The Structure of Global Supply Chains

The Structure of Global Supply Chains The Structure of Global Supply Chains Panos Kouvelis Washington University in S...

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The Structure of Global Supply Chains

The Structure of Global Supply Chains Panos Kouvelis Washington University in St. Louis USA [email protected]

Ping Su SUNY New Paltz USA [email protected]

Boston – Delft

R Foundations and Trends in Technology, Information and Operations Management

Published, sold and distributed by: now Publishers Inc. PO Box 1024 Hanover, MA 02339 USA Tel. +1-781-985-4510 www.nowpublishers.com [email protected] Outside North America: now Publishers Inc. PO Box 179 2600 AD Delft The Netherlands Tel. +31-6-51115274 The preferred citation for this publication is P. Kouvelis and P. Su, The Structure of Global Supply Chains: The Design and Location of Sourcing, Production, and R Distribution Facility Networks for Global Markets, Foundation and Trends in Technology, Information and Operations Management, vol 1, no 4, pp 233–374, 2005 ISBN: 978-1-60198-098-4 c 2007 P. Kouvelis and P. Su

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R Foundations and Trends in Technology, Information and Operations Management Volume 1 Issue 4, 2005 Editorial Board

Editor-in-Chief: Uday Karmarkar Times Mirror Chair in Mgmt Startegy & Policy The Anderson School at UCLA Los Angeles, California 90095-1418 USA [email protected] Editors Uday Apte (Southern Methodist University) Rajiv Banker (Temple University) Gabriel Bitran (MIT) Roger Bohn (UC San Diego) Gerard Cachon (University of Pennsylvania) Morris Cohen (University of Pennsylvania) Sriram Dasu (University of Southern California) Awi Federgruen (Columbia University) Marshall Fisher (University of Pennsylvania) Art Geoffrion (UCLA) Steve Graves (MIT) Vijay Gurbaxani (UC Irvine) Wallace J. Hopp (Northwestern University)

Ananth Iyer (Purdue University) Sunder Kekre (Carnegie Mellon University) Ton de Kok (Technical University Eindhoven) Panos Kouvelis (Washington University) Christoph Loch (INSEAD) Haim Mendelson (Stanford University) Mohanbir Sawhney (Northwestern University) Avi Seidman (University of Rochester) Josep Valor (IESE Business School) Jo van Nunen (Erasmus University) Garrett van Ryzin (Columbia University) Luk van Wassenhove (INSEAD) Andrew Whinston (University of Texas, Austin) Candice Yano (UC Berkeley)

Editorial Scope R Foundations and Trends in Technology, Information and Operations Management will publish survey and tutorial articles in the following topics:

• B2B Commerce

• New Product & Service Design

• Business Process Engineering and Design

• Queuing Networks

• Business Process Outsourcing • Capacity Planning

• Service Logistics and Product Support

• Competitive Operations

• Supply Chain Management

• Contracting in Supply Chains

• Technology Management and Strategy

• E-Commerce and E-Business Models • Electronic markets, auctions and exchanges

• Reverse Logistics

• Technology, Information and Operations in: – Automotive Industries

• Enterprise Management Systems

– Electronics manufacturing

• Facility Location

– Financial Services

• Information Chain Structure and Competition

– Health Care

• International Operations

– Media and Entertainment

• Marketing/Manufacturing Interfaces

– Process Industries

• Multi-location inventory theory

– Telecommunications

– Industrial Equipment

– Retailing

Information for Librarians R Foundations and Trends in Technology, Information and Operations Management, 2005, Volume 1, 4 issues. ISSN paper version 1571-9545. ISSN online version 1571-9553. Also available as a combined paper and online subscription.

R in Foundations and Trends Technology, Information and Operations Management Vol. 1, No. 4 (2005) 233–374 c 2007 P. Kouvelis and P. Su

DOI: 10.1561/0200000003

The Structure of Global Supply Chains: The Design and Location of Sourcing, Production, and Distribution Facility Networks for Global Markets Panos Kouvelis1 and Ping Su2 1

2

Olin School of Business, Washington University in St. Louis, St. Louis, MO 63130, USA, [email protected] School of Business, SUNY New Paltz, New Paltz, NY 12561, USA, [email protected]

Abstract In today’s marketplace, most companies realize that it is essential to be aware of and participate in international markets. Furthermore, it becomes transparent that the footprint of the firm’s global facilities for sourcing, R+D, production, distribution and sales, and the effective coordination of all flows between them become the major determinants of competitive success. In other words, global supply chain management is a core business process of the utmost strategic importance and all firms have to manage it as such. The authors provide a better understanding of the development of the right “footprint” of a global firm in its effort to supply its markets in environments of fast paced competition and tremendous uncertainty. The authors focus on the structure of global supply chains and the detailed choices involving the network of facilities at all stages of the supply chain in order to successfully execute the global business strategy.

Contents

1 Introduction — Issues to Consider

1

1.1 1.2

2

1.3 1.4

Globalization of Operations and Supply Chains Driving Forces of Globalization of Operations Strategies Structure of Global Supply Chains: Issues to Consider Structure of Our Review

3 5 9

2 Conceptual Frameworks for Global Supply Chains

13

2.1 2.2 2.3 2.4

14 25 29 35

Kouvelis and Munson Framework (MA-PLA-NET) Ferdows Framework: Strategic Role of Global Facilities A Typology of Plants in Global Manufacturing Networks Global Resource Deployment Analysis

3 Modeling and Decision Support for Global Supply Chain Design 3.1 3.2 3.3

Global Facility Network Design Model Multi-echelon Supply Chain Networks under Demand Uncertainty Robust Designs for Global Networks and Its Related Applications ix

41 41 47 51

3.4 3.5

Global Supply Chain Design Application Global Facility Network Design Using Newsvendor Network Approach

4 Importance and Implications of Global Factors on Network Design 4.1 4.2 4.3 4.4 4.5

Risk Considerations in Facility Location under Uncertainty Valuing Operational Flexibility Under Exchange Rate Risk Local Content Rules Transfer Pricing Schemes Taxation and Other Factors

5 Classification Scheme 5.1 5.2 5.3

Previous Research Surveys: Global Manufacturing Strategy Literature Stochastic Global Facility Location Models Classification Scheme

61 78

93 93 103 113 119 122 127 127 128 134

References

139

Biographies

143

1 Introduction — Issues to Consider

Over the past two decades, a new global business environment has evolved. World exports of goods and services reached $13.7 trillion in 2006, which was close to 30% of world gross domestic product, up from a mere 10% two years ago. The vast majority of businesses now has some form of global presence through exports, strategic alliances, joint ventures, or as part of a committed strategy to sell in foreign markets or locate production plants or business process services abroad. American manufacturers have 8000 units overseas employing almost 5 million workers, equal to nearly 25% of US manufacturing employment. Previously, large multinational corporations dominated the international marketplace, which domestic firms generally ignored. However, according to the 2001 census, 97% of manufacturers who exported were considered small- or medium-sized. In today’s marketplace, most companies realize that it is essential to be aware of and participate in international markets. Furthermore, it becomes transparent that the footprint of the firm’s global facilities (fully or partially owned, or simply accessed through joint ventures and strategic alliances, or just simply as part of outsourcing deals) for sourcing, research and development, production, distribution and retail sales, and the effective coordination and 1

2

Introduction — Issues to Consider

management of all flows between them (information, physical/product, and financial flows) become the major determinants of competitive success. In other words, global supply chain management is a core business process of the utmost strategic importance, and all firms have to manage it as such. The focus of this paper is on better understanding the development of the right “footprint” of a global firm in its effort to supply its markets in environments of fast paced competition and tremendous uncertainty (from political, macroeconomic, demand, and technological factors contributing to it). We are concerned with the structure of global supply chains and the detailed choices involving the network of facilities at all stages of the supply chain (sourcing, production, distribution, and sales) in order to successfully execute the global business strategy.

1.1

Globalization of Operations and Supply Chains

Let us elaborate on documenting the globalization of firms’ operations and supply chain strategies. The following trends among US businesses illustrate the growing size and importance of global operations: • According to the US Census, from 2003 to October 2005, the value of goods imported rose nearly 45% while the value of goods exported rose only 31.3%. Overall the trade deficit for goods rose 62% in that time. • When other characteristics of companies are held constant, exporting firms perform much better than non-exporters. Worker productivity in exporting firms is 20% higher than that of non-exporting firms. Export jobs are better jobs: production workers in exporting firms earn 6.5% more. They are also more stable jobs: exporting firms are 9% less likely to go out of business than comparable non-exporting firms (Bergsten [3]). • According to US Census information from 2001 to 2002, nearly 20% of US manufacturers participate in exporting, accounting for over 71% of the total known value for exports. • Manufacturing assets held by multinational enterprises in foreign countries are substantial and rapidly increasing.

1.2 Driving Forces of Globalization of Operations Strategies

3

• Much of the US trade deficit represents what US corporations buy from their overseas units. In the late 1990’s such foreign affiliates of US corporations generated close to $3 trillion in sales, with 65% of that sold to local markets and the remaining 35% brought back to United States. • In 2004 about 8% of administrative office work had been outsourced, much of it to India. In IT services, 16% of all IT work is done by an outsourced party. Much like manufacturing in the 1980’s and 1990’s, Business Process Outsourcing (BPO) is a growing trend, estimated to grow from $3.6 billion in 2003 to $21–$24 billion by 2008. Two factors underlie the dramatic rise in globalization. First, global reach is important to a firm’s survival. Second, multinational firms are more profitable and grow faster. Among twenty major US manufacturing industries, multinational firms grew faster than domestics in 19 of the cases and were more profitable in 17 cases (Bergsten [3]).

1.2

Driving Forces of Globalization of Operations Strategies

As clearly explained in the recent work of Kouvelis and Niederhoff [24], the motivating factors, or often stated as the driving forces, for globalization of operations can be grouped into four: Category 1: Global Market Forces. Market forces for globalization include the need to establish a presence in foreign markets to capitalize on foreign demand and recoup domestic demand lost to foreign imports, as well as to build a global presence to minimize foreign threats into the domestic market through a competitive balance. As the existence of secondary markets for end-of-life products begins to fade, speed to market sometimes dictates a global production and distribution network. Finally, as state-of-the-art niche markets develop in specific countries, companies must consider establishing a presence in these markets to stay competitive and abreast of the latest technology developments and demands.

4


Category 2: Technological Forces. Many companies seek a global market in order to achieve economies of scale as they simultaneously narrow the scope of their product to a niche market by differentiating themselves in a commodity market. This, in effect, is the mass customization of a good at a global-level. As technological production skills develop globally, multinational firms need to tap into the technological knowledge of various countries and integrate the new technology into their own product as necessary to stay competitive. In order to stay current and access these new developments in real time, global companies may benefit by forming close relationships with dominant foreign suppliers instead of investing in an in-house capability. Additionally, by placing production facilities close to the state-of-the-art suppliers and competitors, costly delays due to breakdowns are minimized. Globally located firms can also engage in technology sharing and interfirm collaborations, and take advantage of state-of-the-art or lower priced R&D workers in countries such as Taiwan, China, and India. Category 3: Global Cost Forces. Perhaps the most commonly recognized force for globalization, experiences from previous global expansion projects, and some of their failures, indicates that costs to consider for offshore sourcing should go beyond just direct labor and definitely include quality, differential productivity, and design costs, and carefully account for added logistical and transportation costs. Often, direct labor is such a small component of total product cost that it is misleading to offshore solely on the basis reduced labor costs. In industries with capital-intense production facilities, globalization can be a natural result of multiple firms seeking a joint production facility or a single firm seeking economies-of-scale through high utilization of a private production facility. Category 4: Political or Macro-economical Forces. Currency rate fluctuations can help or hurt global operations and require careful analysis and, preferably, a portfolio of options to balance unfavorable fluctuations. Regional trade agreements, such as NAFTA, also influence the decision to globalize operations. Finally, the imposition of trade

1.3 Structure of Global Supply Chains: Issues to Consider

5

protection mechanisms, such as tariffs, trigger price mechanisms, local content requirements, technical standards, health regulations, and procurement policies, influence where a company may choose to locate global operations in order to make the most of its supply chain.

1.3

Structure of Global Supply Chains: Issues to Consider

Strategic planning for global facilities networks is complex, involving decisions of where to locate factories, how to allocate production to the various facilities, how to develop suppliers for the plants, how to manage the distribution of products, and how to organize the interfaces along the global supply chain. The “givens” that frame these decisions are the company’s particular set of markets; products to produce and sell; demand projections for the different markets; and information about future macroeconomic conditions, transportation costs, and production economics (e.g., cost curves as a function of production volumes for each individual process step or component that goes into the product). The very first issue typically addressed in global operations textbooks in an effort to capture, at least at a conceptual level, the issues associated with the structure of global supply chains is the so called “orientation of facility networks” concept (refer to Dornier et al. [10]). The “facility orientation” concepts are struggling to capture the concerns in global supply chain structure in an effort to create supply chains that meet the competitive priorities of the various products at the different markets. These priorities include cost, quality, service, and flexibility criteria, and in a dynamic global environment the added criterion of ability to react to environmental changes (i.e., hedge against uncertainties of the global environment) plays an important role. In general, current textbook theories orient facility networks by market, by product, and by process. (1) Market Focus: In this approach, the firm locates entire supply chains in different markets. The driving force behind location decisions is proximity to markets where products are sold. In such a scenario, the “supply” (supplier network and production) organization is decentralized and each supply

6


chain produces the entire product line for its respective market. The “demand” chain (distribution and retail) is also decentralized and each market is treated separately. (2) Product Family Focus: Under this scheme, the firm locates segments of its supply chain (various facilities) in different parts of the world driven by economies of scale. Typically facilities specialize in a specific product family, with products in a product family sharing technical traits, components, setups and production lines, and often “business” similarities (competitive priorities, order profiles etc.). The “supply” organization is mainly centralized because the company has to manage the allocation of the different products to the different markets from the same set of facilities. Sometimes the organization might be decentralized if some product families belong in specific markets because of structural constraints such as import barriers. The “demand” chain organization may also be either centralized (with distribution and sales offices placing orders to the various facilities in the supply network to meet the needs of their markets) or decentralized (by operating distribution and sales networks at the various markets). (3) Process Focus: Using a process focus, a company locates facilities in different parts of the world, but each facility specializes in specific steps of the supply/production/logistic process (e.g., metal components, assembly facilities, plastic molding, large container transportation, high volume distribution facilities etc.). The driving force behind this strategy is economies of scale in particular processing and logistic steps. Therefore, the supply organization is centralized to coordinate the “bringing together” (e.g., assembly) of the different activities involved. The “demand” chain is also centralized to coordinate the “bringing together” of the logistic and sales activities for the different markets. In reality, it is difficult to find a company that follows any of the above presented approaches exactly. However, by analyzing these different

1.3 Structure of Global Supply Chains: Issues to Consider

7

approaches it is possible to understand some of the trade-offs inherent in structuring global supply chains. The textbook of Dornier et al. [10] does a great job in capturing these trade-offs at an introductory level, and we refer the interested readers to it. To further elaborate at the abstract level on the issues of global supply chain structure, we use a simple two dimensional construct to map the various approaches for “facility orientation” we discussed above. The two dimensions we use reflect essential product characteristics: supply system complexity (abbreviated from now on as “supply” complexity) needed to produce them, and market demand requirements complexity (abbreviated from now on as market complexity). Supply complexity refers to the difficulty of the production processes of the various components and assemblies. For example, if we compare the hand tools industry with the computer industry, we see that the complexity for the first is lower than the second. Processing activity complexity can be based on a variety of factors, such as the number of processing steps, physical characteristics of the product, and environmental requirements. Market complexity captures the specifications and complexities the distribution and sales functions face in executing the delivery and customization requirements for the various customers and markets. The apparel industry, where fashion is the critical driver, has significantly higher “market” complexity than the electronic components industry, where customers are less fashion and more functionality and efficiency driven. Figure 1.1 captures the different approaches as a function of the dimensions discussed. For low supply and market complexity, the market focus fits better. In this environment it is easier to serve customers when one facility or the whole regional chain is responsible for the entire product and the main drivers for customers are service and quality (as opposed to cost). As supply complexity increases, firms must specialize their supply and production facilities into specific activities (tasks), because quality becomes a critical element (i.e., shift to process focus). When combined with economies of scale, quality differentiation is adequate to give the firm a competitive advantage. If market requirements complexity is high, then the driver for going from a product family focus into the process focus is increased importance of economies of

8


Fig. 1.1 Orientation of facility networks.

scale. When the market requirements complexity is low, such as in the apparel industry for some models of jeans with long product lifecycles, firms may decide to automate the supply process and through reduced supply complexity (via standardization and automation) move back from product family to market focus. In other words, the product family focus occupies the middle ground between market and process focus. For an abstract and introductory discussion, global facilities network design issues are captured in such concepts of “facility orientation” and different global supply chain designs can be explained through simple two dimensional constructs along dimensions of “supply complexity” and “market complexity.” However, the main purpose of this research review is to go beyond such elementary exposition of global supply chain network design issues, and using the latest research on the subject to find ways to identify the multiplicity of factors that contribute to designing these networks for competitive advantage of the global firm, while at the same time exposing both the successful features but also the challenges faced by decision support systems developed to address such decisions. Our emphasis is on presenting approaches, which are built on the richness of operations and supply chain modeling research and support tools, going beyond abstract

1.4 Structure of Our Review

9

discussion of trade-offs and into careful quantification of them. And then, such approaches, through systematic evaluation and selection processes often of an algorithmic nature, result in profit maximizing and risk controlling strategies for developing effective global supply chains. All presented approaches are based on rigorously documented academic and industrial research, most of it spanning seminal developments of the last 15–20 years, but with a heavier emphasis on tools and approaches of the last decade. Hopefully, the reader will find in adequate detail a comprehensive answer to the questions on how a global firm should configure its network of facilities (supply, production, and distribution), and what dynamic approaches to use to effectively reconfigure it in an effort to meet demand in global markets in a profit maximizing way of sustainable profitability and of enduring nature competitive advantage. We conclude this introductory section by describing the structure of our research review in answering these questions.

