Chapter 14.2. “Strategic production-distribution models:
A critical review with emphasis on global supply chain models”
Vidal, C.J. and Goetschalckx, M., “A critical review with emphasis on global supply chain models”,
European Journal of Operation Research 98 (1997). 1-18.
1. Introduction
1.1. Motivation/ Objectives
The analysis and design of production-distribution systems has been an active area of research for many
years. Most research addresses a single component of the overall production-distribution system, such as
purchasing, production and scheduling, inventory, warehousing, or transportation. To date there exists
little research that addresses the integration of such single components into the overall supply chain.
Another body of research considers the problem of coordinating two different functions of the system.
Thomas and Griffin (1995) classify this body of research into three categories: buyer-vendor coordination,
production-distribution coordination, and inventory-distribution coordination. Bhatnagar et al . (1993)
present a similar classification, and distinguish between the integration of different functions, such as the
production-distribution integration mentioned above, and the coordination of different levels of the
company within the same function, such as the production planning of several assembly plants that are
vertically integrated.
1.2. Definition
Planning level에 따른 분류 및 정의
Three levels of planning can be distinguished depending on the time horizon, namely, strategic, tactical,
and operational (see Ballou, 1992, pp. 32-35). The strategic level considers time horizons of more than
one year, and requires approximate and aggregated data. The operational level involves short-term
decisions, often less than an hour or a day, and requires transactional data. The tactical level falls in
between those two extremes with respect to the time horizon, and the amount and accuracy of data
required. As an illustration, consider the transportation function of the system. The selection of a
transportation mode, the determination of the fleet size, and the dispatching of different vehicles, are
examples of strategic, tactical, and operational decisions, respectively
Definition of Strategic production-distribution model.
The most comprehensive strategic problem is the optimization of the complete supply chain. The strategic
design of a supply chain requires managers to determine:
· the number, location, capacity, and type of manufacturing plants and warehouses to use;
· the set of suppliers to select;
· the transportation channels to use;
· the amount of raw materials and products to produce and ship among suppliers, plants, ware-houses,
and customers; and
· the amount of raw materials, intermediate products, and finished goods to hold at various locations
in inventory.
Many models have been formulated for the strategic design of supply chains. We will call these models
'strategic production-distribution' models.
We will distinguish between domestic and international
strategic production-distribution models. The former models consider strategic production-distribution
decisions within a single country or a unified group of countries, e.g., the continental United States. On
the other hand, the latter models include global features and consider multiple countries for selecting
vendors, and locating plants and warehouses.
1.3. Literature review
Aikens (1985) presents an early review of the main facility location models, starting from the least
complex, such as the simple uncapacitated model, and progressing to the more complex, such as the
single-echelon multicommodity capacitated model. In addition, the author indicates that the dynamic
multicommodity problem and the consideration of side constraints are the most promising topics for
future research.
Bhatnagar et al. (1993) present a review on models for multi-plant coordination, defining two levels of
coordination. The first one, called 'general coordination', addresses the problem of integrating decisions of
different activities, such as facility location, production, and distribution. The second level of
coordination deals with the problem of linking decisions within the same activity for different levels in
the firm; this level is called 'multi-plant coordination'. The 'general coordination' problem is further
classified into three main categories: coordination between supply and production activities, coordination
between production and distribution activities, and coordination between inventory and distribution
activities.
Geoffrion and Powers (1995) analyze the evolution of logistics as a corporate function, computercommunications technology, algorithms, data development and management tools, model features and
software capabilities, and how companies use software for distribution system design. Additionally, the
authors present some data-related theoretical topics, such as the aggregation of products and customers,
the linearization of functions that describe inventory Issues, and the effect of errors in transportation rates,
as topics for future research
Thomas and Grifnn (1995) present a comprehensive review of the literature related to the coordination of
two or more of the main stages of the supply chain, that is, procurement, production, and distribution.
This is accomplished by describing the main references related to buyer-vendor coordination, productiondistribution coordination , inventory-distribution coordination, and strategic planning. They also present
some topics for further research, which include the modeling of nonlinear transportation costs, life cycle
constraints, general international supply issues, third-parties in international problems, and the
determination of interface points within the supply chain.
Slats et al. (1995) present a description of the characteristics of a logistic chain with emphasis on recent
technological developments, such as Electronic Data Interchange (EDI) and Product Data Interchange
(PDI), which improve processes and facilitate the flow of information along the supply chain. They claim
that Operations Research (OR) and Management Science (MS) techniques such as mathematical
programming, heuristics, and simulation, are essential to support the redesign of logistic processes.
