OOS rate over time. A prospective study with careful
control of the promotional items may provide some insights to the relationship.
65
Chapter 6
Conclusion
Using the inventory data from Beta, we have established in Chapter 3 the empirical
relationship of OOS rate with safety stock, time between orders, and forecast error. We
saw that OOS rate decreases as safety stock increases from 0 to 20 weeks of demand but
remains constant beyond that. This empirical relationship can be used to aid Beta's
managers in determining the level of inventory to have for each SKU; in particular it
provides a way to see for each item class, the benefits in terms of reduced OOS from an
investment in additional safety stock. We also found that OOS rate decreases as the time
between orders increases and increases as the normalized forecast error increases.
In Chapter 4, we saw that 34% of the OOS were caused by forecast error, partly explaining
the empirical relationship between OOS rate and safety stock we saw in Chapter 3. The
fact that up to 22% of OOS was due to some form of order delay suggests that
improvement can be made to improve merchandize in-stock by reducing the rate and
magnitude of order delays. Negative inventory adjustments account for approximately 14%
of the OOSs; this is indicative of how many OOSs are attributable to store execution
problems. Moreover 18% of 00S were caused by factors which we were unable to
determine from the data, further suggesting opportunities for improvement.
In Chapter 5, we investigated the peculiarity that CLASS C items experience a higher OOS
rate in RANK A stores than RANK E stores. We found that differences in the amount of
67
safety stock carried, the time between orders and the forecast error are largely responsible
for the peculiarity.
68
Appendix A
Data for Exchange Curve of OOS
Rate and WEEKS.SS
Table A.1: Data for
OOS Rate versus WEEKS.SS, all SKUs
Safety stock in weeks
(WEEKS.SS)
Grp
1
2
>=
0
<
Average _No. of Observations
0.5
213000
0.5
3
1.5
2.5
3.5
4.5
5.5
6.5
7.5
8.5
9.5
10.5
11.5
12.5
13.5
14.5
15.5
16.5
17.5
18.5
19.5
1.5
2.5
3.5
4.5
5.5
6.5
7.5
8.5
9.5
10.5
11.5
12.5
13.5
14.5
15.5
16.5
17.5
18.5
19.5
20.5
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
1720805
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
20.5
30.5
40.5
50.5
60.5
70.5
30.5
40.5
50.5
60.5
70.5
100.5
20
25.5
35.5
45.5
55.5
65.5
85.5
480805
No. of Stockouts
1394
15127
34487
36571
31257
22482
18090
14692
16572
8443
7418
6963
6175
3834
3389
2846
1196
2882
2400
878
2442
8292
5265
264849
3047
76050
150550
589
1582
3955
765877
1808389
1553429
1210230
1002289
840057
1017093
590111
517024
496675
462710
301882
297458
253878
137693
255372
199884
98363
207187
844386
300761
69
OOS Rate-
0.0065
0.0198
0.0200
0.0202
0.0201
0.0186
0.0180
0.0175
0.0163
0.0143
0.0143
0.0140
0.0133
0.0127
0.0114
0.0112
0.0087
0.0113
0.0120
0.0089
0.0118
0.0098
0.0110
0.0115
0.0077
0.0105
0.0131
|128
| 100.5
>
1 12691
1 738083
|I
1 0.0172
Table A.2: Data for OOS Rate versus WEEKS.SS, CLASS A SKUs only
Safety stock in weeks
(WEEKS.SS)
Grp
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
>=
0
0.5
1.5
2.5
3.5
4.5
5.5
6.5
7.5
8.5
9.5
10.5
11.5
12.5
13.5
14.5
15.5
16.5
17.5
18.5
19.5
20.5
30.5
40.5
50.5
60.5
<
70.5
100.5
0.5
1.5
2.5
3.5
4.5
5.5
6.5
7.5
8.5
9.5
10.5
11.5
12.5
13.5
14.5
15.5
16.5
17.5
18.5
19.5
20.5
30.5
40.5
50.5
60.5
70.5
100.5
Average ,No. of Observations
22938
0
400276
1
563731
2
354428
3
195997
4
106199
5
58575
6
35724
7
23069
8
15818
9
12369
10
9466
11
12
7402
5362
13
4472
14
3756
15
3137
16
2678
17
2301
18
1836
19
20
1649
25.5
8578
35.5
3000
45.5
1432
778
55.5
65.5
409
85.5
828
688
No. of Stockouts
333
6234
7352
4326
2092
947
515
276
166
93
63
55
35
32
22
18
17
11
11
7
13
34
15
5
6
3
4
9
OOS Rate
0.0145
0.0156
0.0130
0.0122
0.0107
0.0089
0.0088
0.0077
0.0072
0.0059
0.0051
0.0058
0.0047
0.0060
0.0049
0.0048
0.0054
0.0041
0.0048
0.0038
0.0079
0.0040
0.0050
0.0035
0.0077
0.0073
0.0048
0.0131
Table A.3: Data for OOS Rate versus WEEKS.SS, CLASS B SKUs only
Safety stock in weeks
(WEEKS.SS)
Grp
1
2
3
4
5
6
7
8
9
10
11
>=
0
0.5
1.5
2.5
3.5
4.5
5.5
6.5
7.5
8.5
9.5
<
0.5
1.5
2.5
3.5
4.5
5.5
6.5
7.5
8.5
9.5
10.5
Average
0
1
2
3
4
5
6
7
8
9
10
No. of Observations
No. of Stockouts
OOS Rate
14609
291967
831974
877231
641168
142
6762
17276
16243
10913
5795
3400
1979
1392
775
556
0.0097
0.0232
0.0208
0.0185
403709
265725
172134
124988
80739
63068
70
0.0170
0.0144
0.0128
0.0115
0.0111
0.0096
0.0088
1