1.4

Structure of Our Review

In Section 2, we introduce the most important and practice relevant concepts in the literature on the issue of “facility orientation” of global supply chain networks. The first of these concepts is based on the recent research of Kouvelis and Munson [23], and classifies global facility network structures along three main dimensions: market focus, plant focus, and network dispersion. The authors argue in a rigorous manner via the use of a structural equations modeling approach that a few key independent variables, which are relatively easy to calculate, capture all essential trade-offs and allow us to classify a firm’s network structure along one of the above three dimensions. Specifically, economies of scale, complexity costs of the production system, transportation costs, and tariffs are the primary levers in determining a global firm’s network structure. The work of Kouvelis and Munson, effectively summarized in our section, develops aggregate ways to measure “economies of scale,” “complexity costs,” and relevant “transportation” and “tariff” costs, and then explicitly describe via empirically derived equations the casual relationship of these measures with appropriately defined measures of “market focus,” “plant focus,” and “network dispersion.”

10


Section 2 also contains discussion of the “popular” MBA classroom framework of Kasra Ferdows [12] of “six types of foreign factories.” The framework classifies foreign factories based on the three primary strategic reasons for the factory’s location (low cost production, access to skills and knowledge, and proximity to market), and the level of the site’s competence (low versus high). The third framework we present in this section is recently proposed by Vereecke et al. [37]. They focus on the intangible characteristics of plants. Along the lines of Ferdows’s work, they focus on the intangible characteristics of plants. This empirically derived typology is based on the knowledge flows between the plants. The fourth framework presented is the one by Cohen and Lee [7]. This is a broad framework addressing the various components of the supply chain and discussing various sourcing, plant charter, and distribution strategies. In Section 3, we present the modeling details and the decision support tools for designing global supply chains. We first start with the global facility network model of Kouvelis and Munson [23], which is used both in the derivation of their conceptual framework and as a decision support tool for global supply chain design. Section 3 also includes the modeling framework proposed by Tsiakis et al. [33] on multi-echelon supply chain network design under scenario-based demand uncertainty. We then spend significant effort in describing an important approach, the “robustness approach,” in making global supply chain designs under significant uncertainty. The designed supply chain is robust in the sense that it hedges the firm’s performance against the worst contingencies in terms of uncertain factors (demand, exchange rates, commodity prices etc.) over a planning horizon. The work of Gutierrez and Kouvelis [14] formally introduced many of those early concepts and presented effective algorithmic procedures for the solution of the resulting difficult mixed-integer programs. The wide applicability of the approach is further illustrated in the work of Lowe et al. [27] in designing the global supply chain of the company illustrated in the popular case study of Applichem (Flaherty [13]), and thus making this material easy to transfer into MBA and executive classrooms. A by-product of this work is an easy quantification of the value of excess capacity in global supply chain networks, by illustrating that it is an essential feature of global supply

1.4 Structure of Our Review

11

chain designs (see discussion in Lowe et al. [27]). We also present one of the better known decision support tools for global supply chain design, which originated from its application in the design of global supply chains for Digital Equipment Company and its early documentation appeared in the work of Arntzen et al. [2]. Finally, we conclude the section with an overview of the recent research that uses the newsvendor network approach to design global facility networks, Lu and Van Mieghem [28] and Biller and Xiang [4]. In Section 4, we devote our attention to modeling and decision support approaches that explicitly deal with some added complexities and uncertainties often dominating and substantially complicating the supply chain design of global firms versus national or regional supply chains. These factors are: fluctuating exchange rates, price uncertainties (both of inputs and outputs), investment financing decisions of global facilities, regional trade agreement complexities and local content rules, international taxation complexities and transfer pricing schemes. We also include the stream of research of applying option valuation approach to value the operational flexibility under exchange rate uncertainty. Among the research works explicitly discussed are seminal work of Hodder and his coauthors (in [15], [16], and [18]), Daskin et al. [8], Huchzermeier and Cohen [19], Kogut [21], Kogut and Kulatilaka [22], Munson and Rosenblatt [29], Villegas and Quenniche [41], and Kouvelis et al. [25]. Finally, our Section 5 concludes with an extensive discussion of previous research survey works in the area of global supply chain design, thus allowing the reader to see the extensive literature from many different perspectives, and in the process we highlight different viewpoints and methodological and managerial insights. At the end we present a comprehensive classification scheme of the most important papers in the area of global supply chain network design.

2 Conceptual Frameworks for Global Supply Chains

For the purposes of our discussion, we conceptualize supply chains as consisting of three main stages, as described in Figure 2.1. Stage 1: outsourced “input to the process” activities (“suppliers”); Stage 2: main production/service process activities performed internally by the firm (“production”); and Stage 3: outsourced “output” (from the “process” to the ultimate “customer”) activities, frequently involving distribution, logistics and/or after-sales service (“distribution”). As firms extend their operations globally, with markets all over the world, sourcing and production activities spreading over different continents, and with a multiplicity of complex distribution and logistic arrangements to match global demand with their supply, the location and needed connecting structure of these supply chain stages becomes a critical design choice. We will start our discussion by introducing four broad conceptual frameworks used for the design of global supply chain networks. The frameworks in Sections 2.1 and 2.2 focus on the production stage. The third framework in Section 2.3 is empirically derived and focuses on the intangible characteristics of global facility networks. The fourth one introduced in Section 2.4 is a broader framework that covers all the three stages of a global supply chain. 13

14

Conceptual Frameworks for Global Supply Chains

Fig. 2.1 A supply chain.

2.1

Kouvelis and Munson Framework (MA-PLA-NET): Market (MA)/Plant (PLA)/Network Dispersion (NET) Focus

The conceptual framework proposed by Kouvelis and Munson [23] is dealing with the “production” stage of the value-added chain. Consider a two level production tree (see Figure 2.2): level 0 is the “final product,” and level 1 is its “core subassemblies” from which the finished product is assembled. Correspondingly there are two facility levels: plants (producing subassemblies) and DCs (distribution centers producing final assembly). A facility network will be designed to produce the final product, and each plant will be allocated to the production of certain types of subassemblies. The firms need to decide where to locate factories, how to allocate production activities to the various facilities of the network, and how to manage the distribution of products (e.g.,

Fig. 2.2 Tree structure.

2.1 Kouvelis and Munson Framework (MA-PLA-NET)

15

where to locate distribution facilities), after accounting for information on which markets to serve, future macroeconomic conditions, and other firm-specific issues like product mix decisions for different markets, transportation costs, and production costs. Kouvelis and Munson’s framework classifies strategic global facility network structures along three main dimensions: market focus, plant focus, and network dispersion. The authors use global sensitivity analysis (using the seminal work of Wagner [42]) to develop a structural equations model based on a mixed-integer program that captures essential design trade-offs of global networks and explicitly incorporates government subsidies, trade tariffs, and taxation issues. The resulting structural equations model classifies a firm’s network structure according to their conceptual framework via the calculation of just a few key independent variables which are called “framework measures.” Thus, managers can make high-level (strategic) decisions about network structure by using less detail, and then for a given structure as suggested by their model, managers could utilize more detailed models at the local level to make more operational (tactical) decisions. The derived structural equations can be used on an ongoing basis for monitoring the appropriateness of the facility network structure for the specific product/global market environment and deciding on structural shifts needed in response to market/macroeconomic environment changes.

2.1.1

A Conceptual Framework to Classify Global Network Structures

The conceptual framework classifies global network structures along three dimensions (see Figure 2.3). (1) Market focus refers to the degree to which each marketing region produces subassemblies needed for that region. A global strategy generally has plants producing large fractions of worldwide demand, while a regional strategy generally segments production by region (see Figure 2.4). (2) Plant focus refers to the degree to which different subassemblies are produced at the same facility. Adedicated strategy generally separates subassemblies into different plants, while a flexible strategy combines subassembly

16


Fig. 2.3 Global network structure classification along three dimensions.

production at the same facilities (see Figure 2.5). (3) Network dispersion refers to the number of different plants producing the same subassembly per marketing region that has any production at all. A concentrated strategy has a single plant for each subassembly type per region of production, while a scattered strategy has multiple (see Figure 2.6). When firms position themselves in the global network, they can choose anywhere between the two extreme strategies they define in each dimension. Therefore, a firm’s network structure strategy is positioned somewhere in the space presented in Figure 2.3. For example, points A, B, C, and D in Figure 2.3 refer to different global network structures. Point A represents a global-flexible-concentrated strategy, having all subassemblies for the entire world’s demand produced at one facility, while point B, a regional-dedicated-scattered strategy would have each marketing region producing its own demand at multiple


17

Fig. 2.4 Framework 1: Market focus dimension.

subassembly-specific facilities. Point C represents a regional-dedicatedconcentrated strategy, and point D refers to a more general strategy, “regional-half-dedicated, half-flexible-half-concentrated, half-scattered strategy.” The detailed measure of each dimension will be discussed later in Section 3.1. Although their descriptions of global network and the three measures are more from a manufacturer’s perspective, it is easy to be applied to the service industry through an appropriately modified and expanded definition of terms.

18


Fig. 2.5 Framework 2: Plant focus dimension.

Fig. 2.6 Framework 3: Network dispersion.

2.1.2

Framework Measures (Independent Variables)

The authors defined four “framework measures” that determine the company’s facility network structure: economies of scale, complexity


19

costs of producing different subassemblies at the same plant, transportation costs, and tariffs. The economies-of-scale measure, EOS, calculates a break-even volume as a percentage of annual worldwide demand, assuming all subassemblies produced at a single plant while ignoring complexity costs. The complexity measure, COM, calculates a ratio of the costs of producing two subassemblies at one plant vs. two subassemblies at two different plants. The transportation measure with tariffs, TRANS1, calculates the distance-related transportation costs plus tariffs, expressed as a percentage of gross margin. The transportation measure without tariffs, TRANS2, is the same as TRANS1, excluding the tariffs. Numerical tests suggest that the four measures are sufficient for managers to design and monitor their strategic network structures. The framework measure calculations are shown in Table 2.1. To illustrate how to calculate the framework measures, we consider a problem of five time periods (T = 5) in which a firm has one final product (ceiling fans) with two subassemblies (I = 2). It has two marketing regions: we have REG1 = {Country A, Country B}, and REG2 = {Country C, Country D, Country E}, MARK = 2. The firm’s global supply chain network structure is described in Figure 2.7. The authors assume that annual fixed costs and up-front investment

Table 2.1 Framework measures used for the structural equations model. [T F +A+SUME]/[P −SUMV−G(T f +a)−SUMe] WORLD

Economies of scale

EOS =

Complexity costs

T (F +B2 )+A+2(WORLD/MARK)G(T f +a) 2×(T F +A+(WORLD/MARK)G(T f +a)) TRANS1 = MILE×1000+TARIFF P −SUMV−v TRANS2 = PMILE×1000 −SUMV−v

Transportation costs with tariffs Transportation costs without tariffs

COM =

Notes: For all the notation, the country indices have been eliminated and all costs and prices are based on a system-wide average. Detailed notation is as follows. T = time horizon. F (f ) = annual fixed base cost (annual fixed linear cost of per square foot) of operating a subassembly plant. A (a) = base investment cost (invest cost per unit) to build a subassembly plant. B2 = annual fixed cost of producing the 2nd subassembly in the same plant. SUMV = sum of unit variable production cost across all assemblies. v = unit variable assembly cost at a distribution center (DC). SUME (SUMe) = sum of base (unit) investment cost to build a production line across all assemblies. P = sales price of the final product. G = average space requirement per subassembly unit. WORLD = average annual worldwide demand. MARK = number of marketing regions. MILE = transportation cost per mile for the final product. TARIFF = average tariff for shipping the final product outside of the marketing region. P − SUMV − v represents gross margin of the product.

20


Fig. 2.7 Global network structure: An example for calculating framework and proxy measures.

costs are an increasing function of capacity and are modeled as a base cost plus a linear function of capacity. F , SUME and A denote the base costs. f , SUMe, and a are linear components correspondingly. T F + A + SUME are the total fixed costs (which do not vary with sales) of building plants, building production lines (equipment costs), and operating plants. SUMV + G(T F + a) + SUMe are the total variable costs (which vary with sales). The break-even quantity (Q) is the volume at which total revenues equal total costs. Therefore, T F +A+SUME Q = P −SUMV−G(T f +a)−SUMe . Cost structure parameters and demands for each country are given in Tables 2.2 and 2.3, respectively. [T F + A + SUME]/[P − SUMV − G(T f + a) − SUMe] WORLD [5 × 2000 + 1000 + 1000]/[100 − 20 − 1(5 × 5 + 5) − 6] = 120, 000

EOS =

= 0.23%


21

Table 2.2 An example: Cost structure parameters for framework measures (Unit: $). F 2000

f 5

SUMV 20

v 5

SUME 1000

SUMe 6

G 1

A 1000

a 5

MILE 0.0025

TARIFF 10% · P

B2 20,000

P 100

Table 2.3 An example: Demand data for framework measures. Country Country Country Country Country Country WORLD

A B C D E

Demand 20,000 20,000 20,000 30,000 30,000 120,000

Economies-of-scale measure, EOQ, calculates the break-even volume (Q) as a percentage of annual worldwide demand. The EOS of 0.23% implies that the firm starts to make money at 0.23% of annual sales. Complexity measure, COM, compares which one is more cost-effective, producing two subassemblies at a single plant, or producing two subassemblies at two different plants. The trade-off is that having one plant saves the fixed costs of operating and building a plant but it has additional costs to have a second subassembly in the same plant. B2 captures the complexity cost of the second subassembly. COM =

T (F + B2 ) + A + 2(WORLD/MARK)G(T f + a) 2 × (T F + A + (WORLD/MARK)G(T f + a))

5 × (2000 + 20, 000) + 1000 + 2(120, 000/2) × 1000 × (5 × 5 + 5) 2 × [5 × 2000 + 1000 + (120, 000/2) × 1 × (5 × 5 + 5)] = 1.0246 =

If the firm has COM value greater than 1 (in this example), it implies that it is more expensive to have more than one subassembly in one plant than two subassemblies at two different plants. If COM is less than 1, it implies that it is more cost effective to do so. MILE × 1000 + TARIFF P − SUMV − v 0.0025 × 1000 + 10% × 100 1 = = 100 − 20 − 5 6

TRANS1 =

22


MILE × 1000 P − SUMV − v 0.0025 × 1000 1 = = 100 − 20 − 5 30

TRANS2 =

TRANS1’s value of 16 represents the distance-related transportation 1 cost plus tariff is one-sixth of gross margin. TRANS2’s value of 30 indicates the distance-related transportation cost without tariff is onethirtieth of gross margin. The reason that the authors have two transportation measures is that tariffs have an obvious impact on market focus, but they have a confounding effect on network dispersion according to their definitions.