Verter and Dincer (1995) discuss the facility location decisions of multinational organizations. They
highlight the need for coordination among all international entities of global companies in order to
improve competitiveness. After discussing the planning process and coordination of a firm's global
manufacturing strategy, Verter and Dincer present a literature review on the production-distribution
system design problem. In the first survey, the authors conclude that most of the existing methods focus
on the optimization of location and allocation decisions, ignoring important structural aspects such as
capacity and technology content of manufacturing facilities. In the second survey, specific references
related to international strategic production-distribution models are identified.
1.4. Complexities/ Difficulty to Solve
Global supply chain models are more complex and difficult to solve than domestic models. In an
international scenario, the flow of cash and the flow of information are more important and difficult to
coordinate than they are In a single-country environment. The inclusion of different taxes and duties,
differential exchange rates, trade barriers, transfer prices, and duty drawbacks is fundamental for a model
to more accurately represent the real system. In addition, sources of uncertainty and qualitative factors,
such as government stability and general infrastructure of a particular country, are critical issues for the
strategic design of a global supply chain. These factors should be considered when de-signing any global
supply chain, but they are very difficult to include in mathematical models. This article describes the
existing models for global supply chain design, highlighting their contributions and limitations.
2. Optimization models
2.1. MIP Models
Main characteristics of selected MIP strategic production-distribution models.
Model characteristics
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
Stochastic features
Material requirements
Material supply lead times
Demand of products and parts
X
X**
Transportation times
Exchange rates
Reliability of vendors
Dynamic characteristics
Static model(single-period)
X
X
X
X
Multi-period model
X
X
X
X
Dynamic demand only
Status of facilities
Fixed number, status, and location
X
X
of facilities (flow optimization)
Fixed location of facilities
X
X
X
X
X
X
Xa
X
X
X
X
X
X
X
X
(discrete location)
Continuous facility location
Capacities
Production capacity at plants
Supply capacity of vendors
X
X
X
X
X
X
Capacity of transportation channels
Distribution Center(DC) capacities
X
X
Manufacturing line capacity
Xb
Other capacities
Multicommodity model
Single sourcing
X
X
X
X
X
X
Customers from DC
X
Customers per commodity
Xc
X
Xd
DC per commodity
Manufacturing plants from vendors
Objective function
Minimization of costs
X
X
X
Xf
Maximization of profits
X
Xg
Xe
X
X
Multiobjective function
Nonlinear costs considered
Nonlinear DC costs
X*
X*
X
Concave production costs
X
Nonlinear transportation costs
Nonlinear purchasing costs
Number of echelons
1
1
0
1
0
0
N/C
X
X
X
X
X
X
X
2h
Fixed costs included
Fixed production costs
Fixed facility costs
X
X
Vendor fixed costs
X
X
X
Fixed transportation channel costs
Manufacturing line costs
X
Side constraints included
Bill of materials
Bounds on the No. of open facilities
X
X*
X*
X
X
X
Xi
Other side constraints
X
Xo
Customer service features
Customer demand satisfaction
X
Maximum time (distance) to
X*
X
X
X
X
X
X
X
X
Serve customers
% of orders satisfied from the shelf
X
Inventory characteristics
Pipeline inventory
Cyclic inventory in facilities
X*
Xj
X
X
X
Safety stock:
• Proportional to throughput
• Stochastic (level of service)
International features
X
Taxes and duties
X
Offset requirements
X
X
X
X
Local content
X
X
Methods of solution applied
Benders decomposition
X
X
Decomposition with goal constraint
X
A variant of Benders decomposition
X
Xk
Factorization
A heuristic method
X
Commercial MIP solver
X
LP solution by fixing
X
binary variables
0-1 variables and CPU time
Maximum number of 0-1 variables
513
N/C
N/C
N/C
N/C
60
l
887
Maximum number of constraints
8441
N/C
19841
3000
N/C
N/C
6000
2297
191
m
58
n
593
Max. computational time (CPU sec)
64
N/C
N/C
Reference considered in this table: [1] Geoffrion and Graves (1974); [2] Geoffrion et al. (1978); [3] Brown et al. (1987); [4] Cohen
and Lee (1989), (5) Cohen et at. (1989); (6) Cohen and Moon (1991); [71 ArntEen et at. (1995); [8] Cole (1995).
*
Optlonal (may be included in the model, according to the authors)
**
Although this aspect is addressed by the authors, it is not explicitly included in the model.
N/C
Not clear from the paper (either the author(5) does (do) not present it, or the information Is very limited) or not applicable for
the specific case.
a
b
The model uses binary variables for vendor selection and plant opening.