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
10.5
11.5
12.5
13.5
14.5
15.5
16.5
17.5
18.5
19.5
20.5
30.5
40.5
50.5
60.5
70.5
11.5
11
12.5
13.5
14.5
15.5
16.5
17.5
18.5
19.5
12
13
14
15
16
17
18
19
51671
42553
27150
24984
20035
15014
14303
12333
8942
20.5
30.5
40.5
50.5
60.5
20
9470
25.5
35.5
45.5
55.5
70.5
100.5
65.5
85.5
100.5
0.0081
45917
17499
421
335
170
146
128
62
75
73
48
72
223
86
7906
35
0.0044
3763
2761
3930
3329
16
21
18
56
0.0043
0.0076
0.0079
0.0063
0.0058
0.0064
0.0041
0.0052
0.0059
0.0054
0.0076
0.0049
0.0049
0.0046
0.0168
Table A.4: Data for OOS Rate versus WEEKS.SS, CLASS C SKUs only
Safety stock in weeks
(WEEKS.SS)
Grp
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
>=
<
Average
0
0.5
0
0.5
1.5
2.5
3.5
4.5
5.5
6.5
7.5
8.5
9.5
10.5
11.5
12.5
13.5
14.5
15.5
16.5
17.5
18.5
19.5
20.5
30.5
40.5
50.5
60.5
70.5
100.5
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
25.5
35.5
45.5
55.5
65.5
85.5
1.5
2.5
3.5
4.5
5.5
6.5
7.5
8.5
9.5
10.5
11.5
12.5
13.5
14.5
15.5
16.5
17.5
18.5
19.5
20.5
30.5
40.5
50.5
60.5
70.5
100.5
No. of Observations
168244
63964
301250
550912
678130
661579
651204
601548
740521
444748
429552
422372
398470
257922
255748
224994
113313
231153
175817
87146
189495
763319
437166
252060
70401
145328
292816
679596
71
No. of Stockouts
907
1836
9152
15440
17504
15102
13916
12001
13481
7102
6657
6267
5671
3470
3134
2625
1044
2715
2100
816
2231
7684
4994
2930
549
1528
3859
7777
OOS Rate
0.0054
0.0287
0.0304
0.0280
0.0258
0.0228
0.0214
0.0200
0.0182
0.0160
0.0155
0.0148
0.0142
0.0135
0.0123
0.0117
0.0092
0.0117
0.0119
0.0094
0.0118
0.0101
0.0114
0.0116
0.0078
0.0105
0.0132
0.0114
Table A.5: Data for OOS Rate versus WEEKS.SS, New SKUs only
Safety stock in weeks
(WEEKS.SS)
Grp
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
>=
0
0.5
1.5
2.5
3.5
4.5
5.5
6.5
7.5
8.5
9.5
10.5
11.5
12.5
13.5
14.5
15.5
16.5
17.5
18.5
19.5
20.5
30.5
40.5
50.5
60.5
70.5
<
0.5
1.5
2.5
3.5
4.5
5.5
6.5
7.5
8.5
9.5
10.5
11.5
12.5
13.5
14.5
15.5
16.5
17.5
18.5
19.5
20.5
30.5
40.5
50.5
60.5
70.5
100.5
28
100.5
>
Average
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
25.5
35.5
45.5
55.5
65.5
85.5
No. of Observations
7209
9670
23850
25818
38134
38743
26785
30651
128515
48806
12035
13166
14285
11448
12254
5093
6229
7238
9433
439
6573
26572
23140
3451
1108
2085
3193
No. of Stockouts
12
295
707
562
748
638
259
436
1533
473
142
220
134
162
87
75
73
81
216
7
126
351
170
77
18
31
76
OOS Rate
0.0017
0.0305
0.0296
0.0218
0.0196
0.0165
0.0097
0.0142
0.0119
0.0097
0.0118
0.0167
0.0094
0.0142
0.0071
0.0147
0.0117
0.0112
0.0229
0.0159
0.0192
0.0132
0.0073
0.0223
0.0162
0.0149
0.0238
54431
4846
0.0890
72
Appendix B
Data for Exchange Curve of OOS
Rate and TBO
Table B.1: Data for OOS Rate versus TBO, all SKUs
Time Between Orders in
weeks (TBO)
Grp
>=
<
Average
No. of Observations
No. of Stockouts
OOS Rate
1
2
3
4
5
6
7
8
9
0
0.5
1.5
2.5
3.5
4.5
5.5
6.5
7.5
8.5
9.5
10.5
11.5
12.5
13.5
14.5
15.5
16.5
17.5
18.5
19.5
20.5
30.5
40.5
0.5
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
688782
1767617
1697682
1436737
1349257
1106069
959957
793915
955833
573082
512017
490061
498924
281433
310533
239639
107988
229496
170644
79651
0.0129
20
209890
8858
31530
32301
26926
26496
20312
18063
14193
14089
8481
7578
6918
6934
3936
3787
3048
1221
2996
2129
852
2577
25.5
35.5
45.5
55.5
65.5
85.5
659022
372780
222403
48433
126183
294039
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
50.5
60.5
70.5
1.5
2.5
3.5
4.5
5.5
6.5
7.5
8.5
9.5
10.5
11.5
12.5
13.5
14.5
15.5
16.5
17.5
18.5
19.5
20.5
30.5
40.5
50.5
60.5
70.5
100.5
7830
3919
3002
412
1714
4460
73
0.0178
0.0190
0.0187
0.0196
0.0184
0.0188
0.0179
0.0147
0.0148
0.0148
0.0141
0.0139
0.0140
0.0122
0.0127
0.0113
0.0131
0.0125
0.0107
0.0123
0.0119
0.0105
0.0135
0.0085
0.0136
0.0152
|128
|
100.5
>
|I
1 11269
1 660562
1 0.0171
Table B.2: Data for OOS Rate versus TBO, CLASS A SKUs only
Time Between Orders in
weeks (TBO)
Grp
<
>
.50
<0.5
0.5
1.5
2.5
3.5
4.5
5.5
6.5
7.5
8.5
9.5
10.5
11.5
12.5
13.5
14.5
15.5
16.5
17.5
18.5
19.5
20.5
30.5
1.5
2.5
3.5
4.5
5.5
6.5
7.5
8.5
9.5
10.5
11.5
12.5
13.5
14.5
15.5
16.5
17.5
18.5
19.5
20.5
30.5
40.5
50.5
60.5
70.5
100.5
40.5
50.5
60.5
70.5
100.5
Average
Ever
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
25.5
35.5
45.5
55.5
65.5
85.5
No. of Observations
55085
479892I
550853
339982
197334
113651
No. of Stockouts
4978
6668
4497
2966
1590
58030
753
33534
20625
13684
8742
408
6006
56
48
35
29
21
13
15
12
256
166
105
4194
3320
2268
1899
1526
1154
1056
6
867
681
7
4