2.1.3

Proxies for the Global Network Structure Dimensions (Dependent Variables)

The market focus measure, MARKET, calculates the percentage of subassemblies imported from other regions, averaged over each region. A high value implies more of a global strategy. The plant focus measure, PLANT, is based on the average number of subassemblies per plant. A high value implies more of a flexible strategy. The network dispersion measure, DIS, calculates the average number of plants per subassembly, as a percentage of the number of possible plant locations per region, averaged over each region that has any subassembly production at all. A high value implies more of a scattered strategy. Each measure is normalized to a range between 0 and 1. Table 2.4 displays the calculations for the dependent variables. To illustrate how they calculate these proxy measures, we still use the network in Figure 2.7. From Figure 2.7, the total number of assemblies in the firm’s global supply chain network TOTALY is 7, total number of 1st subassembly TOTALY1 is 5. For marketing region 1, the total number of production lines for subassembly 1 TOTALZ1 is 2, and for subassembly 2, TOTALZ2 is 2. TOTALZ is 4. Similarly, for marketing region 2, TOTALZ1 = 2, TOTALZ2 = 1, and TOTALZ is 3. Using data listed in Table 2.5, we are ready to calculate


23

Table 2.4 Proxies of network structure dimensions used for the structural equations model. Market focus Plant focus Network dispersion

PLANT =

I P (1/I) P (1 − min(1, TOTALX/TOTALx))

1

MARKET =

MARK − 1 REG

I−1

P

1

REG

M (REG) − 1

DIS =

i=1

TOTALY/TOTALY1 − 1

P I min(1, TOTALZi ) i=1

max 0, TOTALZ/ max 1, −1

P

min{1, TOTALZ}

REG

Notes: The detailed notation used above is as follows. Notation from Section 2.1.2 is used here. REG = a marketing region. MARK = the number of marketing regions. M (REG) = the number of production plants in region REG. I = types of subassemblies. (Note that the authors assume that any type of subassembly can be produced in at most one plant in any given country.) TOTALX = total units of subassembly i made in a marketing region. TOTALx = total units sold in a marketing region. TOTALY = the total number of subassemblies in the global network. TOTALY1 = the total number of 1st subassembly in the global network. TOTALZ = the total number of production lines for all subassemblies in a marketing region. TOTALZi = the total number of production lines for subassembly i in a marketing region.

the proxy measures. In our example, MARKET =

1 MARK − 1 ×

X

(1/I)

1 · 2−1 1 2

+ PLANT =

(1 − min(1, TOTALX/TOTALx))

i=1

REG

=

I X

1 2

1 − min 1,

1 − min 1,

5 25

10 15

+

+

1 − min 1,

1 − min 1,

25 5

=

17 30

TOTALY/TOTALY1 − 1 7/5 − 1 2 = = I−1 2−1 5

P REG

1 M (REG) − 1

(

× max 0, DIS =

P TOTALZ max[1, Ii=1 min(1, TOTALZi )] P ( REG min{1, TOTALZ})

)

+

! −1

1 4 max 0, −1 3−1 max{1, min(1, 2) + min(1, 2)}

=

20 15

1 3 max 0, −1 2−1 max{1, min(1, 1) + min(1, 2)} min{1, 4} + min{1, 3}

=

1 2

24


Table 2.5 An example: Data for proxy measures. Marketing region 1 1 2 2

Subassembly 1 2 1 2

TOTALX 10 5 20 25

TOTALx 15 25 15 5

17 A score of 17 30 on the market focus measure represents a “ 30 -global, 13 13 30 -regional” strategy. That is, 30 of the total demand is satisfied by the plants in the marketing region and 17 30 is imported from the plants outside the marketing region, averaged over each region. PLANT = 25 implies with 40% chances, different subassemblies are produced in the same plant. In our example, two out of five plants produce different subassemblies in a single plant. A score of 12 on DIS indicates a “halfconcentrated, half-scattered” network dispersion strategy. Using extensive experimental data generated from their mixedinteger programming model and the rigorous econometric techniques, they identified key summary measures (independent variables: EOS, COM, TRANS1, TRANS2) that explain the observed key summary output variables of the model (dependent variables: MARKET, PLANT, DIS). From their extensive computational results, the authors observe that:

(a) the transportation measure with tariffs, TRANS1, has the most explanatory power for the market focus, MARKET, measure; (b) complexity costs and economies of scale (as measured by COM and EOS, respectively) have the most explanatory power for the plant focus, PLANT, measure; and (c) the transportation measure without tariffs, TRANS2, has the most explanatory power for the network dispersion, DIS, measure. These results are expected to hold across most reasonable product/ market data sets representing frequently encountered industrial setting. In conclusion, this conceptual framework contributes to decision making on developing and monitoring global networks. During the development/design phase of the network, the framework guides the

2.2 Ferdows Framework: Strategic Role of Global Facilities

25

global manager on a rough cut solution to implement a chosen strategy, with further detailed optimization modeling to make detailed capacity/operational asset allocation decisions. The framework can also be used as an audit tool of an existing network to identify needed changes due to changing market/product/technology conditions. The comprehensive model suggested as a detailed decision support tool (discussed in more detail in Section 3.1) captures the complex facets of global supply networks, explicitly considering factors such as economies of scale, complexity costs, transportation costs, tariffs, subsidized financing, and taxation. Among the authors’ contribution is that they brought to our attention the effects of subsidized financing and taxation on the strategic network structure as well as on the tactical allocation of production among countries.

2.2

Ferdows Framework: Strategic Role of Global Facilities

The first framework by Kouvelis and Munson [23] focuses on the tangible characteristics of plants. Ferdows [12] proposed another useful framework for global facility network from a different prospective. He classifies foreign factories into six categories based on the primary strategic reason for the factory’s location and the scope of its current activities. In addition, he discusses the imperatives of upgrading the strategic roles and the resulting migration from one type to another. Similar to Kouvelis and Munson [23], it focuses on the “production” stage of the supply chain. 2.2.1

Six Types of Foreign Factories

An offshore factory is established for the low-cost production of specific items that are then exported either for further work or for sale. Local managers mainly follow the instructions and plans handed down to them. The factory is not responsible for innovations, developments, and engineering. Outbound logistics is simple and beyond the control of the plant’s management. Foreign factories located in Special Economic Zone in China are examples of offshore factories. They were dedicated to production of simple labor-intensive components at a low cost. A source factory is also established for low-cost production, but

26


unlike an offshore factory, it has the ability to produce a product or a part as the best factory in the company’s global network. Its managers have greater authority over procurement (including the selection of suppliers), production planning, process changes, outbound logistics, and production-customization and redesign decisions. By the mid-1980s, HP’s factory in Singapore offered low wages, low taxes, and efficient production. In addition, it had its own R&D group and was actively involved in redesigning and developing products. It designed HP’s next generation of key-board. The Singapore plant turned to be a source plant from an offshore factory and assumed a much broader strategic role in HP’s global network of factories. A server factory is a production site that supplies specific national or regional markets. It has relatively more autonomy than an offshore plant to make minor modifications in products and production methods to fit local conditions, but its authority and competence in this area are very limited. For example, Coca-Cola Company, has many server factories around the world, each of which serves a relatively small geographic market. These plants adhere to the company’s standards and even minor adjustments in the formula require approval from regional or corporate headquarters. A contributor factory serves a specific national or regional market, and also assumes responsibility for product customization, process improvements, product modifications, or product development. Since late 1980s, Sony’s Bridgend factory has shifted its role from a server to a contributor factory. It not only served the European market but also became more independent from Sony Japan. The Bridgend factory produced most parts itself, and purchased more parts from European Suppliers. The plant also worked on customizing product design and development. An outpost factory is established to gain access to the knowledge or skills that the company needs. The primary role is to be close to competition and key suppliers and to learn about technological development. All outpost factories have a secondary strategic role as a server or an offshore, making products and serving markets. For example, lots of non-US firms launch their outpost factories in Silicon valley. A lead factory creates new processes, products, and technologies for the entire company. Its managers make decisions on key suppliers and also participate in joint development work with suppliers. Its employees

2.2 Ferdows Framework: Strategic Role of Global Facilities

27

directly deal with end customers, suppliers, research laboratories, and other centers of knowledge. They also initiate innovations frequently. For example, HP’s Singapore plant in the 90s turned into a lead factory from an offshore factory. The plant had full responsibility for a business (developing a new DeskJet printer), which included the whole spectrum of activities from the redesign, production and distribution, to the creative marketing of the product in a new market. Factories sometimes play more than one strategic roles. For example, a factory may be a server for a specific region and an offshore site for production of certain components. A factory’s strategic role can be changing over time affected by internal or external events. Internal events include changes in product mix, a merger adding new factories to the network, or other factories’ growth or shrinkage in the company’s global network. External events, such as advent of NAFTA (North American Free Trade Agreement) and CAFTA (Central American Free Trade Agreement), pose questions to the manufacturers on whether they have too many or too few certain types of factories to serve the markets. Other subtle external factors, such as increasing wages, declining tariffs, and a growing local market, also lead to the change of a factory’s role. Ferdows positions the six types of foreign factories in a strategic matrix: along the vertical dimension, the site’s competence, and along the horizontal dimension, the site’s strategic reason. Strategic reasons are one of the following three: easy access to low-cost production, access to skills and knowledge, or proximity to market. (See Figure 2.8). To change a factory’s strategic contribution, a company may choose to move it up the matrix, to move it down the matrix or if it is already at the bottom of the matrix, to close or divest it. To keep a factory’s current role, a company can move it horizontally across the matrix. Each move has its own challenges. Moving a plant horizontally requires a substantial overhaul of its organization, control systems, and equipment. 2.2.2

Upgrading the Strategic Role

In Figure 2.9 “Primary strategic reason for the site,” Ferdows demonstrates all the possible ways of changes of upgrading a factory’s strategic

28


Fig. 2.8 Primary strategic reason for the site.

Fig. 2.9 Paths to higher strategic roles.

role. Moving a plant up the matrix is very challenging and also rewarding. To fulfill an upgrade in the strategic role, there are three imperatives. First, focus on the intangible benefits. Ferdows divides the benefits that a plant can bring to a company into two types: tangible benefits such as measurable cost reduction, and intangible benefits such as learning and knowledge, and proximity to skilled labor. Intangibles expand the scope of a plant’s capabilities and lead to higher strategic roles of its

2.3 A Typology of Plants in Global Manufacturing Networks

29

manufacturing operations in the future. HP’s plant in Singapore started as an offshore factory. HP chose Singapore over cheaper Asian locations because of several intangible long-term benefits. Second, develop a variety of competencies, which can be achieved in the following three stages. At HP, managers of the Singapore factory knew that they needed to expand the factory’s competencies and to upgrade its strategic role. Stage 1: Improving the inside. It includes improving the plant’s physical layout, machinery, work design, and production quality; provide employee training and education; innovate work and production processes. Stage 2: Expanding external capabilities. Moving upward needs additional competencies. The plant is expected to strengthen communications with outside technology providers, retailers, distributors, and end customers. Stage 3: Taking on a global mandate. Upgrading a factory to a lead position is a big decision demanding substantial capabilities and serious commitment by both corporate and plant management. Third, create a robust network which is capable of coping changes in the competitive environment. A robust network contains many upgraded factories and provides stable environment for developing a site’s competencies, which in turn creates conditions for plants to expand their strategic roles and increases the robustness of the whole network.

2.3

A Typology of Plants in Global Manufacturing Networks

The third conceptual framework of global facility networks we introduce is recently proposed by Vereecke et al. [37]. Along the lines of Ferdows’s work, they focus on the intangible characteristics of plants. This new empirically derived typology is based on the knowledge flows between the plants. Four types of plants with different network roles have emerged: the isolated plants, the receivers, the hosting network players, and the active network players. Different types of plants play a different strategic role in the company, have a different focus, and differ in age, autonomy, and level of resources and investments. The evolution of the plant depends to some extent on the network role of the plant.

30


2.3.1

Four Clusters of Plants in Global Facilities Network

The global manufacturing network of a multinational company is treated as an information and people network, and the network units considered are all the plants and the group of managers in headquarters responsible for manufacturing. The plant types differ in the following network relationships (1) the flow of innovations between the units in the network; (2) the extent to which coordination exists in the network through managers traveling between the units; (3) the frequency of communication between the units in the network. Network analysis has been used for understanding different roles of the plants. The primary network measure used in their research is the centrality of the plant in the network. If network relations are mutual, centrality of the unit is measured through its degree. The degree of a unit is defined as the proportion of other units with which a unit has a direct relationship. If network relations are not mutual, two degree measures are used: the unit’s indegree and outdegree. The indegree of a unit is defined as the proportion of relations received by the unit from all other units. The outdegree of a unit is defined as the proportion of relations from that unit to all other units. Each network variable has three levels: Low, medium, and high. The following network variables have been defined: • The communication centrality of plant i captures the frequency of communication of the manufacturing staff of plant i with the manufacturing staff of the other units in the network. • The innovation indegree of plant i captures the intensity of the innovation flow transferred (and implemented) from the other units to plant i. • The innovation outdegree captures the intensity of the innovation flow transferred (and implemented) from plant i to the other units. • The people indegree of the plant captures the number of days plant i has received visitors from the manufacturing staff team of the other plants.


31

• The people outdegree of plant i captures the number of days manufacturing staff people of plant i have been visiting other plants in the plant configuration. The case research has been carried out in eight manufacturing companies headquartered in Europe, in different industries: food products, textile goods, plastic products, leather products, primary metal, fabricated metal, and electrical goods. Therefore, no single industry dominated the sample. The sample is a diverse one at the level of the company as well as the plant. The authors conclude a clustering of the data into four clusters, each representing a different position of plants in the plant network of information and people. The network variables for each cluster of plants are summarized in Table 2.6. Plants in Cluster A are called “isolated” in the plant network. Few innovations reach the plant, few innovations are transferred to other units, few manufacturing staff people come to visit such a plant, few manufacturing staff people from this plant go to visit other plants, and there is little communication between the manufacturing staff people of this plant and the other manufacturing managers in the network. A plant in Cluster B is similar to a plant in Cluster A on all but one variable, innovation indegree: it receives more innovations from the other units in the networks. They are called “receivers.” The plants in Clusters A and B are only weakly embedded in the manufacturing network. Clusters C and D consist of plants that are true network players. A type C plant frequently exchanges innovations, both ways, with

Table 2.6 Network topology of plants.