Multiproduct capacity constraints and upper bounds on products produced on each production facility (for example, ovens and
packing lines) at each plant.
c
Single sourcing of customers per commodity and distribution channel.
d
Single sourcing of warehouses per commodity and distribution channel.
e
Savinfs from duty drawbacks are considered in the objective function.
f
Profitab31ity analysis may be included, but it does not influence the optimal solution.
e
Maximization of after-tax profit in all the countries.
h
At most two love]s of warehousing are allowed.
i
A production facility (ovens and packing lines) can be assigned only to one production plant.
j
Pipeline Inventories are implicitly considered in the costs included in the objective function.
k
Although factorization seems to be applied, the real method of solution is not clearly described.
l
According to the authors, the problems they solve have ‘a few hundred’ of binary variables.
m
The authors say that solutions require “about half an hour and the equivalent of several megabytes of main storage on an IBM
370/168”.
n
According to the authors, their methods of solution suffice to solve the problems “In a minute or so on a personal computer or
workstation to within an integrality gap of 0.01 percent or better”
o
Configuration constraints are Included to represent piecewise-linear concave production costs.
Geoffrion and Graves(1974) present an algorithm based on Benders De-composition to solve a
multicommodity single-period production-distribution problem. The model represents a productiondistribution system with several plants with known capacities, distribution centers, and a number of
customer zones; discrete candidate locations are considered for opening DC. Fixed and variable (linear)
costs for DC, production costs, and linear transportation costs are included in the objective function. The
constraints considered in the model are capacity at plants, customer demand satisfaction, single sourcing
by customer zone, bounds on the throughput at DC, and linear configuration constraints on binary
variables (logical constraints).
Geoffrion et at. (1978) present a status report in strategic distribution system planning based on docomposition techniques. These model has single sourcing of customer zone by commodity, nonlinear
facility throughput constraints, and tradeoffs between distribution and customer service.
Cohen and Lee (1985) present a complete analysis related to the development of strategies to improve
general manufacturing operations. The structure of the network consists of raw material vendors,
intermediate and final product plants, DC, and customer zones. These model is a deterministic, periodic,
mathematical program to minimize costs with a nonlinear objective function that extends the model by
Geoffrion and Graves (1974) and it additionally considers opening and closing of plants, attendant
production planning decisions, inbound raw material, and intermediate product flows. The method of
solution is a heuristic embedded in a larger computerized manufacturing planning sup-port system
(MPSS).
Nodder and Dincer (1986) presented an international plant location model with financial capabilities.
These formulation considers exchange rate fluctuations, market prices, international interest rates, and
fixed costs in a stochastic environment. Production costs, transportation costs, import tariffs, and export
taxes are implicitly included in the calculation of net revenue. The objective function is obtained as the
difference between the expected value of after-tax profit and the product of a risk a version factor with the
variance of profit. The constraints include the capacity at plants, an upper bound on market demands,
financial constraints, and bounds on decision variables. But it does not consider multiple products and
transportation channels, suppliers, multi-echelon distribution centers, inter-facility transshipments, and
inventory costs.
Brown et al. (1987) present a MIP multicommodity model that determines the opening/closing of plants,
the commodities produced at each plant anddelivered to each customer, and the assignment of equipment
(represented by facilities) to plants at NABISCO. Variable production and shipping costs, fixed costs of
equipment assignment (facilities to plants), and fixed costs of plant operations are included in the
objective function. The constraints considered in the model are customer demand satisfaction, balance
constraints, multi-product capacity constraints, maximum number of facilities(equipment) assigned to
each plant, single sourcing of facilities to plants, and upper bounds on products produced on each
equipment at each plant.
Cohen et al. (1989) present the main features that differentiate an international supply chain model from a
single-country model. The most important characteristics are the necessity of treating multinational firms
as global systems to obtain economies of scale in order to reduce raw material and production costs; the
existence of duties, tariffs, and differential tax rates among countries; random fluctuation of currency
exchange rates; and the existence of constraints not considered in single-country models, such as local
content rules. To consider these characteristics, the authors formulate a normative model that is a dynamic,
nonlinear MIP model. The main contributions of this model are the explicit inclusion of vendor supply
contracts, which leads to the consideration of fixed vendor costs to opening contracts, and the inclusion of
local content constraints.