36
OOS
Rate
0f.0121ut
0.0104
0.0121
0.0132
0.0150
0.0140
0.0130
0.0122
0.0124
0.0121
0.0120
0.0093
0.0114
0.0105
0.0128
0.0111
0.0085
0.0130
0.0114
0.0069
0.0103
0
0.0063
0.0112
0.0076
0.0036
0.0000
260
1
0.0038
386
829
3
0.0078
10.0109
640
3223
1314
561
388
10
2
9
Table B.3: Data for OOS Rate versus TBO, CLASS B SKUs only
Time Between Orders in
weeks (TBO)
Grp
1
2
3
4
5
6
7
8
9
10
11
>=
0
0.5
<
1.5
2.5
3.5
4.5
5.5
6.5
7.5
8.5
9.5
2.5
3.5
4.5
5.5
6.5
7.5
8.5
9.5
10.5
0.5
1.5
Average
0
1
2
3
4
5
6
7
8
9
10
No. of Observations
No. of Stockouts
OOS Rate
185436
863002
752158
606916
478592
337616
244479
162168
124938
76351
54383
3307
15257
12850
10037
8344
5500
3931
2462
1674
1032
680
0.0178
0.0177
0.0171
0.0165
0.0174
0.0163
0.0161
0.0152
0.0134
0.0135
74
0.0125
1
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
10.5
11.5
12.5
13.5
14.5
15.5
11.5
12.5
13.5
14.5
15.5
16.5
17.5
18.5
19.5
11
12
13
14
15
16
17
18
19
46176
33386
20102
15518
13199
6688
8013
6709
3679
20
5630
40.5
20.5
30.5
40.5
50.5
50.5
60.5
60.5
70.5
70.5
25.5
35.5
45.5
55.5
65.5
85.5
19073
5991
2518
1034
1139
1464
2576
16.5
17.5
18.5
19.5
20.5
30.5
100.5
100.5
508
400
199
168
153
73
95
61
35
55
234
62
33
9
10
11
41
0.0110
0.0120
0.0099
0.0108
0.0116
0.0109
0.0119
0.0091
0.0095
0.0098
0.0123
0.0103
0.0131
0.0087
0.0088
0.0075
0.0159
Table B.4: Data for OOS Rate versus TBO, CLASS C SKUs only
Time Between Orders in
weeks (TBO)
Grp
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
>=
0
0.5
1.5
2.5
3.5
4.5
5.5
6.5
7.5
8.5
9.5
10.5
11.5
12.5
13.5
14.5
15.5
16.5
17.5
18.5
19.5
20.5
30.5
40.5
50.5
60.5
70.5
100.5
<
Average
No. of Observations
No. of Stockouts
0.5
1.5
2.5
3.5
4.5
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
19975
326306
574597
607813
703872
664784
653381
582685
509
8947
14126
13414
15465
13495
13409
11129
11203
6926
6518
6115
6154
3524
3457
2791
1099
2805
1914
788
2367
7308
3746
2914
401
1690
5.5
6.5
7.5
8.5
9.5
10.5
11.5
12.5
13.5
14.5
15.5
16.5
17.5
18.5
19.5
20.5
30.5
40.5
50.5
20
60.5
70.5
100.5
55.5
25.5
35.5
45.5
705
65.5
85.5
702507
450227
436481
425172
434724
247276
269378
218505
98744
213263
154928
73264
182422
622547
355634
216204
46747
123716
289383
594499
838,.04
75
4077
6173
OOS Rate
0.0255
0.0274
0.0246
0.0221
0.0220
0.0203
0.0205
0.0191
0.0159
0.0154
0.0149
0.0144
0.0142
0.0143
0.0128
0.0128
0.0111
0.0132
0.0124
0.0108
0.0130
0.0117
0.0105
0.0135
0.0086
0.0137
0.0141
0.0104
Table B.5: Data for OOS Rate versus TBO, New SKUs only
Time Between Orders in
weeks (TBO)
Grp
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
>=
0
0.5
1.5
2.5
3.5
4.5
5.5
6.5
7.5
8.5
9.5
10.5
11.5
12.5
13.5
14.5
15.5
16.5
17.5
18.5
19.5
20.5
<
Average
0.5
0
1.5
2.5
3.5
4.5
5.5
6.5
7.5
8.5
9.5
10.5
11.5
12.5
13.5
14.5
15.5
16.5
17.5
18.5
19.5
1
2
3
4
5
6
7
8
9
20.5
30.5
20
30.5
40.5
50.5
60.5
40.5
50.5
70.5
100.5
100.5
I _____________
60.5
70.5
10
11
12
13
14
15
16
17
18
19
25.5
35.5
45.5
55.5
65.5
85.5
I _______
No. of Observations
3479
27456
30945
24674
53142
45639
28563
28437
114704
37762
15147
14519
27494
11787
23738
6409
1402
7164
8140
2027
21198
14179
9841
3120
264
1120
2898
62514
L
76
No. of Stockouts
64
658
828
509
1097
564
315
346
1046
418
324
247
345
184
141
91
34
84
148
22
151
252
101
53
2
16
371
5041
OOS Rate
0.0184
0.0240
0.0268
0.0206
0.0206
0.0124
0.0110
0.0122
0.0091
0.0111
0.0214
0.0170
0.0125
0.0156
0.0059
0.0142
0.0243
0.0117
0.0182
0.0109
0.0071
0.0178
0.0103
0.0170
0.0076
0.0143
0.1280
0.0806
Appendix C
Data for Exchange Curve of OOS
Rate and NFE
Table C.1: Data for
OOS Rate versus NFE, All SKUs
Normalized Forecast Error
(NFE)
Grp
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
>=
<
-1.25
Average
-1.25
-1
-0.75
-1
-0.5
-0.25
0
0.25
-1.125
-0.875
-0.625
-0.375
-0.125
0.125
0.375
0.625
0.875
1.125
1.375
1.625
1.875
2.125
2.375
2.625
2.875
3.125
3.375
3.625
3.875
4.125
4.375
4.625
4.875
5.5
- 00
-0.25
0
0.25
0.5
0.75
1
1.25
1.5
1.75
2
2.25
2.5
2.75
3
3.25
3.5
3.75
4
4.25
4.5
4.75
5
-0.75
-0.5
0.5
0.75
1
1.25
1.5
1.75
2
2.25
2.5
2.75
3
3.25
3.5
3.75
4
4.25
4.5
4.75
5
6
No. of Observations
86847
11211337
47659
266895
425601
470147
445043
412223
345978
314387
248311
229187
189255
167028
155149
133467
118234
154389
80766
82109
74988
91433
40240
62460
57184
50061
152232
77
No. of StockoutsjOGS Rate
778
0.0090
128262
0.0114
533
0.0112
2090
0.0078
3357
0.0079
4105
0.0087
4219
0.0095
4609
0.0112
4594
0.0133
4953
0.0158
4289
0.0173
4684
0.0204
4310
0.0228
4091
0.0245
4214
0.0272
3827
0.0287
3866
0.0327
5175
0.0335
3049
0.0378