Network variable Communication centrality Innovation indegree Innovation outdegree People indegree People outdegree

Cluster A isolated Low

Cluster B receiver Low

Cluster C hosting network player Medium

Cluster D active network player High

Low

Medium

Medium

High

Low

Low

Medium

High

Low Low

Low Low

High Medium

Medium High

32


the other units, and its manufacturing staff communicates extensively with the other manufacturing managers in the network. The type C plant takes the role of the “hosting network players” because it frequently hosts visitors from other units in the network, and the inflow of visitors is significantly higher than the outflow. The type D plants differ from the type C plants in two aspects: First, the level of communication centrality and the innovation outdegree are even higher in the type D plants. Second, the outflow of the visitors is higher than the inflow. They are called “active network players” since the D plants are highly involved in the network, and take a more active role than the C plant. 2.3.2

Characteristics of the Plant Types

To better understand the network typology of plants, the four types of plants have been compared on a set of plant characteristics. These characteristics are defined as follows: • The age of the plant (number of years the plant has been part of the company). • The size of the plant (expressed in number of employees). • The focus of the plant. Product focus: the extent to which the plant focuses on a narrow portion of the company’s product range; Market focus: the extent to which the plant focuses on a narrow portion of the geographical market served by the company. See Kouvelis and Munson [23]. • The supplier/user relationship with other plants in the network: the extent to which a plant supplies components or semifinished goods to or uses components or semifinished goods from another plant in the network. It has been measured as the centrality (outdegree and indegree) of the plant in the physical network of goods. • The level of investment: four types of investment have been identified through factor analysis: — Investments in the production process. — Investments in planning.


— Investments in managerial improvement programs, that is, in statistical process control, supplier partnerships, total quality management, and employee participation programs. — Investments in new product development. • The autonomy of the plant: strategic autonomy and operational autonomy. • The level of capabilities. Two types of capabilities are distinguished: the capabilities to develop new products and managerial capabilities. • The performance of the plant. Performance has been measured relative to the target set for the plant. Two dimensions of performance have been identified through factor analysis: — Performance on time measures, such as throughput time, delivery lead time, and on-time delivery to customers. — Performance on cost and quality measures, such as unit production cost, productivity of direct workers, defect rates, and overall product quality. The conclusions from these comparisons are reported in Table 2.7. Table 2.7 Summary of plant characteristics by cluster. A

B

C D

Plant characteristics Relatively young; market focused; little inflow and outflow of components and semifinished goods; relatively low level of strategic autonomy in plant design; relatively high level of managerial investment. Relatively young; little outflow of components and semifinished goods; relatively low level of managerial investment; relatively low level of capabilities. Relatively old; broad market; high inflow of components and semifinished goods; relatively low level of managerial investment. High inflow and outflow of components and semifinished goods; relatively high level of strategic autonomy in plant design; relatively high level of process investment.

33

34


2.3.3

Summary

The authors draw the following conclusions from the plant typology and the characteristics of the four types of plants. First, the plants providing innovations to the manufacturing network, the “hosting network players” and the “active network players,” are at the same time receivers of innovations for other units in the network. Second, the different roles in the intangible knowledge network coincide with roles in the tangible network of goods. The “isolated” plant is also isolated in the supply chain: there are very little flows of components or semifinished goods from these plants to the other plants in the network, and vice versa. The network players (types C and D), are typically suppliers to the other plants (in the case of Cluster D) or customers of the other plants (in the case of Cluster C) for components or semifinished goods. Third, it takes time to build network relations. The average age of the networked plants (types C and D) is much longer than that of the two more isolated types of plants (types A and B). A fourth conclusion as summarized in Table 2.7 is that the four different network roles reflect very different plant characteristics. The “isolated” plant in Cluster A is very independent and has the capability to manage itself independently. The receivers in Cluster B typically are local players that need support of headquarters or the other plants in the network. The hosting network players (Cluster C) are typically in the network for a very long time, they supply a broad market, they are characterized by a low level of managerial investment, and they are located close to headquarters or to an active network player. The typeD plants play a more dynamic and active role in the manufacturing network. These plants has high level of autonomy and actively building network relationships by sending manufacturing staff to other plants and through extensive communication. Fifth, in terms of performance, there is no significant difference between the clusters. Finally, the analyses suggest that the future perspectives of the plant depend on the plant’s network position. Following Ferdows [12], they define the importance of the strategic role of the plant as the extent

2.4 Global Resource Deployment Analysis

35

to which the plant contributes to the other units in the manufacturing network. They conclude that the importance of the strategic role of the plants in Clusters A and B should be low because these nonintegrated plants make little contribution to the plant network. The C plants play a strategic role of medium importance and the D plants play a strategic role of high importance. Moreover, their data suggest that the plants in Clusters C and D play a stable strategic role in the company. Some of the A and B plants, on the other hand, are expected an increase in strategic role, and these plants will probably be moving from Clusters A or B toward Clusters C or D. Some of the other plants in Clusters A and B are expected to experience a decrease in strategic role. This framework provides the managers a methodology to classify their plants, and identify the gaps or unbalances existing in their current network. Managers may find the existence of isolated plants and receivers gives the manager some structural flexibility in managing his network. On the other hand, managers can foster plants which have active and hosting capabilities.

2.4

Global Resource Deployment Analysis

The fourth framework for global facility networks is proposed in Cohen and Lee [7]. The authors develop a model that analyzes the resource deployment decisions in a global supply chain as described in Figure 2.1. Different from the other three frameworks we have introduced, this one is a broader framework which addresses all three components of the supply chain: sourcing, production, and distribution. The firm’s objective is to maximize global after-tax profit by choosing both the design of the network and the management of material flow within the network. The design problem deals with the location and capacity of all production and distribution sites around the world. The material flow management problem deals with supply, production, and distribution stages, respectively: (1) Sourcing of materials: which vendors to use, volume of flows and transfer of materials across plants; (2) Plant charter : which products to produce, processes to use, distribution facilities to supply, and transfer pricing schemes (we will define and discuss “transfer pricing” in more detail in Section 4.4:

36


a “transfer price” is the price used for intra-firm trade of resources, goods, and services between subsidiaries or divisions of a multinational firm) between plants and distribution centers (DCs); (3)Distribution mission: which products to be direct shipped from vendors to DCs, markets to serve, transshipments across DCs, and transfer pricing schemes. 2.4.1

Strategies and “Policy Options”

The authors consider a three-level product structure (as in Figure 2.2): major components to make up subassemblies, subassemblies to make up finished products, and the finished products themselves. Their approach is to design a model to determine the optimal deployment of resources associated with a particular global policy option. A global policy option is a specific combination of supply chain strategies for each of the three stages (i.e., production, supply, and distribution). The particulars of a global policy option restrict the feasible set of the resource deployment solutions and also affect costs and other parameters. Their model is developed as an option evaluating tool for the global supply chain design. Now, we introduce stage strategies that the authors consider for each stage: First, Plant Charter Strategies include: (a) Regionalization Strategy: each plant will serve customers in a geographical region with a full product line of the company. Manufacturing and marketing are closely linked and customer service is guaranteed. (b) Consolidation Strategy: centralized production takes place at a single plant, which serves a large geographic region. (c) Product Focus Strategy: each plant specializes in the production of a single class of finished products. (d) Process Focus Strategy: each plant specializes in a particular stage of manufacturing. (e) Vertical Integration Strategy: plants expand design and manufacturing capabilities for a wide range of products, including components, subassemblies, and peripherals. Each plant charter strategy can find its correspondence in the three dimensions of facility network structure proposed in Kouvelis and Munson [23]. Strategies (a) and (b) address the “Market focus”


37

measure. They refer to the degree to which each region produces to satisfy the demands for that region. The difference is that “Market focus” measure focuses on the subassembly level, while strategies (a) and (b) focus on the final product level. Strategies (c) and (d) correspond to the dedicated strategy of the “Plant focus” measure in Kouvelis and Munson [23]. Each plant is dedicated to the production of certain kinds of final products, subassemblies or processes. Strategy (e) is similar to a flexible strategy in terms of the “Plant focus” measure in Kouvelis and Munson [23]. Each plant charter strategy has its own strengths and weaknesses. Regionalization requires plants to be flexible and capable of producing a wide range of products. Consolidation and product focus strategies can exploit the potential for economies of scale and scope but result in higher distribution costs. Process focus requires greater investment in corresponding aspects and vertical integration requires development and mastery of additional manufacturing technologies. Second, Supply Strategies include: Centralized Control Strategy; Regionalized Control Strategy; Consolidation Strategy, which deals with fewer vendors to lower purchasing costs due to quantity discounts and enhance the quality; Diversification Strategy, which uses multiple sourcing to hedge risk against the failure of some vendors and sometimes absorb currency exchange rate fluctuations if vendors are located different counties. Third, Distribution Strategies include: Consolidation Strategy utilizing a single major DC to lower costs; Co-location Strategy, which develops some manufacturing capabilities at the DCs; Market Service Strategy, which suggests locating DCs close to market regions. 2.4.2

A Model for Resource Deployment Decisions

The authors formulate the problem into a single-period and deterministic mixed integer, nonlinear program. If multi-period decision is needed, they suggest running their model sequentially over some finite time horizon. We will describe the structure of this very interesting model at a conceptual level, but we will avoid the tedious details of mathematical representation of all involved constraints and

38


variables. We refer the readers to the original paper for this detailed treatment. Decision variables. Their optimization is achieved by selecting two groups of decision variables: binary variables that jointly decide which plant and DC sites are to be used, indicating a firm’s selection on its global policy option and detailed quantity decisions at each stage on the material flow after a particular policy option has been selected. Objective function. The objective function is to maximize the total after-tax profits which are the differences between before-tax profits and the total costs from the country. 1. Total revenues derived from the country include total revenues from sales of finished products in the country, from sales of subassemblies and components between different divisions within the firm outside the country, and from shipment of finished products out of plants in the country to DCs. 2. Total costs from the country which include total fixed costs and variable costs and total transportation costs associated with all stages. Major constraints. There are two classes of constraints: Managerial constraints and logical consistency constraints. Managerial constraints include: Capacity constraints, such as plant production capacities and supplier capacities; offset requirements (e.g., in order to gain entry into the market of that country and to receive promised government subsides, a minimum level of manufacturing, originating from that particular country, must be carried out); minimum taxes to be paid in the respective countries etc. Logical consistency constraints among the variables are imposed to avoid pathological solutions (such constraints as demand limits, feasible flow constraints, and non-negativity of all variables). Major data. To solve the model, there is need for data on cost parameters, selling price, demand, production (e.g., Bill of materials, resource


39

capacities at plants, and resource capacity utilization rates for production), and data on currency exchange rates, tax rates, and offset requirements. 2.4.3

Summary

This model analyzes deployment of resources in a global manufacturing and distribution network, using a deterministic mixed-integer nonlinear program. The authors explicitly consider the key factors that affect the international manufacturing strategy of a global firm, such as duties and tariffs, fluctuating currency exchange rates, significant differences in corporate tax rates in each country, difficulty in global sourcing, product design, market penetration, and centralizing control of operation in a multinational environments. This model can also be used as a global supply chain option-evaluation tool, and for setting global manufacturing and supply strategy. Once a global supply chain policy option is given, the values of binary parameters are fixed. The resulting problem is linear programming (LP). Then a detailed resource deployment strategy is solved. The authors reported a case study of applying their model for a personal computer manufacturer. The manufacturer has 16 major classes of finished products, 16 families of subassemblies, and five major component families. The finished products are marketed in all five continents. The supplier base spans more than 15 countries and is located in four continents. The problem is solved by the GAMSMINOS optimization software. They used the model to evaluate the base case (status quo) and the three global policy options, centralized production strategy, product specialization strategy, and market regionalization strategy.

3 Modeling and Decision Support for Global Supply Chain Design

3.1

Global Facility Network Design Model

In this section, we present the modeling details and the decision support tools for designing global supply chains. In designing international facility networks, Kouvelis and Munson [23] develop a structural equations model (using the global sensitivity approach of Wagner [42]) based on a mixed-integer program that captures the facilities network design complexities and trade-offs. The firm’s objective is to develop a network of plants and DCs that maximizes its discounted after-tax profit over the planning horizon. For this particular model, it will be easier for the readers to follow through its detailed mathematical programming formulation, and we will proceed to present it this way. The detailed model formulation is as follows: 3.1.1

Model Assumptions

• There are two facility levels: plants (producing subassemblies) and DCs (final assembly). • The plants and DCs remain open throughout the finite planning horizon. • The firm is a price taker in each market. All prices are quoted in local currency and then translated into common currency (say $) by using the real exchange rate. 41

42

Modeling and Decision Support for Global Supply Chain Design

• The market demands, selling prices, and transfer prices are independent of the structure of the facility network. • At most one Distribution Center (DC) (assumed to have adequate capacity to cover any one country’s demand) is allowed in each country. The rationale behind this assumption is that as shipment cost of a subassembly or final product within a country is assumed constant in our model, the opening of a second DC will result in additional fixed costs with no transportation cost savings. (Geographical large countries can easily be split into subcountries, as needed, to coincide with this assumption.) • Any type of subassembly can be produced in at most one plant in any given country. • Costs, prices, tax rates, interest rates, plant capacities, and discount rates remain constant over time. Demand and depreciation rates, however, may vary over time. • Annual fixed costs and up-front investment costs are an increasing function of capacity and are modeled as a base cost plus a linear function of capacity. • Capacities and costs are modeled for both plants and production lines within the plants. Production line variable investment and operating costs are linear functions of the number of subassemblies produced on those lines. Plant variable investment and operating costs are linear functions of the size of production lines (expressed as space requirements in square feet) installed in the plants. 3.1.2

Notation

Indices Table 3.1 lists the Indices of the Notation. Table 3.1 Notation: Indices. i : subassembly index, i = 1, . . . , I, n : country of operation index, n = 1, . . . , N , k : country of locating a distribution center (DC) index, k = 1, . . . , N , m : country of locating a plant index, m = 1, . . . , N , q : subassembly plant index within a given country, q = 1, . . . , I, j : country (market) index, j = 1, . . . , J, t : time period, t = 1, . . . , T , z : number of subassemblies produced at the same plant index, z = 1, . . . , I.

3.1 Global Facility Network Design Model

Parameters Table 3.2 lists the Parameters of the Notation. Table 3.2 Notations: Parameters. Vim : unit variable production cost of subassembly i produced in country m, vk : unit variable assembly cost at a DC in country k, Fm : annual fixed cost of operating a subassembly plant in country m (base cost), fm : annual fixed cost per square foot of operating a plant in country m (linear component), Bzm : annual fixed cost of producing the zth subassembly in the same plant in country m, z = 2, . . . , I (Bzm is increasing in z), Uk : annual fixed cost of operating a DC in country k (base cost), uk : annual fixed cost of operating a DC in country k (linear component), Kim : maximum capacity (in units) of a production line for subassembly i in country m, Cm : maximum capacity (in sq. feet) of a subassembly plant built in country m, ck : maximum capacity (in units) of a DC built in country k, Gim : space requirement (in square feet) per unit of a production line for subassembly i in m, Eim : investment cost for equipment to build a production line for subassembly i in m (base investment), eim : investment cost per unit for equipment to build a production line for subassembly i in m (linear component), Am : investment cost for land and building to build a subassembly plant in country m (base investment), am : investment cost per square foot for land and building to build a plant in country m (linear component), Hk : investment cost to build a DC in country k (base investment), hk : investment cost per unit to build a DC in country k (linear component), Skj : cost to ship one unit of the final product from a DC in country k to market j (shipment costs include any assessed trade tariffs and other duties), λi Smk : cost to ship one unit of subassembly i from country m to country k (i.e., subassembly transportation cost is expressed as a fraction of the transportation cost of the final product, with λi the fraction for subassembly i), Djt : demand of the final product in country j in period t, rn : per-period interest rate on the loan in country n, R(rn , T ) : loan payment factor given interest rate r and planning horizon T , ρt (rn , T ) : interest calculation factor for period t given interest rate r and planning horizon T , τn : marginal corporate income tax rate in country n, Pj : sales price of the final product (translated into $ with real exchange rate) in country j, pimk : transfer price of subassembly i made in country m shipped to DC in country k, dnt : applicable depreciation rate in country n in period t (% per period), βn : discount rate of after tax cash flows in country n, ln : maximum loan that country n can give to the firm.