Cohen and Lee (1989) present a single-period multlcommodity model that analyzes resource deployment
decisions for an international firm. it is a deterministic formulation that considers the maximization of
after tax profit in all countries. while including variable production and purchasing costs, fixed setup and
warehousing costs, transportation costs, and fixed vendor costs. Within the constraints, the model
considers plant production capacity, material requirements at each plant (major components and subassemblies), balance constraints at plants and DC, demand limits, feasible flow constraints (system configuration constraints), capacity of suppliers, and offset requirements.
Cohen and Moon (1991) present a mixed integer multicommodity model to find inbound raw material
flows, assignment of product lines and specification of production volumes, and outbound finished
product flows in a production-distribution network. Here, the location of facilities (vendors, plants, and
DC) is given and fixed. The main contribution of this re-search is to provide an algorithm to solve some
production-distribution models with piecewise linear concave costs of production. However, the model is
very restricted because the plant loading problem under consideration assumes a fixed facility network
configuration, with the DC as the final demand points.
Cohen and Kleindorfer (1993) extend the work by Cohen et at. (1989) by describing a normative model
framework for the operations of a global company Location, capacity, product mix, material flow, and
cash flow features are decisions included in the model. The model framework consists of a Master
Problem, which is a multi-period stochastic program; a single-period stochastic program subproblem; and
a set of submodels that interact with both programs, such as a stochastic supply chain network model, a
financial flow model, a stochastic exchange rate model, and a price/demand model.
Brown and 01son (1994) present a new mathematical framework for dynamic row factorization with three
algorithms for three different row structures: generalized upper bound rows, pure network rows, and
generalized network rows. A common key aspect of these factorization methods is the identification of
special structures in the bases of the LP. These structures are very common in supply chain models, and
the authors apply their method in two of them. The first, ODS, is a multicommodity capacitated singleperiod model similar to the problem presented by Geoffrion and Graves (1974); here, the application of
factorization to the Master Problems leads to very few Benders cuts. The second problem is DEC,
presented in Arntzen et al. (1995), which is discussed below. The application of factorization to these
supply chain models appears very promising for future developments in this area.
Goetschalckx et al. (1994, 1995) present a generic model for the strategic design of productiondistribution systems, including visual capabilities. They present a generic production-distribution model
of which certain features can be ignored depending on the application.
Arntzen et at. (1995) present a multi-period, multicommodity mixed integer model to optimize a global
supply chain. Its objective function includes variable production, inventory, and shipping costs; fixed
production and production 'style' costs, and savings from credit earned for reexporting products. The
constraints include customer demand satisfaction, balance of materials, global Bill of Materials(BOM),
throughput capacity at each facility, production capacity for each facility per production style, system
configuration constraints, and bounds on decision variables. Offset trade and local content, duty drawback,
and duty relief are the international constraints included in the model. The main contribution of this
model is the inclusion of offset trade, local content, and duty considerations in an international supply
chain model that also includes BOM constraints.
Cole (1995) develops a Strategic Inventory Location Allocation System (SILAS), in which he presents a
multicommodity, multi-echelon, single-period mixed integer model for optimizing a strategic productiondistribution system. The main contribution of Cole's work is the consideration of normal demands and
stochastic customer service by carrying safety stock. together with warehouse location, customer
allocation, and channel selection. This model is applicable when safety stock costs are significant. The
objective function includes plant fixed and closing costs, plant production and inventory costs, trunking
transportation and inventory costs, fixed operating and closing costs of depots, variable ware-house costs,
and total average warehousing inventory costs. The constraints include plant production capacity, logical
constraints on channels and ware-houses, channels capacity, customer demand satisfaction, single
sourcing of customers by distribution channel and product, limits on the distance and time from a
warehouse to serve a customer, maximum on-hand inventory at warehouses, warehouse storage and
handling capacities per warehouse type, balance constraints at warehouses, warehouse single sourcing by
distribution channel and product, a set of constraints describing demand variances at warehouses, a set of
linearized safety stock constraints, and bounds on decision variables.
Vidal and Goetschalckx (1996) present the first attempt to include supplier reliability in the formulation
of a strategic production-distribution model. Their formulation represents a zero-echelon system, and
includes deterministic exchange rates, material flow linkage constraints, and a set of linearized suppliers'
reliability constraints. These constraints assure that the probability of being on time of all suppliers
shipping to each plant is at least a specified target value.
2.2. Other optimization approaches
Burns et al. (1985) present an analytic approach to optimize freight distribution by truck from a supplier
to many customers, considering transportation and inventory costs. The analytical formulas may be used
to approximate distribution costs, requiring less data in comparison to traditional network modeling
approaches
Cohen and Lee (1988) develop a set of stochastic submodels including the optimization of material
control operations, a serial production process, finished goods stockpile, and a distribution process. These
submodels are linked and related to each other using a set of variables. Under some assumptions, the
authors are able to optimize each submodel independently.