3297
0.0402
2919
0.0389
3798
0.0415
1933
0.0480
2957
0.0473
2627
0.0459
2540
0.0507
8387
0.0551
28
29
6
7
30
8
31
32
33
34
35
36
37
38
39
40
41
42
9
10
11
12
13
14
15
16
17
18
19
20
7
8
9
10
11
12
13
14
15
16
17
18
19
20
6.5
7.5
8.5
9.5
10.5
11.5
12.5
13.5
14.5
15.5
16.5
17.5
18.5
19.5
00
7745
4741
5218
2791
3619
2296
123449
76002
80583
35406
47786
35555
23851
29588
17686
22142
10024
9961
22118
5222
185300
2073
1887
1638
1437
895
1040
1541
457
14430
0.0627
0.0624
0.0648
0.0788
0.0757
0.0646
0.0869
0.0638
0.0926
0.0649
0.0893
0.1044
0.0697
0.0875
0.0779
Table C.2: Data for OOS Rate versus NFE, CLASS A SKUs
Normalized Forecast Error
(NFE)
Grp
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
>=
- 00
-1.25
-1
-0.75
-0.5
-0.25
0
0.25
0.5
0.75
1
1.25
1.5
1.75
2
2.25
2.5
2.75
3
3.25
3.5
3.75
4
4.25
4.5
4.75
5
6
7
8
9
10
11
12
<
-1.25
-1
-0.75
-0.5
-0.25
0
0.25
0.5
0.75
1
1.25
1.5
1.75
2
2.25
2.5
2.75
3
3.25
3.5
3.75
4
4.25
4.5
4.75
5
6
7
8
9
10
11
12
13
Average
-1.125
-0.875
-0.625
-0.375
-0.125
0.125
0.375
0.625
0.875
1.125
1.375
1.625
1.875
2.125
2.375
2.625
2.875
3.125
3.375
3.625
3.875
4.125
4.375
4.625
4.875
5.5
6.5
7.5
8.5
9.5
10.5
11.5
12.5
No. of Observations
No. of Stockouts
OOS Rate
8482
503582
38566
169659
213184
201945
166258
128820
92814
69463
50605
39219
28354
22021
17070
13491
10848
9439
6941
64
8765
415
1128
1196
1172
1015
950
0.0075
0.0174
841
800
676
678
544
429
406
378
307
339
237
235
150
185
142
154
6072
4991
4601
3486
3345
2829
2478
7254
4667
3254
2493
1742
1361
106
112
308
196
128
112
82
63
39
48
1060
844
78
0.0108
0.0066
0.0056
0.0058
0.0061
0.0074
0.0091
0.0115
0.0134
0.0173
0.0192
0.0195
0.0238
0.0280
0.0283
0.0359
0.0341
0.0387
0.0301
0.0402
0.0407
0.0460
0.0375
0.0452
0.0425
0.0420
0.0393
0.0449
0.0471
0.0463
0.0368
0.0569
35
36
37
38
39
40
41
42
14
15
16
17
18
19
20
13
14
15
16
17
18
19
20
13.5
14.5
15.5
16.5
17.5
18.5
19.5
00
696
586
508
378
352
316
251
2344
48
24
25
22
21
19
15
125
0.0690
0.0410
0.0492
0.0582
0.0597
0.0601
0.0598
0.0533
Table C.3: Data for OOS Rate versus NFE, CLASS B SKUs only
Normalized Forecast Error
(NFE)
Grp
>=
- 00
-1.25
-1
-0.75
-0.5
-0.25
0
0.25
0.5
0.75
1
1.25
1.5
1.75
2
2.25
2.5
2.75
3
3.25
3.5
3.75
4
4.25
4.5
4.75
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
<
-1.25
-1
-0.75
-0.5
-0.25
0
0.25
0.5
0.75
1
1.25
1.5
1.75
2
2.25
2.5
2.75
3
3.25
3.5
3.75
4
4.25
4.5
4.75
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Average
-1.125
-0.875
-0.625
-0.375
-0.125
0.125
0.375
0.625
0.875
1.125
1.375
1.625
1.875
2.125
2.375
2.625
2.875
3.125
3.375
3.625
3.875
4.125
4.375
4.625
4.875
5.5
6.5
7.5
8.5
9.5
10.5
11.5
12.5
13.5
14.5
15.5
16.5
17.5
18.5
19.5
No. of Observations
25034
2134692
7832
87036
184485
215144
205801
191983
158207
138771
106860
93488
73398
62262
53751
42667
36040
34474
22356
21892
17850
19158
11058
12924
11102
9147
27763
18379
11268
9198
5435
4936
3359
2773
2368
1759
1526
1203
1010
1201
647
No. of Stockouts
187
25543
100
842
1755
2130
2085
2231
2111
2155
1883
1973
1665
1707
1589
1358
1423
OOS Rate
0.0075
0.0120
0.0128
0.0097
1504
1069
0.0436
0.0478
0.0530
1161
916
1075
664
770
668
668
1959
1362
902
754
444
422
309
259
195
146
115
129
102
79
0.0095
0.0099
0.0101
0.0116
0.0133
0.0155
0.0176
0.0211
0.0227
0.0274
0.0296
0.0318
0.0395
0.0513
0.0561
0.0600
0.0596
0.0602
0.0730
0.0706
0.0741
0.0800
0.0820
0.0817
0.0855
0.0920
0.0934
0.0823
0.0830
0.0754
0.1072
0.1010
101
0.0841
51
0.0788
142
1 20
>
i
1686
1 8062
1 0.0851
Table C.4: Data for OOS Rate versus NFE, CLASS C SKUs only
Normalized Forecast Error
(NFE)
Grp
>=
- 00
-1.25
-1
-0.75
<
-1.25
-1
-0.75
-0.5
-0.25
-0.25
0
0.25
0.5
0.75
0
0.25
0.5
0.75
1
1.25
1.5
1.75
2
2.25
2.5
2.75
3
3.25
3.5
3.75
4
4.25
4.5
4.75
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
-0.5
1
1.25
1.5
1.75
2
2.25
2.5
2.75
3
3.25
3.5
3.75
4
4.25
4.5
4.75
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
00
Average _No. of Observations
8482
-1.125
503582
-0.875
38566
-0.625
169659
-0.375
213184
-0.125
201945
0.125
166258
0.375
128820
0.625
92814
0.875
69463
1.125
50605
1.375
39219
1.625
28354
1.875
22021
2.125
17070
2.375
13491
2.625
10848
2.875
9439
3.125
6941
3.375
6072
3.625
4991
3.875
4601
4.125
3486
4.375
3345
4.625
2829
4.875
2478
5.5
7254
6.5
4667
7.5
3254
8.5
2493
9.5
1742
10.5
1361
11.5
1060
12.5
844
13.5
696
586
14.5
15.5
508
378
16.5
17.5
352
18.5
316
19.5
251
2344
80
No. of Stockouts
64
8765
415
1128
1196
1172
1015
950
841
800
676
678
544
429
406
378
307
339
237
235
150
185
142
154
OOS Rate---
0.0075