43

44


Decision Variables Table 3.3 lists the decision variables of the notation. Table 3.3 Notation: Decision variables. Ximqkt : units of subassembly i made in country m at plant q and assembled in country k during t, xkjt : units assembled at a DC in country k and sold in market j during t, Ln : the loan that the company will take from the country n government for investment in n, Zimq : = 1 if a production line for subassembly i is built in country m at plant q, and 0 otherwise, Yzmq : = 1 if a z t h subassembly is produced in country m at plant q, and 0 otherwise, yk : = 1 if a DC is operated in country k, and 0 otherwise, Wimq : size (in units) of production line i built in country m at plant q, Qmq : size (in square feet) of plant q in country m, wk : size (in units) of a DC operated in country k.

3.1.3

The Objective Function

Revenue from units assembled and subassemblies produced in country n in period t: αnt =

J X

Pj xnjt +

I X I X N X

pink Xinqkt

i=1 q=1 k=1

j=1

Variable production costs and cost of goods sold in country n in period t: δnt =

J X

vn xnjt +

I X N X I X

pimn Ximqnt +

i=1 m=1 q=1

j=1

I X I X K X

Vin Xinqkt .

i=1 q=1 k=1

Annual fixed costs of a DC and subassembly plants in country n: ! I I X X γn = Un yn + un wn + Fn Y1nq + fn Qnq + Bzn Yznq q=1

z=2

Transportation costs from facilities (plants and DCs) located in country n in period t: ηnt =

J X j=1

Snj xnjt +

I X I X N X

λi Snk Xinqkt .

i=1 q=1 k=1

Loan payment in country n in period t: ϕnt = Ln R(rn , T ).

3.1 Global Facility Network Design Model

45

Loan interest payment in country n in period t: ϕ0nt = Ln ρt (rn , T ). Investment cost in country n: ξn = Hn yn + hn wn +

I X

(An Y1nq + an Qnq )

q=1

+

I X I X

(Ein Zinq + ein Winq ).

i=1 q=1

Depreciation expense in country n in period t: ψnt = ξn dnt Before-tax income in country n in period t: πnt = αnt − (δnt + γn + ηnt + ϕ0nt + ψnt ). Corporate income tax paid in country n in period t: ωnt = πnt τn Cashexpenditures in fixed assets in year 0 that are not financed by external sources: µ=

N X

(ξn − Ln ).

n=1

So the objective function which maximizes the net present value is: "N T # XX (πnt + ϕ0nt + ψnt − ϕnt − ωnt )/(1 + βn )t − µ. OBF = max n=1 t=1

3.1.4

The Set of Constraints

The Constraints are: P (1) Demand Constraints: N k=1 xkjt ≤ Djt , ∀j, t. (2) Subassembly Line Capacity: N X

Ximqkt ≤ Wimq ,

∀i, m, q, t

k=1

Wimq ≤ Kim Zimq , I X q=1

Zimq ≤ 1,

∀i, m

∀i, m, q

46

Modeling and Decision Support for Global Supply Chain Design I X

Zim(q+1) ≤

i=1

I X

∀m, q < I (for solution efficiency)

Zimq ,

i=1

Zimq = 0

∀i, m, q > i (for solution efficiency)

(3) Plant Capacity Constraints: I X

Gim Wimq ≤ Qmq ,

∀m, q

i=1

Qmq ≤ Cm Y1mq Y1m(q+1) ≤ Y1mq ,

∀m, q ∀m, q < I (for solution efficiency)

(4) DC Capacity Constraints: J X

xkjt ≤ ωk ,

∀k, t

j=1

ωk ≤ ck yk

∀n

PN PI (5) Conservation of Subassembly Flows: q=1 Ximqkt = m=1 PJ j=1 xkjt , ∀ i, k, t. (6) Loan Ceilings: Ln ≤ ln , ∀n, and Ln ≤ ξn , ∀n, ωk ≤ ck yk , ∀n. (7) Nonnegative Profit in Each Country in Each Period (assumption of convenience to avoid unnecessarily complicated tax calculations): πnt ≥ 0 ∀n, t. (8) Count the Number of Different Subassemblies Produced at Each Plant: I X i=1

Zimq =

I X

Yzmq

∀m, q

i=1

Y(z+1)mq ≤ Yzmq

∀z 6= I, m, q

(9) Specification of Decision Variables: Ximqkt , xkjt , Ln , Wimq , Qmq , wk ≥ 0 for all indices Zimq , Yzmq , yk = binary for all indices.

3.2 Multi-echelon Supply Chain Networks under Demand Uncertainty

47

In their numerical study, the authors solved a problem with two subassemblies, three marketing regions, six potential countries of operations, 30 markets, and five time periods, using standard mathematical programming software (specifically GAMS/OLS2) on a Cyrex 685-P90 processor. According to their computational experience, a problem up to the combination of nine countries of operation, 30 markets, four subassemblies, and five time periods can be solved on a standard PC, which indicates implementation potential for frequently encountered supply chain design problems in industrial settings.

3.2

Multi-echelon Supply Chain Networks under Demand Uncertainty

Tsiakis et al. [33] present a mixed-integer linear programming (MILP) model for multi-product, multi-echelon supply chain networks, aiming to minimize the expected cost by determining production, facility location and capacities, product transportation and distribution to the customer zones. This model extends the work of Cohen and Lee [7] by taking into account of the demand uncertainty.

3.2.1

Model Assumptions

This work considers the design of multi-product, multi-echelon production and distribution network. The network comprises a number of manufacturing sites at given locations, a number of potential warehouses and distribution centers at locations to be selected from a set of candidate locations, and a number of customer zones at fixed locations. The goal of the firm is to minimize the total expected cost of the network, by determining middle-echelon facility (warehouses and distribution centers) locations and capacities, the transportation links, and the material flows and production. • The production capacity of each manufacturing site is modeled in terms of a set of linear constraints relating the mean production rates of the various products to the availability of one or more production resources.

48


• Warehouses and distribution centers have upper and lower bounds on their material handing capacity. Warehouses can be supplied from more than one manufacturing site and can supply more than one distribution center. Each distribution center can be supplied by more than one warehouse. This model accommodates the “single sourcing” constraints, which require that a distribution center be supplied by a single warehouse (to be determined by the optimization). • This model considers stationary demand, but possibly with scenario-based demand uncertainty. A customer may be served by more than one distribution center. Similarly, this model accommodates the “single sourcing” constraints, which require that a customer zone be supplied by a single distribution center (to be determined by the optimization). • The total costs include the infrastructure costs associated with establishment of warehouses and distribution centers, and operating costs associated with production, material handling, and transportation. Transportation costs are piecewise linear concave in the actual flow of the product. 3.2.2

Model Setup

This work considers the deterministic demand case, and formulates it as a mixed-integer linear programming. Use m, k, and l to denote the warehouse position, distribution center position, and customer zone, respectively. 3.2.2.1

Variables

There are two kinds of variables, binary variables and continuous variables. Binary variables are used to indicate whether the warehouse or distribution center is selected, (Ym and Yk ), or whether a transportation link is established, (Xmk and Xkl ). Continuous variables are used to describe the network: decision variables include (i) Pij is the rate of production of product i by plant j. (ii) Qijm is the rate of flow of product i from plant j to warehouse m.

3.2 Multi-echelon Supply Chain Networks under Demand Uncertainty

49

(iii) Qimk is the rate of flow of product i from warehouse m to distribution center k. (iv) Qikl is the rate of flow of product i from distribution center k to customer zone l. Two parameters: (i) Wm is the capacity of warehouse m. (ii) Dk is the capacity of distribution center k. 3.2.2.2

Constraints

• Network Structure Constraints, nonnegativity constraints on continuous variables, logical constraints on transportation flows, and material balances (see Cohen and Lee [7] in Section 2.4). These constraints are imposed to rule out pathological solutions. • Constraints on production rate. Production rate has to meet its lower and upper specifications. There is another constraint on production rate to ensure the availability of resources (such as equipment, utilities, manpower, that could be shared by several production lines) at the plant. It is expressed as follows: X ρije Pij ≤ Rje , ∀ j, e i

The coefficient ρije expresses the amount of resources e used by plant j to produce a unit amount of product i, and Rje represents the total rate of availability of resources e at plant j. • Constraints on capacity of warehouses and distribution centers. Capacities of the warehouses and the distribution centers have to meet the lower and upper bound of their material handling capacity. It is further assumed that the capacities of the warehouses and distribution centers are related linearly to the flows of materials that they handle, which are expressed as X Wm ≥ αim Qimk , ∀m i,k

Dk ≥

X i,l

βik Qikl ,

∀k

50


3.2.2.3

Objective Function

The total expected cost include the fixed infrastructure (one-time) costs and operating costs (daily cost), which include production cost, material handling costs at warehouses and distribution centers, and transP P D WY + portation cost. m Cm m k Ck Yk represent the total cost of the establishment of a warehouse and a distribution center. The production cost incurred at a plant j is assumed to be proportional to the producP P P . Material handling costs at warehouses and distrition rate, i,j Cij ij bution center are modeled as linear functions of the throughput of each P P P P WH( DH product being handled, i,m Cim j Qijm ) + i,k Cik ( m Qimk ). Transportation cost, including the cost associated with the transportation between plants and warehouses, between warehouses and distribution centers, and between distribution centers and customer zones, is models as a piecewise linear function of the flow of the material, respectively. The total transportation cost is given in the expression P P P f,j,m Cf jm + f,m,k Cf mk + f,k,l Cf kl . The objective function is given by the following expression:   X X X X X P WH  W Cij Pij + Cim Qijm  min Cm Ym + CkD Yk + m

i,j

k

i,m

j

! +

X i,k

3.2.2.4

DH Cik

X m

Qimk

+

X f,j,m

Cf jm +

X

Cf mk +

f,m,k

X

Cf kl .

f,k,l

Scenario-based Demand Uncertainty

In this work, the authors adopt a scenario planning approach for handling the uncertainty in product demands. It is assumed that there is a systematic to generate a number of demand scenarios, s = 1, . . . , N S, PN S with each scenario occurring with probability ψs , and s=1 ψs = 1. Assume that the structure of the distribution network is independent of the scenarios, then the binary variables are independent of the scenarios. Decision variables relating to production and transportation flows, and any constraint relating to these variables are scenario-dependent. If we relax the assumption, the binary variables that describe the transportation links, Xmk and Xkl are also scenario-dependent.

3.3 Robust Designs for Global Networks and Its Related Applications

3.2.3

51

Summary

This authors present a supply chain network design model that captures the complexity of the multi-echelons and interactions among the echelons, as well as taking into account the demand uncertainty. The proposed model is formulated as a large-scale MIP and solved using CPLEX. This model can be used as a quantitative tool to support strategic planning decisions in supply chain network design.

3.3 3.3.1

Robust Designs for Global Networks and Its Related Applications A Robustness Approach to International Sourcing

A global sourcing network can provide operational flexibility and the resulting hedging power against fluctuations of macroeconomic parameters, e.g., real exchange rate, in the international environment. Gutierrez and Kouvelis [14] present a robust approach in designing a global sourcing network. The designed sourcing network is robust in the sense that it hedges the firm’s performance against the worst contingencies in terms of realizable real exchange rate changes over a planning horizon. The global managers have strong incentives to adopt the robust approach to international sourcing. Global manufacturing managers usually face an ex post evaluation of the decisions over a rather short-term period and with the use of cost data that reflects the actually realized macroeconomic data. A deterministic approach may yield very poor performance if the realized exchange rate and inflation values are substantially different from the assumed ones. Similarly, a stochastic approach is to optimize the long-run expected performance assuming certain probabilities for each macroeconomic scenario to happen. However, when coming to the design of a global sourcing network, it is usually evaluated on a one-time scenario, or only a few realizations of macroeconomic scenarios. A stochastic approach may yield a suboptimal solution for the specific realizations. The robustness approach produces a reasonable relevant cost

52


under all realizations of exchange rate scenarios for the planning horizon. Definition of robustness. The main uncertainty under consideration is in the macroeconomic variables (exchange rate, inflation) of various countries where factories and/or suppliers are located. The authors use a scenario-based approach to represent the uncertainty. A specific scenario represents a potential realization of values for all macroeconomic variables of interest. Let S = {1, . . . , s, . . . , ns } be the set of all potential scenarios over the planning horizon. I represents the set of indices of potential suppliers, and for each i ∈ I, let yi be a binary variable that takes the value of one whenever supplier i is developed as part of the firm’s supplier network (and it can supply more than one manufacturing sites). yi = 0 if supplier i is not developed. A vector Y = (yi , i ∈ I) indicates the suppliers that are available in the sourcing network and Y is also referred as a “sourcing network.” Ys∗ denotes the optimal supplier selection under scenario s. Let Zs (Y ) denote the minimum cost of supplying the manufacturing network under scenario s given that we have available the suppliers in Y . A sourcing network Y is called “robust” if for every scenario s ∈ S, it has,

where

Rs (Y ) ≤ p, Zs (Y ) − Zs (Ys∗ ) Rs (Y ) = Zs (Ys∗ )

(3.1) (3.2)

and p is a prespecified number that reflects desired percentage deviation in the worst case from the optimal solution. Then a sourcing network Y is considered robust if the cost of supplying all factories is within p of the cost induced by the best configuration of each scenario for all scenarios in S. This definition of robustness is first brought up by Gutierrez and Kouvelis [14] and later referred as “p-robustness.” The standard stochastic approach whose objective is to minimize the expected cost can be considered as a special case of p-robustness with p = 100%. By reducing the value of p, we will end up with smaller number of robust solutions. To help readers better understand the “p-robustness,” we use the following example: assume that a US manufacturer has two potential


53

Table 3.4 An example for “p-robustness”: Units $1000. Scenarios (s) 1 2 3

Zs (Y1 ) 100 110.25 98.8

Zs (Y2 ) 108 105 99.75

Zs (Y3 ) 103 102.9 95

Ys∗ Y1 Y3 Y3

Zs (Ys∗ ) 100 102.9 95

suppliers I = {1, 2}. Supplier 1 is in the United States, and supplier 2 is in Mexico. The only uncertainty in this problem is the exchange rate of US dollar versus Mexican Peso. We assume three scenarios (S = {1, 2, 3}): exchange rate will stay at the current level (s = 1), 10.58, will increase by 30% (s = 2), 13.75, or will decrease by 30% (s = 3), 7.41. Under each scenario s, we have the following three possible sourcing networks, Y = (yi , i ∈ I = {1, 2}), where Y1 = (1, 1), Y2 = (0, 1), Y3 = (1, 0). Suppose the cost structure indicates the following optimal supplier selections under each scenario s in Table 3.4. For each scenario s and a given sourcing network Y, the minimum cost of supplying the manufacturing network, Zs (Y ) (see Table 3.4), is calculated by solving a cost minimization problem, and Zs (Ys∗ ) is the minimum among all the sourcing networks given the exchange rate scenario s. Then we use (3.2) to obtain Rs (Y ) (see Table 3.5) and check “p-robustness.” If a sourcing network Y satisfies Condition (3.1) for all scenarios s, s = 1, 2, 3, Y is called a “p-robust” sourcing network. For example, let p = 0.05. Sourcing network Y3 is p-robust, given Rs (Y3 ) ≤ 0.05 for each exchange rate scenario. For sourcing network Y1 , Rs (Y1 ) = 0.07 > 0.05 for scenario 2. For sourcing network Y2 , Rs (Y2 ) = 0.08 > 0.05 for scenario 1. Therefore neither Y1 nor Y2 is p-robust. In Gutierrez and Kouvelis [14], their modeling objective is to find the N best robust solutions to the sourcing network design problem. An ordering scheme of robust solutions is needed. A solution Y1 is more robust than Y2 , written as Y1 ≥R Y2 if and only if R(Y1 ) ≥ R(Y2 ). Table 3.5 An example for “p-robustness”: Rs (Y ). Scenarios (s) 1 2 3

Rs (Y1 ) 0 0.07 0.04

Rs (Y2 ) 0.08 0.02 0.05

Rs (Y3 ) 0.03 0 0

54


The relationship ≥R has the following properties: Yi ≥R Yi

for all i

(P1)

Y1 ≥R Y2

and Y2 ≥R Y3 ⇒ Y1 ≥R Y3

(P2)

Y1 ≥R Y2

and Y2 ≥R Y1 ⇒ Y1 =R Y2

(P3)

This relationship cannot rank every solution, because R(Y ) is a vector and that the property (P4 ) is not always satisfied. For any Y1 and Y2

either Y1 ≥R Y2 or Y2 ≥R Y1

(P4)

An alternative measure of robustness is given by ˆ ) = maxRs (Y ). R(Y s∈S

ˆ than Y2 , written as Then, a solution Y1 is more robust under R ˆ 1 ) ≥ R(Y ˆ 2 ). The scaler R ˆ satisfies the equivY1 ≥Rˆ Y2 if and only if R(Y alent properties (P1)–(P4). We will now proceed to formulate variants of the robust sourcing problem. But in doing so, we will need to first formulate the single scenario (deterministic) international sourcing problem. The deterministic international sourcing formulation. First, the authors model the deterministic international sourcing problem for a given macroeconomic scenario. They consider a firm that is selecting suppliers from its established international factory network to meet the demands over a prespecified planning horizon. Notation is summarized as in Table 3.6. Table 3.6 Notation. I = {1, . . . , i, . . . , nI } = the set of indices for potential international suppliers, P = {1, . . . , j, . . . , nP } = the set of indices of all factories in our manufacturing network, Pi , i ∈ I = the set of indices of factories that can source from supplier i, Dj , j ∈ P = the total supply requirement of factory j over the planning horizon, Ki = a minimum volume purchase from supplier i, vis = the variable cost of acquiring a unit of production from supplier i, tsij = any unit costs specific to the supplier-factory pair i ∈ I, j ∈ P , fis = fixed cost of developing supplier i.