3. Additional issues for modeling
In the design of a global supply chain model, it is strictly necessary to aggregate the suppliers, customers,
and products into some kind of 'zones' for suppliers and customers, and into groups for products.
Geoffrion (1977) presents a description of how to obtain an adequate method of aggregation of suppliers,
when the analyst wants to gather a subset of items in a logistic planning model.
Geoffrion and Powers (1980) present the main reasons for the need of optimization capability when
solving comprehensive distribution planning problems. It allows the analyst to evaluate different' what-if'
question that must be considered when studying the flexibility of the model. Among these what-if
questions, we have changes in demands and costs, closing of facilities and transportation channels, plant
capacity expansions, introduction of anew product or elimination of one, inventory policy comparisons,
tradeoffs between customer service and costs, and changes in echelon structures.
Lee and Billington (1992) present a qualitative discussion concerning the pitfalls and opportunities of
managing supply chain inventory. The main pitfalls that can influence model formulation for a global
supply chain are the inadequate performance measures for the complete supply chain, the inadequate
definition of customer service, the exclusion of uncertainties. poor coordination, the consideration of
incomplete methods of shipment, the incorrect treatment of inventory costs, and the separation of supply
chain design from operational decisions.
Ballou (1994) states the importance of the approach that analysts adopt when aggregating customers in
location studies. He presents two major sources of error: the estimation of the total transportation cost to
the cluster rather than to each customer individually, and the allocation of customers to facilities based on
clustered demand instead of individual demands. The main goal of Ballou's research is to determine the
influence of the number of clusters, their size, and the number of source points, on the total error obtained
in location models for the continental United States.
4. Review on Cases Studies/ Applications
Kogut (1985) discusses the importance of flexibility in global companies as a response to fluctuations in
exchange rates, changes in government policies, and complexities in competitive moves. Lessard and
Lightstone (1986), and Carter and Victory (1989)present a more detailed analysis on exchange rate
fluctuations, describing the risks of the operating exposure of multinational companies, and the possible
methods for hedging and managing this expo-sure. Ohmae (1989) discusses the basic characteristics of
strategic alliances as fundamental tools for succeeding in a highly competitive global market. Fagan
(1991), and Monczka and Trent (1991) pre-sent the benefits of global sourcing and discuss some of its
disadvantages. In contrast, Davis (1992) discusses the inconveniences and possible negative consequences for companies that source globally. Fawcett (1992) highlights the importance of into-grated,
strategic logistics to provide a coordinating mechanism for the efficient management of global
manufacturing strategies. Min et at. (1994) present a generic stepwise approach based upon multiple
criteria for selection of suppliers in an international purchasing scenario. Klassen and Whybark (1994)
describe a study to determine and rank key barriers for the effective management of manufacturing
operations under an international environment. Among the highest ranked barriers, the authors found the
management's lack of global view, international manufacturing strategy, the management of global
logistics, and cultural and linguistic differences among countries.
As part of the integrative analyses, Goldsborough (1992) presents a complete analysis on global logistics
management, establishing comparisons between domestic and international logistics, and describing basic
factors of global information systems and Decision Support Systems (DSS). Bartmess and Corny(1993)
illustrate the fundamental differences between location decisions based upon the traditional approach that
overemphasizes direct labor costs, and location decisions based on the core competencies of the company.
By presenting similar ideas, Maccormack et al. (1994) highlight the importance of making international
location decisions based on key qualitative factors, such as adequate infrastructure and managerial issues,
instead of doing it based only on cost factors, whose advantages are usually transitory. The authors
present a four-phase decision making process for location decisions.
5. Further Research Issues
There exist many research opportunities for developing more comprehensive global supply chain models
that include BOM constraints, more stochastic factors, and qualitative aspects that are very important
within a global environment. Specific opportunities for research are the following:
 explicit inclusion of more stochastic features in modeling international supply chains;
 consideration of vendor and transportation channel reliability in the selection of vendors and
transportation channels;
 inclusion of customer service level as part of the set of constraints;
 explicit modeling of potential economies of scale existing in international supply chains;
 simulation of qualitative factors, such as the general infrastructure of a country;· differentiation of
products by country;
 determination of adequate excess capacity in different countries;
 coordination of commodity flows, cash flow, and information flow within an international
environment;
 modeling of alliances and multi-company network configurations; and
 development of specialized methods of solution.
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