0.0174
0.0108
0.0066
0.0056
0.0058
0.0061
0.0074
0.0091
0.0115
0.0134
0.0173
0.0192
0.0195
0.0238
0.0280
0.0283
0.0359
0.0341
0.0387
0.0301
0.0402
0.0407
0.0460
106
0.0375
112
308
196
128
112
82
63
39
48
48
24
25
22
21
19
15
125
0.0452
0.0425
0.0420
0.0393
0.0449
0.0471
0.0463
0.0368
0.0569
0.0690
0.0410
0.0492
0.0582
0.0597
0.0601
0.0598
0.0533
1
Table C.5: Data for
OOS Rate versus NFE, New SKUs only
Normalized Forecast Error
(NFE)
Grp
>=
1
- 00
2
3
4
5
6
7
8
9
-1.25
-1
-0.75
-0.5
-0.25
0
10
0.75
11
12
13
14
15
16
17
18
19
1
1.25
1.5
1.75
2
2.25
2.5
2.75
3
3.25
3.5
3.75
4
4.25
4.5
4.75
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
0.25
0.5
20
<
-1.25
-1
-0.75
-0.5
-0.25
0
0.25
0.5
0.75
1
1.25
1.5
1.75
2
2.25
2.5
2.75
3
3.25
3.5
3.75
4
4.25
4.5
4.75
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
00
L __________________
No. of Observations
Average
2560
-1.125
-0.875
-0.625
-0.375
-0.125
0.125
0.375
0.625
0.875
1.125
1.375
1.625
1.875
2.125
2.375
2.625
2.875
3.125
3.375
3.625
3.875
4.125
4.375
4.625
4.875
5.5
6.5
7.5
8.5
9.5
10.5
11.5
12.5
13.5
14.5
15.5
16.5
17.5
18.5
19.5
A_________
516669
127
1026
2027
2899
3375
3575
2925
4037
2771
3602
2451
1941
1369
13699
1364
1513
4723
2339
396
1465
1477
1158
4591
5819
2302
4084
562
2552
1053
998
1190
682
900
179
607
1757
46
15485
81
OOS Rate
0.0137
0.0167
0.0315
0.0088
0.0089
0.0138
0.0193
0.0199
0.0226
0.0201
0.0220
93
69
273
69
66
0.0211
0.0355
0.0258
0.0322
0.0290
0.0504
0.0199
0.0506
0.0436
106
0.0224
137
35
68
54
60
250
380
99
242
63
240
40
110
35
94
63
13
0.0586
0.0884
0.0464
0.0366
0.0518
0.0545
0.0653
70
104
0.1153
7
1242
0.1522
65
2020
3202
A
No. of Stockouts
35
8606
4
9
18
40
65
71
66
81
61
76
87
50
0.0430
0.0593
0.1121
0.0940
0.0380
0.1102
0.0294
0.1378
0.0700
0.0726
0.0592
0.0802
Appendix D
Data on OOS Causes
Table D.1: Data on frequency of occurrence of OOS conditions
Number of OOS
115143
40176
47912
65473
52806
128444
70974
25429
50112
8140
274959
Cause or Condition
Flow Through
DC Out at t
DC Out at t-1
Order Delayed
Negative Inventory Adjustment
Non-Positive Forecast Error
Small Positive Forecast Error
Medium Positive Forecast Error
Large Positive Forecast Error
Insufficient Replenishment
All
Relative Frequency
41.88%
14.61%
17.43%
23.81%
19.21%
46.71%
25.81%
9.25%
18.23%
2.96%
100.00%
Table D.2: Data on frequency of occurrence of OOS conditions, split by SKU CLASS
Cause or Condition
Flow Through
DC Out at t
DC Out at t-1
Order Delayed
Negative Inventory Adjustment
Non-Positive Forecast Error
Small Positive Forecast Error
Medium Positive Forecast Error
Large Positive Forecast Error
Insufficient Replenishment
All
CLASS A
11330
1554
2240
6253
5536
8829
8268
1846
3751
1209
22694
Number of OOSs
New SKUs
CLASS C
CLASS B
1174
69128
33511
2494
29943
6185
2993
34744
7935
2906
42526
13788
1938
31073
14259
8060
85826
25729
1767
38606
22333
834
15718
7031
1894
32342
12125
195
4168
2568
12555
172492
67218
83
Total
115143
40176
47912
65473
52806
128444
70974
25429
50112
8140
274959
Appendix E
Data on OOS Rate of CLASS C
SKUs By Stores
Table E.1: Data on the
RANK
Store
GOS
#
37
Rate
106
108
0.0211
0.0245
0.0193
147
154
166
176
187
188
197
0.0167
200
0.0234
0.0219
0.0176
0.0168
0.0135
0.0207
0.0191
0.0222
0.0350
0.0177
0.0239
0.0251
0.0297
0.0183
0.0216
0.0197
0.0313
0.0194
0.0199
215
223
287
294
335
348
646
653
666
746
824
862
873
953
957
1219
1257
1
0.0249
0.0170
0.0209
0.0203
0.0196
0.0165
OOS rate of CLASS C SKUs by stores
Store
RANK
#
143
146
158
185
189
224
231
248
295
296
309
349
353
426
439
447
495
648
727
822
907
928
947
1000
1043
1079
1100
1116
1117
85
OS
Rate
0.0219
0.0177
0.0235
0.0199
0.0225
0.0152
0.0196
0.0172
0.0240
0.0168
0.0186
0.0181
0.0141
0.0170
0.0130
0.0232
0.0235
0.0129
0.0203
0.0162
0.0197
0.0147
0.0153
0.0150
0.0118
0.0222
0.0139
0.0173
0.0123
I
RANK
Store
00S
#
Rate
1506
1520
0.0235
0.0148
0.0236
1551
1566
1574
1641
18
63
76
91
96
120
130
181
194
280
313
339
356
373
394
425
543
605
712
728
836
908
958
0.0136
0.0245
0.0164
0.0141
0.0175
0.0171
0.0099
0.0108
0.0110
0.0196
0.0208
0.0155
0.0110
0.0145
0.0161
0.0185
0.0100
0.0147
0.0162
0.0173
0.0139
0.0110
0.0108
0.0141
0.0114
0.0180
2
6
8
11
40
54
56
61
65
109
142
171
183
193
217
220
246
277
281
297
354
374
402
406
595
599
766
806
841
897
1095
1124
1195
1232
1268
1537
3
4
5
36
38
44
47
48
51
59
69
83
133
0.0245
0.0183
0.0146
0.0228
0.0191
0.0231
0.0245
0.0144
0.0178
0.0182
0.0206
0.0246
0.0179
0.0254
0.0183
0.0202
0.0156
0.0160
0.0193
0.0149
0.0123
0.0293
0.0215
0.0148
0.0290
0.0169