55

The sourcing firm is assumed to be a price taker and the total supply requirements of the factories are known. Different macroeconomic scenarios affect the variable purchasing cost vis , unit shipping cost tsij , and the fixed cost of including a supplier fis . The contractual agreement with supplier i involves a minimum volume purchase of Ki units over the planning period. To model the minimum volume requirement, they split every factory h ∈ P with a minimum volume commitment Ki into “two equivalent” factories, a “dummy factory” h0 and a “reduced 00 factory” h , with Dh0 = Ki and Dh00 = Dh − Ki , and tih00 = tih . Total fixed cost is computed as Fis = fis + Ki (vis + tsih ) and total variable cost 00 of supplying a reduced factory h from supplier k are given by ckh00 = Dh00 (vks + tskh )

for any k ∈ I.

For a dummy factory h0 , the total variable costs will be ( 0 for k = i ckh0 = Dh0 (vks + tskh0 ) for k 6= i. For a given macroeconomic scenario s ∈ S, the deterministic international sourcing problem can be modeled as an uncapacitated plant location problem: XX X Zs (Ys∗ ) = min csij xij + Fis yi (DISP) i∈I j∈Pi

subject to

X

i∈I

xij ≥ I

for all j ∈ P

(3.3)

xij ≤ yi

for all i ∈ I and for all j ∈ P

(3.4)

0 ≤ xij ≤ 1

for all i ∈ I and for all j ∈ P

(3.5)

for all i ∈ I

(3.6)

i∈I

yi ∈ {0, 1}

If the sourcing network Y is given, Zs (Y ) can be formulated as follows: X X Zs (Y ) = min csij + Fis yi . (3.7) j∈P

i:j∈Pi and yi =1

i∈I

Based on the structure of the problem, the Efroymson and Ray [11] algorithm, a branch and bound procedure with a lower bounding procedure, can be used to solve the optimal sourcing network.

56


A Min–Max formulation. Managers identify a set of likely real exchange rate scenarios, without attaching probabilities, then find a supplier network that has the best worst-case performance. The robust sourcing network over a set S of macroeconomic scenarios is formulated as follows: Zs (Y ) − Zs (Ys∗ ) min max , (RISP) s∈S Y Zs (Ys∗ ) where Zs (Y ) is as defined in (3.7), and Zs (Ys∗ ) is solved through (DISP). Use YR to denote the optimal solution to (RISP). We would like to note that variants of the robust sourcing problem could optimize the min–max deviation, i.e., minY maxs∈S {Zs (Y ) − Zs (Ys∗ )}, or the absolute scenario performance, i.e., minY maxs∈S Zs (Y ). For more details on variants of robust discrete optimization problems see Kouvelis and Yu [26], with Section 5 in this research review devoted to robust international sourcing problems. Let us now illustrate this Min–Max criterion (for percentage deviation) using our previous example. Table 3.7 provides the percentage deviation in the worst case from the optimal solution for each scenario s and then the min–max objective is to find the minimum among the maximum percentage deviations across all the scenarios. The min–max value in our examples is 0.03, and sourcing network Y3 is optimal under this Min–Max formulation. An equivalent formulation is the following: min z

(ERISP)

subject to Zs (Ys∗ )(z + 1) ≥

XX

X

csij xij +

i∈I j∈P

Fis yi

for s ∈ S;

j∈P

(3.8) (3.3), (3.4), (3.5), (3.6), and z ≥ 0.

(3.9)

Table 3.7 An example for “a Min–Max objective.” Scenarios (s) 1 2 3

Rs (Y1 ) 0 0.07 0.04

Rs (Y2 ) 0.08 0.02 0.05

Rs (Y3 ) 0.03 0 0

Max Rs (Y )

0.07

0.08

0.03


57

(ERISP) problem is NP-complete and has the structure of an uncapacited plant location problem with additional constraints (3.8). Consider the stochastic international sourcing problem that minimizes the total expected cost. Assume with probability ws , a scenario P s occurs. Then Z = Z(Y ∗ ) = minY Z(Y ) = mins∈S ws Zs (Y ). Total cost of a robust sourcing network YR is guaranteed to deviate at most p from the optimal cost of any realizable scenario, Z(Y (R)) = (1 + p)Z, P where Z = s∈S ws (minZs (Y )) ≤ Z. Therefore, a “p-robust” sourcing Y

network not only guarantees to deviate at most p from the optimal cost for all macroeconomic scenarios, but also deviates at most p from the optimal expected cost solution. Robust international sourcing algorithm (RISA). Gutierrez and Kouvelis [14] propose an algorithmic procedure to find N best robust solutions to the international sourcing problem. The value of p and N are specified by the decision maker. They adopt the Efroymson and Ray algorithm for the uncapacitated plant location problem to branch from a node and for evaluating its lower bound. They need the |S| single scenario (DISP) branch-and-bound trees. A node ks in a tree s corresponds to a node kt in another tree t, if these two nodes have identical positions in their respective branch-and-bound trees. Whenever a node in a tree is branched to two child-nodes, the same corresponding node is branched in all scenario trees. The details of the algorithm is outside the scope of this review (and can be found in the original reference). Their experiences show that the computational efficiency and effectiveness is not determined by the number of factories in the network, but by the number of suppliers. The robust sourcing networks not only demonstrate a reasonable cost performance, p deviation from the optimal cost, but also have a substantially better performance in terms of expected cost over longer horizons. 3.3.2

Applications of Robust Design

Lowe et al. [27] presents an application of robust design for global sourcing/production network using a popular Harvard Business School case: Applichem (A) (reference number HBS 9-685-051, or also found as Case 2–3 in the textbook, Flaherty [13]). They consider a global firm

58


who faces significant financial risks due to exchange rate fluctuations and relative rates of inflations in various countries where its production facilities are located. The key consideration in the case is the decision of dealing with excess capacity which involves choices of sourcing locations and shutting down some plants. Applichem is a manufacturer of Release-ease, a chemical product which is used in the plastic molding industry. For convenience, we consider this is the only product of Applichem when making operations decisions. It had a 20% extra capacity in the manufacturing network and the demand of this kind of product was expected to remain flat. The company wants to consider plant shutdown possibilities beginning the following year assuming the demand for Release-ease remains constant at the projected quantities for future years of interest. Applichem has a world-wide market and has production facilities in several countries including Mexico, Canada, Venezuela, Germany, Japan, and the United States. The goal of their study is to find plant configurations (which possibly involves shutting down some of the current plants) to meet demand at minimum total cost. To still be able to meet the world-wide demand, they listed as in Table 3.8 nine different configurations where operations at some plants are eliminated. In practice, there are lots of other feasible configurations, however, they restrict themselves to these nine configurations and number them from C1, C2, . . . ,C9. To model the financial uncertainty, they derived 22 exchange rates scenarios for their year of consideration (1994 was the year in consideration in the case) as in Table 3.9 based on the information of nominal Table 3.8 Possible plant configurations. ID C1 C2 C3 C4 C5 C6 C7 C8 C9

Total capacity 100.7 97 96.2 95.7 92.5 92 91.2 87.5 82.2

Plants closed None Canada Venezuela Sunchem Canada and Venezuela Canada and Sunchem Venezuela and Sunchem Canada, Venezuela, and Sunchem Gary


59

Table 3.9 Historical exchange rate scenarios for the year in consideration. Historical scenarios 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

Mexico 3.04 3.10 3.12 2.87 3.10 3.13 4.31 2.69 2.88 2.97 2.95 3.12 7.52 2.26 2.49 3.92 3.96 3.24 1.60 3.25 2.91 2.70

Canada 1.28 1.34 1.27 1.16 1.37 1.36 1.33 1.42 1.41 1.29 1.39 1.32 1.33 1.31 1.38 1.37 1.25 1.25 1.21 1.31 1.37 1.34

Venezuela 107.94 103.37 105.64 104.51 110.89 103.64 105.04 102.39 105.58 109.21 102.20 102.76 99.82 100.52 160.26 89.72 168.28 74.46 91.80 166.79 100.72 106.17

Frankfurt 1.69 1.54 1.71 1.46 1.66 2.00 1.60 1.60 1.59 1.76 2.11 2.04 1.77 1.97 1.98 1.33 1.35 1.48 1.99 1.67 1.55 1.72

Sunchem 111.92 102.82 110.14 95.57 111.77 122.77 108.75 96.22 99.83 144.98 93.40 132.27 120.63 114.23 123.83 90.77 94.17 92.54 119.35 130.52 106.53 104.61

exchange rates and price indices provided by the International Monetary Fund. Given each scenario and each candidate plant configuration, the minimum total cost is determined by solving a transportation problem. Table 3.10 summarizes the minimum cost for each configuration and exchange rate scenario combination for the year under consideration. Finally, to screen sourcing locations, they propose and discuss the advantages in using a number of criteria: Pareto optimality, near-Pareto optimality, maximum regret, mean–variance efficiency, stochastic dominance, and pairwise stochastic comparisons. Other criteria, such as downside risk and value-at-risk can also be used. Their approach is an extension of Gutierrez and Kouvelis [14]’s robust optimization, utilizing the maximum percentage regret criteria to model the global sourcing problem. Different from Gutierrez and Kouvelis [14], they use min–max deviation criterion (refer to as minimizing the maximum dollar regret) instead of maximum percentage regret to factor in non-quantifiable factors in evaluating alternative configurations in dollars. We will use

60


Table 3.10 Minimum cost for each historical scenario/configuration for the year under consideration. Historical scenario 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

Configurations C1 111.98 118.50 111.35 124.30 112.66 100.73 112.20 117.87 117.17 106.55 101.76 99.10 99.58 105.14 101.64 126.90 124.49 123.21 108.27 109.02 118.28 112.27

C2 117.82 124.74 116.96 130.67 118.62 106.69 116.58 125.64 124.18 112.71 108.78 105.01 100.53 115.06 110.38 132.60 129.58 129.39 123.96 114.26 124.9 119.71

C3 124.25 130.75 123.25 137.84 124.69 112.28 122.06 131.64 130.16 119.10 114.30 110.68 104.85 121.64 117.67 137.61 136.85 134.53 131.86 121.48 130.85 126.11

C4 114.01 119.27 112.86 125.26 114.28 103.61 110.96 119.58 118.39 111.85 102.21 102.9 98.47 112.75 108.32 125.43 123.07 122.6 124.71 111.84 120.05 115.27

C5 131.68 138.44 130.36 145.65 132.37 119.64 126.45 141.33 138.92 126.83 122.40 117.97 105.79 133.16 127.95 143.30 141.93 141.38 149.43 128.43 139.38 135.21

C6 121.44 126.95 119.97 133.07 121.96 110.97 115.35 129.27 127.16 119.58 110.32 110.20 99.42 124.27 118.61 131.12 128.15 129.44 142.28 118.70 128.58 124.37

C7 127.94 133.02 126.34 140.30 128.09 116.66 120.83 135.34 133.20 126.05 115.95 115.96 103.74 131.01 126.02 136.13 135.42 134.64 150.39 125.97 134.59 130.85

C8 135.41 140.73 133.47 148.14 135.81 124.02 125.24 145.06 142.00 133.79 124.06 123.26 104.68 142.53 136.32 141.83 140.51 141.51 167.98 132.86 143.15 139.99

C9 150.90 156.44 148.85 166.83 150.45 138.15 135.85 164.14 159.20 146.78 142.87 136.83 107.87 163.93 153.24 155.47 152.44 159.62 198.63 144.20 159.42 158.29

the maximum regret criterion in the following example to illustrate how to evaluate the candidate sourcing networks. To use the maximum dollar regret, there are three steps to follow: first, for each given scenario, calculate the cost difference from Pareto optimality (the lowest cost under a certain exchange rate scenario among all plant configurations) for each configuration; second, find the maximum dollar regret for a certain configuration across all exchange rate scenarios. Finally, rank the configurations from smallest to largest maximum regret, and keep the good ones (see Table 3.11). The value of excess capacity. In analyzing the nine candidate configurations, in terms of total capacity, configurations C2, C3, and C4 are quite similar. C5, C6, and C7 are similar. Hence, we only have five distinct configurations: C1, C20 , C50 , C8, and C9 ranked in order of decreasing capacity. Using the maximum dollar regret criteria, the configurations are ranked C1, C20 , C50 , C8, and C9. The authors also

3.4 Global Supply Chain Design Application

61

Table 3.11 Dollar regret matrix. Historical scenario 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Max. regret Ranking

Configurations C1 0.00 0.00 0.00 0.00 0.00 0.00 1.23 0.00 0.00 0.00 0.00 0.00 1.11 0.00 0.00 1.48 1.42 0.61 0.00 0.00 0.00 0.00

C2 5.84 6.25 5.60 6.37 5.96 5.96 5.62 7.77 7.01 6.17 7.03 5.91 2.05 9.91 8.74 7.17 6.51 6.79 15.69 5.25 6.62 7.44

C3 12.27 12.26 11.90 13.53 12.03 11.55 11.09 13.77 12.99 12.55 12.54 11.58 6.37 16.50 16.03 12.18 13.78 11.93 23.60 12.46 12.57 13.84

C4 2.03 0.77 1.50 0.96 1.62 2.87 0.00 1.71 1.22 5.30 0.46 3.80 0.00 7.61 6.68 0.00 0.00 0.00 16.44 2.83 1.77 3.00

C5 19.70 19.94 19.01 21.34 19.71 18.91 15.49 23.46 21.75 20.28 20.64 18.87 7.32 28.02 26.31 17.88 18.86 18.77 41.16 19.41 21.10 22.94

C6 9.46 8.46 8.62 8.77 9.30 10.24 4.39 11.40 9.99 13.03 8.56 11.10 0.94 19.13 16.97 5.70 5.09 6.84 34.01 9.68 10.30 12.10

C7 15.96 14.52 14.98 16.00 15.43 15.93 9.86 17.47 16.03 19.50 14.19 16.86 5.26 25.87 24.38 10.71 12.36 12.04 42.12 16.95 16.31 18.58

C8 23.43 22.24 22.12 23.84 23.15 23.29 14.27 27.19 24.83 27.24 22.30 24.16 6.21 37.39 34.68 16.40 17.44 18.91 59.71 23.84 24.87 27.72

C9 38.92 37.95 37.50 42.53 37.79 37.42 24.89 46.27 42.03 40.23 41.11 37.73 9.40 58.79 51.60 30.04 29.37 37.02 90.36 35.18 41.14 46.02

1.48

15.69

23.60

16.44

41.16

34.01

42.12

59.71

90.36

1

2

4

3

6

5

7

8

9

find the same rank under other cost-based criteria. This implies that excess capacity is valuable in managing exchange rate uncertainties. In other words, C1 is an attractive choice for Applichem in the long run to operationally hedge some of the exchange rate risks via the use of excess capacity in the network.