0.0211
0.0185
0.0189
0.0165
0.0190
0.0187
0.0172
0.0169
0.0209
0.0229
0.0162
0.0402
0.0202
0.0205
0.0162
0.0163
0.0152
0.0214
0.0166
0.0157
0.0281
0.0195
0.0172
1165
0.0272
1238
1555
22
43
57
73
137
153
167
178
184
186
195
219
225
236
253
259
267
0.0213
0.0250
0.0203
307
341
388
434
446
521
527
556
704
755
772
837
871
874
1082
1093
1099
1106
1132
1189
1193
1216
1218
1228
1231
1255
1258
1291
1295
86
0.0158
0.0126
0.0172
0.0138
0.0159
0.0182
1036
1039
1088
1108
1119
1130
1133
1138
1154
1205
0.0196
1217
0.0192
0.0175
0.0153
1230
0.0135
0.0244
0.0152
0.0174
0.0160
0.0205
0.0109
0.0131
0.0310
0.0244
0.0177
0.0134
0.0122
0.0171
0.0124
0.0144
0.0167
0.0138
0.0157
0.0127
0.0126
0.0199
0.0153
0.0180
0.0110
0.0136
0.0114
0.0133
0.0169
0.0084
0.0137
0.0141
0.0219
0.0109
0.0122
1234
1259
1261
1263
1272
1274
1275
1277
1294
1505
1509
1510
1513
1516
1525
1536
1540
1553
1554
1558
1563
1573
1576
1582
1587
1648
1652
1660
1663
1666
1701
1703
1715
1722
1725
1739
0.0116
0.0152
0.0141
0.0117
0.0115
0.0105
0.0161
0.0221
0.0177
0.0158
0.0140
0.0112
0.0209
0.0084
0.0150
0.0081
0.0090
0.0141
0.0108
0.0108
0.0206
0.0264
0.0213
0.0079
0.0137
0.0109
0.0090
0.0224
0.0134
0.0136
0.0085
0.0144
0.0087
0.0177
0.0158
0.0093
0.0100
0.0098
0.0122
0.0142
0.0118
0.0146
0.0132
0.0159
0.0148
0.0123
0.0161
0.0131
Appendix F
Data on Relative Frequency of
WEEKS.SS of CLASS C SKUs in
RANK A Stores
Table F.1: Data on relative frequency of SS of CLASS C SKUs in RANK A Stores
Safety stock in weeks
(WEEKS.SS)
Grp
>=
<
1
2
0
0.5
1.5
2.5
3.5
4.5
5.5
6.5
7.5
8.5
9.5
10.5
11.5
12.5
13.5
14.5
15.5
16.5
17.5
18.5
19.5
20.5
30.5
40.5
50.5
0.5
1.5
2.5
3.5
4.5
5.5
6.5
7.5
8.5
9.5
10.5
11.5
12.5
13.5
14.5
15.5
16.5
17.5
18.5
19.5
20.5
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
30.5
40.5
50.5
60.5
Average
0
No. of Observations
19803
27010
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
25.5
35.5
45.5
55.5
113169
151136
135061
109298
92346
75562
80574
48153
44427
41672
37342
23377
22978
19311
10256
19603
14412
7047
16304
61340
32967
19290
5003
87
Relative Frequency
1.5%
2.1%
8.6%
11.5%
10.3%
8.4%
7.1%
5.8%
6.2%
3.7%
3.4%
3.2%
2.9%
1.8%
1.8%
1.5%
0.8%
1.5%
1.1%
0.5%
1.2%
4.7%
2.5%
1.5%
0.4%
26
27
28
60.5
70.5
100.5
70.5
100.5
65.5
85.5
10437
22333
48402
0.8%
1.7%
3.7%
Table F.2: Data on relative frequency of SS of CLASS C SKUs in RANK E Stores
Safety stock in weeks
(WEEKS.SS)
Grp
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
28
27
>=
0
0.5
1.5
2.5
3.5
4.5
5.5
6.5
7.5
8.5
9.5
10.5
11.5
12.5
13.5
14.5
15.5
16.5
17.5
18.5
19.5
20.5
30.5
40.5
50.5
60.5
70.5
100.5
<
Average
0.5
1.5
0
2.5
3.5
4.5
5.5
6.5
7.5
8.5
9.5
10.5
11.5
12.5
13.5
14.5
15.5
16.5
17.5
18.5
19.5
20.5
30.5
40.5
50.5
60.5
70.5
100.5
100.5
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
No. of Observations
48072
5992
23834
57236
102766
130930
150654
154858
220657
130039
131133
131302
127066
83985
83900
75427
37614
79731
61994
30732
66511
276625
163987
94442
27270
56879
111910
274687
18
19
20
25.5
35.5
45.5
55.5
65.5
85.5
111910
274687
85.5
88
Relative Frequency
1.6%
0.2%
0.8%
1.9%
3.5%
4.5%
5.1%
5.3%
7.5%
4.4%
4.5%
4.5%
4.3%
2.9%
2.9%
2.6%
1.3%
2.7%
2.1%
1.0%
2.3%
9.4%
5.6%
3.2%
0.9%
1.9%
3.8%
9.3%
3.8%
9.3%
Appendix G
Data on Relative Frequency of
TBO of CLASS C SKUs in RANK
A Stores
Table G.1: Data on relative frequency of TBO of CLASS C SKUs in RANK A Stores
Grp
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
Time Between Orders in
weeks (TBO)
_
_
>
Average
No. of Observations
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
10969
114886
154730
127340
114191
93540
84196
68030
0
0.5
1.5
2.5
3.5
4.5
5.5
6.5
7.5
8.5
9.5
10.5
11.5
12.5
13.5
14.5
15.5
16.5
17.5
18.5
19.5
20.5
30.5
40.5
50.5
<
0.5
1.5
2.5
3.5
4.5
5.5
6.5
7.5
8.5
9.5
10.5
11.5
12.5
13.5
14.5
15.5
16.5
17.5
18.5
19.5
20.5
30.5
40.5
50.5
60.5
20
25.5
35.5
45.5
55.5
_ _ _ _ _
No._ofObseration
_ _
75326
46924
43649
41279
39613
21821
23335
17945
8168
17510
12519
5585
15213
48772
27274
16444
3314
89
Relative Frequency
0.8%
8.8%
11.8%
9.7%
8.7%
7.1%
6.4%
5.2%
5.8%
3.6%
3.3%
3.2%
3.0%
1.7%
1.8%
1.4%
0.6%
1.3%
1.0%
0.4%
1.2%
3.7%
2.1%
1.3%
0.3%
26
27
28
60.5
70.5
100.5
70.5
100.5
65.5
85.5
9299
21800
44974
0.7%
1.7%
3.4%
Table G.2: Data on relative frequency of TBO of CLASS C SKUs in RANK E Stores
Time Between Orders in
Weeks (TfBO)
Grp
>=
0
0.5
1.5
2.5
3.5
4.5
5.5
6.5
7.5
8.5
9.5
10.5
11.5
12.5
13.5
14.5
15.5
16.5
17.5
18.5
19.5
20.5
30.5
40.5
50.5
60.5
70.5
100.5
<
Average
No. of Observations
0.5
1.5
2.5
3.5
4.5
5.5
6.5
7.5
8.5
9.5
10.5
11.5
12.5
13.5
14.5
15.5
16.5
17.5
18.5
19.5
20.5
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
2100
37843
94827
30.5
40.5
50.5
60.5
70.5
100.5
20
25.5
35.5
45.5
55.5
65.5
85.5
130380
158838
152653
149564
145377
198076
127523
130500
130248
141173
79465
90375
72313
33323
74689
53577
26172
64773
224678
132339
81377
17660
46123
111820
232523
90
Relative Frequency
0.1%
1.3%
3.2%
4.4%
5.4%
5.2%
5.1%
4.9%
6.7%
4.3%
4.4%
4.4%
4.8%
2.7%
3.1%
2.5%
1.1%
2.5%
1.8%
0.9%
2.2%
7.6%
4.5%
2.8%
0.6%
1.6%
3.8%
7.9%
Appendix H
Data on Relative Frequency of
NFE of CLASS C SKUs in RANK
A Stores
Table H.1: Data on relative frequency of NFE of CLASS C SKUs in RANK A Stores
Normalized Forecast Error
(NFE)
Grp
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
>=
- 00
-1.25
-1
-0.75
-0.5
-0.25
0
<
-1.25
-1
-0.75
-0.5
-0.25
0
0.25
0.5
0.25
0.5
0.75
0.75
1
1.25
1.5
1.75
2
2.25
2.5
2.75
3
3.25
3.5
3.75
4
4.25
4.5
1
1.25
1.5
1.75
2
2.25
2.5
2.75
3
3.25
3.5
3.75
4
4.25
4.5
4.75
Average _No. of Observations
9086
897441
-1.125
-0.875
441
4633
-0.625
13413
-0.375
-0.125
22711
0.125
25629
26680
0.375
24707
0.625
24113
0.875
19662
1.125
19375
1.375
1.625
16503
15302
1.875
14590
2.125
12534
2.375
11265
2.625
14169
2.875
7498
3.125
8015
3.375
7196
3.625
9115
3.875
3873
4.125
6086
4.375
5767
4.625
91
Relative Frequency
0.69%
68.61%
0.03%
0.35%
1.03%
1.74%
1.96%
2.04%
1.89%
1.84%
1.50%
1.48%
1.26%
1.17%
1.12%
0.96%
0.86%
1.08%
0.57%
0.61%
0.55%
0.70%
0.30%
0.47%
0.44%
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
4.75
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
00
4.875
5.5
6.5
7.5
8.5
9.5
10.5
11.5
12.5
13.5
14.5
15.5
16.5
17.5
18.5
19.5
4923
14622
11700
7265
7630
3566
4523
3434
2401
2867
1659
2057
979
971
2050
538
17067
0.38%
1.12%
0.89%
0.56%
0.58%
0.27%
0.35%
0.26%
0.18%
0.22%
0.13%
0.16%
0.07%
0.07%
0.16%
0.04%
1.30%
Table H.2: Data on relative frequency of NFE of CLASS C SKUs in RANK E Stores
Normalized Forecast Error
(NFE)
Grp
- 00
-1.25
-1
-0.75
-0.5
-0.25
0
0.25
0.5
0.75
1
1.25
1.5
1.75
2
2.25
2.5
2.75
3
3.25
3.5
3.75
4
4.25
4.5
4.75
5
6
7
8
9
10
>=-1.25
-1
-0.75
-0.5
-0.25
0
0.25
0.5
0.75
1
1.25
1.5
1.75
2
2.25
2.5
2.75
3
3.25
3.5
3.75
4
4.25
4.5
4.75
5
6
7
8
9
10
11
<
Average
- 00
-1.125
-0.875
-0.625
-0.375
-0.125
0.125
0.375
0.625
0.875
1.125
1.375
1.625
1.875
2.125
2.375
2.625
2.875
3.125
3.375
3.625
3.875
4.125
4.375
4.625
4.875
5.5
6.5
7.5
8.5
9.5
10.5
-1.25
-1
-0.75
-0.5
-0.25
0
0.25
0.5
0.75
1
1.25
1.5
1.75
2
2.25
2.5
2.75
3
3.25
3.5
3.75
4
4.25
4.5
4.75
5
6
7
8
9
10
No. of Observations
10743
2466059
139
771
1676
3366
4996
7458
9624
12969
12110
14745
15039
15173
16237
15519
14914
23801
11488
12266
11019
16685
5778
11347
10496
9683
29035
25845
16324
18697
7394
11572
92
Relative Frequency
0.37%
83.91%
0.00%
0.03%
0.06%
0.11%
0.17%
0.25%
0.33%
0.44%
0.41%
0.50%
0.51%
0.52%
0.55%
0.53%
0.51%
0.81%
0.39%
0.42%
0.37%
0.57%
0.20%
0.39%
0.36%
0.33%
0.99%
0.88%
0.56%
0.64%
0.25%
0.39%
11
12
13
14
15
16
17
18
19
20
12
13
14
15
16
17
18
19
20
- 00
-1.25
11.5
12.5
13.5
14.5
15.5
16.5
17.5
18.5
19.5
11
12
13
14
15
16
17
18
19
20
- 00
8831
5449
7869
4380
6074
2438
2241
6128
1222
51473
10743
93
0.30%
0.19%
0.27%
0.15%
0.21%
0.08%
0.08%
0.21%
0.04%
1.75%
0.37%
Appendix I
Distribution of Stores by OOS Rate
of CLASS C SKUs
Distribution of Stores (Rank A)
by Stockout Rate of (C items)
7
5
4
32
14
0-0.0020004 0.006
0.008
O.l01
0.012 0.014 0.016 0.018 0.02 0.022 0.024 0.026 0.028 0.03 0.032 0.4 0.036 0.038 0.04 0.042 0,044 0.046 more
.016 0.018 0.02 0.022 0.024 O.M260.028 0.03 0.032 0.034 0.038 0.038 0.04 0.042 O.044 0.046
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014
Stockout Rate
Figure 1.1: Distribution of RANK A stores by OOS of CLASS C SKUs
Distribution of Stores (Rank B)
by Stockout Rate of (C Items)
10
81
7
65
4
3-
0-
0.002 0.004 0100 0.008 0.01 0.012 0.014 0.016 0.01 0.02 -.022 0.024 0.026 0.028 0.03 0.032 0.034 0.036 0.038 0.04 0.042 0.044:0.046 More
00.002 0.004 O.OS 0.008 0.01 0.012 ,.10.01 :0.01 .0 0.022 0.024 0.026 0.028 0.03 0.032 0.034 0.036 0.038 0.04 0.04210.044 0.04:
Stockout Rate
Figure 1.2: Distribution of RANK B stores by OOS of CLASS C SKUs
95
Distribution of Stores (Rank C)
by Stockout Rate of (C Items)
10
9
8
0
i
2
1
0
0.00200040.006 0.008
0
0.01
0.01210.014 0.0160.018
0.02
0.02210.02410.026
0.028 0.03 0.03210.03410.036
0.038
0.04
0.042 0.0440048
More
0.00200040006008 0.01 0.012 0.0140016 0018 0.02 0022002400260028 0.03 0.032 0034.03038 0.04 0042 00440046
Stockout Rat.