3.4

Global Supply Chain Design Application: Digital Equipment Corporation Network Design

One of the better known decision support models for global supply chain networks with a successful corporate implementation models appears in Arntzen et al. [2]. It presents the application of their global supply chain design decision support tool (referred to as Global Supply Chain Model (GSCM)) for Digital Equipment Corporation. Digital

62


Equipment Corporation, the world’s third-largest vertically integrated computer company at the point of this application experienced dramatic changes in their market demands in the late 80s. The demand for high-end and mid-range systems and for large complex modules had shrunk and been replaced by simple and low-margin personal computers (PCs) and workstations with powerful microprocessors. This change left the manufacturers with a mismatch among capacity infrastructure and demands of the new markets. Digital needed to reshape its operations to keep up with the new trend. GSCM was developed to balance the multiple, conflicting priorities of manufacturing and distribution: time, cost, and capacity while considering the global issues of duty and duty relief (defined in Section 3.4.2), local content (see Section 4.3: Local content rules requires manufacturers to purchase a certain amount of components from suppliers located in that country (or the protected region)), and offset trade (see Section 2.4.2, p. 38). We will provide more detailed description of these terms and their calculations later in Section 3.4.2. Implementation of this model at the Digital Equipment Corporation led to savings in the order of $1 billion. 3.4.1

Model Design

The global supply chain network decisions considered in this particular application project not only take into account all three components of the supply chain, but also address the new product pipeline design related questions, and key global factors such as the offset trade and local content rule constraints. • In designing a worldwide supply base (“Supply”): (1) What design is optimal for shipping spare parts between plants, vendors, and customers; (2) How many repair centers there should be and which products should each repair. • In setting a global supply strategy for manufacturing (“Production”): (1) How many plants they need, where to locate them, and what technologies and capacities each should have; (2) What degree of vertical integration is best; (3) Should a product be built at one plant or more, and at what volumes


63

do the answers change; (4) Are tax havens worth the extra freight and duty. • In designing a global logistics network (“Distribution”), they must decide (1) How many distribution centers there should be, where they should be located, and what methods of distribution and capacity each should have; (2) Which distribution centers should serve which customers of each type of order and product. • In designing a new product pipeline: (1) What design provides the best balance between total cost and cumulative manufacturing and distribution time; (2) How alternate volume forecasts affect unit costs and the choice of plants and suppliers. • In meeting the set targets for offset trades and local content, deciding (1) Which products they should manufacture or buy in a given nation to satisfy their offset trade requirement; (2) How much extra it will cost or how much longer it will take to buy a product in a given nation. GSCM is a deterministic multi-period, multi-commodity mixedinteger model that minimizes a weighted combination of total cost and time elements, where total cost includes production costs, inventory costs, material handling costs, taxes, facility fixed charges, production line fixed costs, transportation costs, fixed costs associated with a particular method of manufacturing, and duty costs less duty drawback and duty avoidance (we will discuss more in Section 3.4.2). Time elements include manufacturing lead times and transit times. GSCM also model the duty drawback and duty avoidance as part of the overall supply chain design, different from the traditional approach in which the duty issue was handled separately by other functional areas. This optimization is subject to the following constraints: customer demand satisfaction for each product, in each time period, in each customer region; balance of materials; Global Bill of Materials (GBOM) (we will describe the term in detail in Section 3.4.2); production capacity constraints; product mix constraints; production style at each facility; international constraints such as local content and offset trade, and credit for duty drawback and duty relief.

64


Taking so many trade-offs into consideration, GSCM problems of realistic size and detail are difficult mixed-integer programs. The authors’ approach is to divide the constraints into two groups, hard constraints (must be respected) and soft constraints (may be violated at a penalty cost), which simplifies the computation. The employed solver software uses row-factorization, and branch-and-bound enumeration with generalized types of branches. Based on the authors’ successful experiences solving particular types of GSCM, they developed a set of most-successful tuning parameters for their algorithms. All these help ensure optimal or near optimal solutions of the large-scale GSCM model applications they encountered in their corporate environment of study. 3.4.2

Detailed Model Formulation

As this model is one of the most comprehensive, representative, and applicable for real corporate world global concerns and issues in facility network and sourcing design issues, we will devote the needed space to describe it in adequate detail for the readers of this review to comprehend its nature. However, our description is no substitute for reading the original work. 3.4.2.1

Index Use

Primary indices and index sets p, q ∈ P = product(part,component, and so forth), n ∈ N = nation, f ∈ F = facility, c ∈ C = customers, and t ∈ T = time period. Secondary indices h ∈ H = facility type, r ∈ R = manufacturing style (method), l ∈ L = transportation link, and m ∈ M = transportation mode


65

Nation group. A nation group is a collection of one or more nations that permit free trade within the group and charge uniform duties to nations outside the group; Each nation n belongs to a nation group, for indexing shipping between nation groups: o, d = origin, destination nation groups {o 6= d}. Product Content Description: Global Bill of Materials (GBOM). A global bill of materials is a generalization of the classical bill of materials and final products together, and there may be sourcing options for components that depend upon product, location, and stage of assembly. The GBOM can be viewed as a collection of rooted arborescences, with each vertex representing a product and the facility that fabricates it. A root vertex represents a finished product and its final fabrication facility, called an ultimate ancestor product. Each level in one of the GBOM arborescences represents a stage of fabrication. An intermediate edge at home level in an arborescence represents assembly of the immediate ancestor, or parent product and facility using its recipe number of units of the component from the immediate descendant, or child product and facility. Parent and child differ by one generation. The ultimate descendant products are leaf vertices. Each vertex has at least one child for each required component, more if there are alternate sourcing opportunities in the supply chain. A product may appear at more than one assembly stage and in more than one arborescence within the GBOM: each appearance must exhibit the same recipe, but not necessarily the same potential sourcing of components, and no product can be its own ancestor. Herein, GBOM vertices are numbered in preorder, also called depth-first-search order, or dynastic order: a root is the first vertex, and vertices are numbered so that all descendants of a vertex are numbered before descendants of any other vertex. b ∈ B = GBOM entry in preorder and, g ∈ G = generation

66


Induced index sets It is convenient to access sets of products as follows: Pc = products with external demand in customer c (not restricted to finished products), Pf = products that can be manufactured at facility f , Pr = products that use manufacturing style r, βp,d = entries in GBOM for product p made by facilities in nation-group d, and pb = product at GBOM entry b. A global bill of materials defines partial orders among products p: DESCN DS gp = descendant products of product p for g generations, AN CST RS gb = ancestor products of product pb for g generations. Facilities f are referred to via Fp = facilities Fh = facilities Fr = facilities Fn = facilities

capable of producing product p, of type h, capable of employing production style r, and in nation n.

For customers c, Cn = customers in nation n Manufacturing styles r: Rf = manufacturing styles available at facility f , and Rp = manufacturing styles possible for product p. Transportation links l: Lf, ∗ = transportation links originating from facility f (and including f as a destination), L∗, f = transportation links ending at facility f , L∗, c = transportation links ending at facility c, Lo, d = transportation links between nation groups o and d, (Lo,∗ represents links between nation-group o and some other nation group).


67

For transportation modes m: Ml = transportation modes available on link l. 3.4.2.2

Data

(Units shown in parentheses. Product units are either “p-units” or “q-units,” and style units are “r-units”). Production/inventory/shipping DEMANDpct = external demand from customer c for product p during period t (p-units), RECIPEpq = units of child product q required to make one unit of parent product p (q-units/p-unit), WEIGHTp = weight of product p (weight/p-unit), WEIGHTf t = total throughput limit at facility f in period t (weight). STYLEpf r = amount of style r consumed in the manufacture of product p in facility f (r-units/p-unit). STYLEf rt = amount of style r available at facility f in period t (r-units). xpf t , xpf t = lower, upper bounds on production of product p at facility f in period t (p-units). hpf t , hpf t = lower, upper bounds on inventory held of product p at facility f during period t (p-units). splmt , splmt = lower, upper bounds on shipments of product p at facility f in period t (p-units). System configuration F p , F p = lower, upper bounds on number of facilities that may produce product p. F h , F h = lower, upper bounds on number of facilities of type h. F r , F r = lower, upper bounds on number of facilities that may use manufacturing style r.

68


Offset trade and local content INCVpf t = incremental value added to product p at facility f in period t ($/p-unit). TEVnpt = total expected value (computed assuming uniformly-distributed sourcing alternatives throughout the GBOM supply-chain) of product p in nation n in period t ($/p-unit). TEVNn = total expected value of product demand in nation n ($). TEVW = total expected value of worldwide demand ($). LOCALnt = fraction of local content required by nation n in period t. Duty drawback and duty relief. Duty is an import tax that may be charged to a product when it is imported into a nation. Some nations have formed nation groups (for example, The European Union (EU)), within which products move duty-free. Duties range from 0% to 200% of the value of the product being imported, and typical duty rates are 5%–10% of product value, which can easily be a significant amount. Duty drawback and duty avoidance options should always be considered. There are three ways to avoid or draw back duty charges: (1) A firm can import a product and subsequently reexport it (without change), claiming duty drawback for reexport in same condition; (2) A firm can import a product, add value by using it to make a subassembly, and then export the subassembly, claiming duty drawback for reexport in a different condition; and (3) A firm may export a product and later reimport it as part of a larger assembly, claiming duty avoidance for domestic goods returned in a different condition. EXPLODEpq = units of product q required to make one unit of product p(q-units/p-unit).


69

Objective α = objective weight factor, 0 ≤ α ≤ 1, used for convex linear combination of cost and weighted activity time. VPCpf t = variable cost of producing product p at facility f in period t ($/p-unit). VFCpf = variable cost of producing product p through facility f ($/weight). HCPROCpf t = inventory surcharge for holding the value of unavoidable minimum in-process inventory while producing product p at facility f throughout period t ($/p-unit). HCPIPEpf t = pipeline inventory charge for value held in-process while producing product p at facility f throughout period t ($/p-unit). TAXpf t = tax on product p at facility f in period t ($/p-unit). VPCOSTpf t = variable production cost, the sum of cost components VPCpf t , VFCpf × WEIGHTp , HCPROCpf t , HCPIPEpf t , and TAXpf t . HCpf t = cost of holding the value of one unit of inventory of product p at facility f throughout period t ($/p-unit). SHIPClmt = cost to ship on link l via mode m in period t($/weight). HCSHIPplmt = pipeline inventory charge for value held in-transit while shipping product p on link l via mode m during period t ($/p-unit). DUTYplt = duty charge for shipping product p on link l during period t($/p-unit). VCSHIPplmt = variable shipping cost, the sum of cost components SHIPClmt × WEIGHTp , HCSHIPplmt , and DUTYplt . FIXPCpf = fixed cost of producing product p at facility f ($). FIXFCf = fixed cost of using facility f for any production ($). FIXSTf r = fixed cost to use style r at facility f ($).

70


DUTY Ao,d p = duty drawback credit for product p imported into nation-group d from nation-group o and reexported in the same condition($/p-unit). DUTYIo,d = duty drawback credit for product p imported into p nation-group d from nation-group o and reexported in a different condition (also called manufacturing drawback)($/p-unit). o,d DUTYWp = duty relief credit for product p imported into nation d from nation-group o containing domestic goods returned in a different condition ($/p-unit). PDAYSpf t = processing activity days to produce product p at facility f during period t (days/p-unit). TDAYSplmt = transit activity days product p on link l via mode m in period t (days/p-unit). 3.4.2.3

Decision Variables

Production/inventory/shipping xpf t = production variables, units of product p produced by facility f during period t,(p-units) ∀f, p ∈ Pf , t. hpf t = inventory variables, units of inventory held at facility f of product p at the end of period t, (p-units)∀f, p ∈ Pf , t. splmt = shipping variables, units of product p shipped on link l via mode m during period, t (p-units) ∀p, l, m ∈ Ml , t. System configuration zpf = product-made-by-facility indicator variable, 1 if facility f produces product p during any time period (that is, if any xpf t > 0 for any t); 0 otherwise, ∀f, p ∈ Pf . yf = production-by-facility indicator variable, 1 if facility f has any production during any time period; 0 otherwise, ∀f . vf r = style-used-by-facility indicator variable, 1 if style r is used in facility f ; 0 otherwise, ∀f, r ∈ Rf .


71

Duty drawback and duty relief Define import and export as directed flows into and out of nationgroup d. Duties for importing products may be offset by exports. Exports of product p can be used to offset import duties paid either to import products directly or to import descendants of p, which are then exported as part of p, or to import ancestors of p that already contain p. ao,d p = duty drawback credit variables: credit for export of product p out of nation-group d as reexport in the same condition to offset the import of product p into nation-group d from nation-group o (p-units) ∀p, o, d. o,d ipq = duty drawback credit variables: credit for export of product p out of nation-group d as reexport in a different condition to offset the import of descendant product q into nationgroup d from nation-group o (p-units) ∀p, q, o, d. o,d wpq = duty relief credit variables: credit for export of product p out of nation-group d to offset the import of ancestor product q into nation-group d from nation-group o as domestic goods returned in different condition (p-units) ∀p, q, o, d.

3.4.2.4

Objective Formulation

The objective function (3.10) is a composite of “cost” and “time.” The weight factor α is applied to cost terms, such as the variable cost of product, facility throughput costs, and taxes; inventory costs; fixed production costs; and net duty charges. Time is measured in weighted activity days spent in production and in transit with its weight (1 − α).  min α 

X

VPCOSTpf t xpf t +

p,f,t

+

X f,p

X

HCpf t hpf t +

p,f,t

FIXPCpf zpf +

X f

FIXFCf yf +

X

VCSHIPplmt splmt

p,l,m,t

X f,r

FIXSTf,r vf

72


−

X

X

o,d DUTYAo,d p ap −

o,d o,d DUTYIpq ip |G|

p,o,d

p,q∈DESCN DS p ,o,d

 X

−

o,d  DUTYWpo,d wpq  |G|

p,b∈Bp,d ,q∈AN CST RS b ,o,d

 + (1 − α) 

 X

PDAYSpf t xpf t +

p,f,t

3.4.2.5

X

TDAYSplmt splmt  .

(3.10)

p,l,m,t

Constraint Formulation

Subject to (a) Production/inventory/shipping constraints: X

splmt = DEMANDpct

∀c, p ∈ Pc , t.

(3.11)

l∈L∗c ,m∈Ml

xpf t + hpf (t−1) =

X

splmt + hpf t ∀f, p ∈ Pf , t.

l∈Lf ∗ ,m∈Ml

(3.12) xpf t =

X

RECIPE−1 pq sqlmt

l∈L∗f ,m∈Ml

∀f, p ∈ Pf , q ∈ DESCN DS 1p , t.

X

WEIGHTp xpf t ≤ WEIGHTf t

∀f, t.

(3.13)

(3.14)

p∈Pf

X

STYLEpf r xpf t ≤ STYLEf rt

∀f, r ∈ Rf , t.

(3.15)

p∈Pf

xpf t ≤ xpf t ≤ xpf t

∀f, p ∈ Pf , t.

hpf t ≤ hpf t ≤ hpf t

∀f, p ∈ Pf , t.

splmt ≤ splmt ≤ splmt

∀p, l, m ∈ Ml , t.