Figure 1.3: Distribution of RANK C stores by OOS of CLASS C SKUs
Distribution of Stores (Rank D)
by Stockout Rate of (C items)
14
12
10
a
8
6
4
2
0
0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02 0.022 0.02410.026 0.028 0.03 0.032 0.03410.036 0.038 0.04 0.042 0.044 0.046 More
0
A
003 0032 0.034 0.036 0.038 0.04 0.042 0.04410.046
0.002 0.004 00060008 0.01 0.012 0.014 0.018 0.018 0.02 00220.024 0.02 0.028
Stockout Rat.
Figure 1.4: Distribution of RANK D stores by OOS of CLASS C SKUs
Distribution of Stores (Rank E)
by Stockout Rate of (C items)
14
12
10
0
i
a
6
4
2
0
0.002 0.0040.0060 008 0.01 0.012
0
0.002 0.004 0.006 0.
0.01
0.014 0.016 0.018 0.02 0.022 0.024
0.028
0.028 0.03
0.032
0034 0.036
0.012 0.014 0.016 0.018 0.02 0.022 0.024 0.0280028 0.03 0.0320 0
0.038
0.04
0.042 0.044 0.046
Stockout Rat.
Figure 1.5: Distribution of RANK E stores by OOS of CLASS C SKUs
96
More
0360038 0.04 0.042 0.044.0.04
Appendix
J
Analysis to Reject the Hypothesis
that RANK A Stores Carry more
SKUs that have Higher OOS Rate
Here, we consider only CLASS C items. The set of active SKUs in each store varies from
week to week, and varies from store to store. In general, stores with higher volumes will
carry more distinct SKUs; this is especially true for CLASS C items. One hypothesis is that
RANK A experiences a higher OOS rate because it carries a broader line of CLASS C
SKUs. For instance, it might carry more items that have highly variable or unpredictable
demand, and hence suffer more out of stocks.
To examine this hypothesis, we compute for each SKU its relative store frequency for
each RANK of stores. We do this by dividing the number of times the SKU is active in
stores of that RANK by the maximum possible number of observations. For example,
suppose that we have 100 observations of a particular SKU, there are 28 RANK A stores
and we have 11 weeks of observations; then the relative frequency of this SKU for RANK
A stores is equal to 100/(28 x 11) = 0.35.
Let
xA
and
xE
be this relative frequency for a specified SKU for RANK A and RANK E
stores respectively. For convenience, we let
dAE = XA -E
97
.
Then, we group SKUs with similar dA,E values together; for each group of SKUs with
similar dA,E values, we compute their OOS rate in RANK A stores versus RANK E
stores.
By comparing the OOS rate in RANK A versus RANK E stores, we see that the OOS rate
in RANK A stores is still higher than that of RANK E stores. Figure J1 shows the
graphical representation of the results. This shows that the difference in OOS rate is
present over all groups of SKUs, regardless of the frequency with which they are stocked in
each rank of store.
Out-of-Stock Rate of SKUs Grouped By Difference in Relative Frequency
0.0250.02
0.015
S0.01
0
0.005
0-
-0.375
-0.625
-0.625
-0.875
0
-0.125
-0.375
0.125
0.375
0.625
0.875
0
0.125
0.375
0.625
-0.125
Difference
In Relative
Frequency, d
Figure J.1: OOS Rate of CLASS C items grouped by difference in relative frequency in
RANK A and RANK E stores
Table J.1: Data on
OOS Rate of CLASS C items grouped by difference in relative frequency
in RANK A and RANK E stores
SKU Grouping,
-0.875
-0.625
-0.375
-0.125
to
0
0.125
0.375
to
dA
to
-0.625
-0.375
-0.125
to
0
to
0.125
0.375
0.625
to
to
No. of
Rank A
No. of
Rank A
00S
No. of
Rank E
No. of
Rank E
00S
Rank A
Stockout
99
2843
86022
293990
753509
490772
1
47
1603
6492
14968
8443
467
2545
23909
376290
870978
1703651
863885
33086
5
0.0101
0.0165
0.0186
0.0221
0.0199
0.0172
OBS
30301
GBS
98
208
4781
13758
21746
10133
374
Rate
0.0154
Rank E
OOS Rate
0.0020
0.0087
0.0127
0.0158
0.0128
0.0117
0.0113
0.625
to
0.875
8395
0.875
to
1
243
61
8
5954
27
21
3
0.0073
0.0329
0.0035
0.1111
We note here that a more straight forward but inappropriate way to do the comparison
would be to first compute the average OOS rate of each SKU by considering all stores and
all weeks, group SKUs with similar OOS rate together and then compare the frequencies at
which they appear in RANK A and RANK E stores. This method is inappropriate as it
would not be able to differentiate between causality and correlation between the
proportion of RANK A stores that carry the SKU and OOS rate. To illustrate this point,
let us make a simple hypothesized assumption that RANK A stores simply have higher
OOS rate (i.e. for the same SKU, RANK A stores simply have a higher OOS rate than
RANK E stores) Then, SKUs that are more common in RANK A stores would also have
a higher OOS rate since there are more observations of these SKUs from RANK A stores.
Keeping this in mind, we will see that there is a correlation between OOS rate and the
proportion of RANK A stores that carry the SKU and may wrongly conclude that RANK
A stores have high OOS rate because RANK A stores carry more SKUs that have high
OOS rate even though the high OOS rate is caused (based on our hypothesized example)
by virtue of the fact that RANK A stores simply have higher OOS rate.
99
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[3]
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[4]
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101