(3.16)


(b) System configuration: xpf t ≤ xpf t zpf

∀f, p ∈ Pf , t.

(3.17)

zpf ≤ yf ∀f, p ∈ Pf X zpf ≤ F p ∀p. Fp ≤

(3.18) (3.19)

f ∈Fp

Fh ≤

X

yf ≤ F h

∀h.

(3.20)

vf ≤ F r

∀r.

(3.21)

f ∈Fh

Fr ≤

X f ∈Fr

xpf t ≤ xpf t vf r

∀f, p ∈ Pf , r ∈ Rp , t.

zpf ∈ {0, 1}

(3.22)

∀f, p ∈ Pf ;

yf ∈ {0, 1}

∀f ;

vf r ∈ {0, 1}

(3.23)

∀f, r ∈ Rf .

(c) Offset trade and local content:

0 @

1 INCVpf t xpf t A

X 0 ≥@

1 LOCALnt TEVnpt × DEMANDpct A

f ∈Fn ,p∈Pf ,t

X

∀n.

(3.24)

c∈Cn ,p∈Pc ,t

0 @

X

1 INCVpf t xpf t A TEVW

0 X ≥@

f ∈Fn ,p∈Pf ,t

1 LOCALnt TEVnpt . × DEMANDpctA TEVNn

∀n.

c∈Cn ,Pc ,t

(3.25) (d) Duty drawback and duty relief: X X splmt ≥ ao,d p + l∈Ld,∗,m,t

o

+

X

io,d pq |G|

o,q∈DESCN DS p

X o,b∈Bp,d,q∈AN CST

o,d wpq

∀p, d.

|G| RS b

(3.26)

73

74


X

X

splmt ≥ ao,d p +

EXPLODEqp io,d qp |G|

l∈Lo,d,m,t

b∈Bp,d q∈AN CST RS b

+

X

o,d EXPLODE−1 pq wqp

∀p, o, d.

|G| q∈DESCN DS p

(3.27) 3.4.2.6

Interpretation of Constraints

(a) Production/Inventory/Shipping constraints — Constraints (3.11) ensure that customer demand (p-units) is met. — Constraints (3.12) conserve the flow of product (p-units) among production, inventory, and shipping variables. — Constraints (3.13) express the global bill of materials: production of a parent product (p-units) induces demand for all of its incoming child products (q-units). — Constraints (3.14) limit total throughput weight for each facility. — Constraints (3.15) limit the use of a given style (r-units) to its availability, by facility, style, and period. — Constraints (3.16) are simple bounds on respective production and inventory variables on the flow over distribution links(p-units). (b) System configuration constraints — Constraints (3.17) use the production variables and capacities to define the product-made-by-facility indicator variables, which incur a fixed production cost by product by facility.


— Constraints (3.18) use the product-made-by-facility indicator variables to define the production-byfacility indicator variables, which incur a facility fixed charge. — Constraints (3.19) use the product-made-by-facility indicator variables to control the number of facilities producing each product. — Constraints (3.20) use the product-made-by-facility indicator variables to limit the number of facilities of each type. — Constraints (3.21) use the product-made-by-facility indicator variables to limit the number of facilities using each manufacturing style. — Constraints (3.22) use the production variables and capacities to define the style-used-by-facility indicator variables. — Constraints (3.23) are respective binary restrictions on the indicator variables for product-made-by, production-by, and style-used-by facility. (c) Offset trade and local content constraints — Constraints (3.24) enforce value-based offset trade restriction, requiring that the local value added in nation n be at least some minimum faction of the value sold there. — Constraints (3.25) are an approximate expression of the country content requirements typical in the US Buy American Act and similar regulations in Europe but more restrictive than the actual legislation. (d) Duty drawback and duty relief constraints — Constraints (3.26) limit the redemption of duty credits to total export of product p units out of nationgroup d.

75

76


— Constraints (3.27) total imports of product p units into nation-group d from nation-group o and use this to limit the redemption of duty credits achievable by offsetting exports of product p back to nationgroup o, either by directly exporting product p, or by exporting products containing p or products that will contain p. 3.4.3

Model Applications at Digital

GSCM is a comprehensive deterministic model for global supply chain design. It is used at Digital by the sourcing and capacity planning (SCP) group. GSCM is used in the analyses of the following three types of decisions: (1) New product pipeline analyses: Digital applied GSCM to optimize new product pipelines and later extends the use of GSCM to the single, dual, and triple sourcing questions and the selections of plants and suppliers. (2) Commodity supply base analysis: GSCM can handle multiple products simultaneously, reducing the supplier base and achieving competitive cost and cycle times. (3) Companywide or divisionwide supply chain studies: The supply chain for the whole company involves too many products to include individually. GSCM is able to aggregate the complex problem to a manageable size. For example, to study a global supply chain, they use representative composite products to represent large product families. GSCM is applied in the following major studies. First, manufacturing supply chain study. The study recommended an 18-month plan to restructure manufacturing infrastructure examining the trade-offs between measures of time, cost, capacity, duty, taxes, and international trade. This single study saved Digital’s annual manufacturing costs by $167 million and also saved Digital’s annual logistics cost by over $200 million by spring 1994. According to the authors, the total benefit from manufacturing supply chain studies attributed to the use of the GSCM has been a $500 million cost reduction in manufacturing and a $300 million cost reduction in logistics as well as a reduction in required assets of over $400 million.


77

Second, services supply chain study. The objective of this study was to determine the number, location, capacity, and service areas for repair centers and parts distribution centers. This study is expected to reduce the number of service facilities from 34 to 17; reduce costs by $81 million per year; reduce assets by $34 million in property, plant, and equipment; reduce inventory by $74 million; and improve return on assets for the services business by 7.1%. Third, network study. This study was conducted to examine the optimal supply chain design for its set of products. The study confirmed that the current design is near optimal and suggested relocation of some manufacturing to meet offset trade requirements. Fourth, Americas distribution study. This study was dedicated to finding the best distribution network design for the Americas. They used GSCM to evaluate several alternatives and determine the optimal one. The study could potentially save Digital up to $7.9 millions (about 5%). Finally, Global Supply Chain study. At the time this review was being written, the global supply chain study was being performed to examine all computers, networks, components and peripherals, and storage subsystem products at Digital. GSCM played an important role in Digital’s global supply chain transition. GSCM modeled global supply chain problems that included multiple products, facilities, production stages, technology choices, time periods, and transportation modes. Its ability of balancing cost with activity time is useful for firms facing short product life cycles and rapid technological change. GSCM provides to firms strategic and integrated decisions across the supply chain, including production, location, inventory, supply, and transportation. Given its very nature, GSCM is a very large scale mixed-integer linear program which is often difficult to solve to optimality. However, with the continuous and rapid advance of hardware and software tools, combined with some modeling flexibility on the part of the decision maker, the solution of these problems is not anymore the “bottleneck” of their corporate implementation. The requisite top management support with appropriate resource allocation might often be the real constraint.

78

3.5


Global Facility Network Design Using Newsvendor Network Approach

In a recent stream of research in global supply chain design, researchers effectively combine the geographical network and product-process focus approaches. We present two examples, Lu and Van Mieghem [28] and Biller and Xiang [4]. Both papers study the capacity investment decision faced by a global firm which sells non-homogeneous products with different demand characteristics to serve two geographically separated markets under demand uncertainty. On the one hand, to produce two products, firms invest in two types of capacity for two production processes: basic capacity (producing common features) and customizing capacity (producing product-specific features). On the other hand, the nonnegligible transportation cost is an important driver of the capacity strategy, as emphasized in geographical network analysis. They adopt the newsvendor network approach proposed in Van Mieghem and Rudi [35] to derive the optimal capacity investment strategies that maximize the firm’s expected profit under demand uncertainty. In Lu and Van Mieghem [28], product-specific capacity is assumed to be located in the market the product serves. Basic capacity is the flexible capacity that can serve both markets and the global firm can choose where to locate it. In Biller and Xiang [4], neither basic capacity nor customizing capacity is a flexible capacity. Operational flexibility comes in a different form: the firm has the flexibility to choose where to locate base and customizing capacities. Therefore, the customizing capacity located in a market to customize the product for the other market makes it possible for the firm to produce both types of products in the same manufacturing facility without the use of flexible capacity. The two papers also explore the impact of the key drivers of the capacity investment strategies, cost and price differentials, demand volatilities, and demand correlation. Both papers point out under demand uncertainty, the global firm exploits both the risk pooling benefit and the ex-post revenue maximization option (allocate more capacity to the market with higher contribution margin).

3.5 Global Facility Network Design Using Newsvendor Network Approach

3.5.1

79

Multi-Market Facility Network Design with Offshoring Applications

Lu and Van Mieghem [28] study a firm that produces two products and serve two geographically separated markets using a common component and two other product-specific components. The common component can be produced in either market and transported between each other. This model can be used to evaluate the global firm’s offshoring decision, balancing between the unit production cost savings and increased logistic costs and foreign trade barriers. Two strategic network design questions arise when deciding on offshoring: (1) Should the common part be produced in a single central facility or in two local facilities? (2) If a centralization strategy is adopted for the common component, which market should the facility be located in?

3.5.2

Model Formulation

The global firm makes its decision for four resources to produce two products to serve two non-homogeneous markets. In the capacity strategy K = (K1 , K2 , K3 , K4 ), Ki corresponds to product-specific capacity in market i = 1, 2, which are dedicated capacities. Ki+2 represents common component capacity in market i. Capacities K3 and K4 can be shared by the two products via transshipment at a positive cost cT per unit. Following the convention by Van Mieghem and Rudi [35], notation used is as follows: • p = (p1 , p2 ), where pi is the per unit sale price of product i; • cM = (cM,1 , cM,2 ), where cM,i is the per unit common component manufacturing cost in market i; • cT = (cT,1 , cT,2 ), where cT,i is the total transportation cost of one unit of common part from market i to market j including associated tariffs and duties; • cK = (cK,1 , cK,2 , cK,3 , cK,3 ) is the constant marginal capacity investment cost. Assume common component capacity cost is the same for both locations, and relax this later.

80


Fig. 3.1 Common component: Graphical representation of newsvendor network with activity decisions.

Three price and cost differentials arise naturally: ∆p = p1 − p2 ,

∆cM = cM,1 − cM,2 ,

∆cT = cT,1 − cT,2 .

The processing network of Figure 3.1 has four contingent activities: xi is the number of common parts used locally in market i, while xi+2 is the number of common parts transshipped from market i. The net values of the four processing activities are denoted by v: v1 = p1 − cM,1 ,

v2 = p2 − cM,2 ,

v3 = p2 − cM,1 − cT,1 ,

v4 = p1 − cM,2 − cT,2 .

To eliminate trivialities, they assume positive net values so that production and transshipment are ex-post profitable. In addition, it is economically justified to produce both end products, which means investment in the dedicated resources is always positive. Without loss of generality, to illustrate the offshoring setting, they label market 1 (USA) the high-price market, i.e. p1 ≥ p2 , and it has higher manufacturing costs, i.e., cM,1 ≥ cM,2 . Market 2 (Asia) is called the low-cost market. They model the capacity decision as a two-stage stochastic program. In the first stage, the firm makes its capacity decision K to maximize its expected profit V (K) before observing demand. In the second stage, the realization of demand is observed, and the firm maximizes its revenue through allocating capacity, constrained by its earlier investment


81

decisions. V ∗ = max Eπ(K, D) − C(K) K∈R4+

π(K, D) = max v 0 x K∈R4+

subject to

(3.28)

Ax ≤ K RD x ≤ D,

where primes denote transpose and the consumption and output matrices are   1 0 0 1   1 0 0 1 0 1 1 0 A= .  RD = 0 1 1 0 1 0 1 0 0 1 0 1 They assume the capacity cost function is linear, i.e., C(K) = c0K K. Later in their paper, they add a fixed cost to study economies of scale. The optimal policy has the following four network configurations: the hybrid strategy, market-focused strategy, centralization in USA (“Onshore”), and centralization in Asia (“Offshore”), as displayed in Figure 3.2. The hybrid (strategy 1) and the market-focused (strategy 2) configurations source the common component locally, while the other two configurations (strategy 3 & 4) centralize it in a single market. In the hybrid strategy, common component is transshipped between two markets in both ways. The market-focused strategy is a special case of the hybrid configuration, where no common component is transshipped between the markets. 3.5.2.1

Optimal Network Configurations

Deterministic Demand Case. In the simple base case of deterministic demand, the centralization decision solely depends on transportation and manufacturing costs. Centralizing in the high-price market (USA) is never optimal. If the unit transportation cost from the low-cost market (Asia) to the high-price market (USA) is higher than the unit manufacturing cost differential between the two markets, it is optimal to adopt the market-focused configuration and produce common parts in

82


Fig. 3.2 Four possible configurations of a global facility network.

both markets. Otherwise, it is optimal to centralize commonality in Asia to save manufacturing costs. Stochastic Demand Case. When the unit transportation cost is lower than the unit manufacturing cost advantage between the two markets, it is optimal to centralize commonality in one of the markets to save manufacturing costs. When the unit transportation cost is higher than the unit manufacturing cost advantage, they have the following findings: the optimal investment in the common component is always weakly less than in the dedicated component in both markets because common parts can be pooled across markets. If centralization is optimal for common component, there will be equal investment in the common and dedicated components in the market where the common part is produced. Therefore, depending on the price differentials, manufacturing cost differentials and demand distribution, two centralization configurations can be optimal: centralization in market 1 and in market 2. Two thresholds on transportation cost, c¯T and cT are defined to help structure the optimal capacity investment strategies.


83

When price differential is high enough ∆p > max(∆cM , −∆cM − ∆cT ): it is optimal to centralize commonality in market 1, if the transportation cost from market 1 to market 2 is less than the threshold c¯T ; otherwise, it is optimal to invest in commonality in both markets. Moreover, they specify the conditions under which market-focused configuration is optimal (which is a special case of hybrid strategy). In contrast to the deterministic demand case, centralizing in the high-price market (“onshoring”) could be optimal. Offshoring is never optimal is this case. When price differential is low (−∆cM − ∆cT ≤ ∆p ≤ ∆cM ): it is optimal to centralize commonality in market 2 (“offshoring”) if the transportation cost from market 2 to market 1 is less than the threshold cT ; otherwise, it is optimal to invest in commonality in both markets. Moreover, they specify the condition under which marketfocused configuration is optimal (which is a special case of hybrid strategy). Therefore, offshoring is not an optimal solution when price differential is substantial and demand is highly volatile. 3.5.2.2

Key Factors that Have Impact on Optimal Network Configuration

Impact of Costs and Prices. Thresholds on transportation cost, c¯T and cT , determine the optimal network configuration. The authors explore how cost and price factors affect the thresholds to study how these factors may impact the global firm’s decisions on offshoring, onshoring or hybrid strategies. Some factors have definite impact: for example, a decrease in Asian price or a decrease in Asian manufacturing cost makes offshoring more attractive. Centralization strategy remains optimal for larger values of transportation costs when the investment cost of common component increases. The movements of some of the factors, such as US price, manufacturing cost, or dedicated component investment cost, have ambiguous effect on the strategy because of the trade-offs in centralization. Impact of Demand Size, Volatility, and Correlation. When demand is stochastic, demand size has impact on the optimal network

84


configuration. Suppose centralization in Asia is optimal given current global demand. If Asian demand grows larger, centralization in Asia stays optimal. If we suppose centralization in the United States is optimal given current global demand, when Asian demand grows larger, localization of commonality becomes optimal. As Asian demand surges, we expect to observe that more configurations of localization commonality or centralizing in Asia to happen. As noticed in Section 3.5.2.1, the optimal facility network design also depends on demand volatility and correlation. Under certain conditions (when market 1’s price is significantly higher than market 2), they conclude that increased market correlation decreases the network value. They explore the two extreme cases of demand correlation: perfectly positively correlated demands and perfectly negatively correlated demands. They find that when demands are perfectly negatively correlated, centralization is optimal only when the profit advantage of the centralizing market is sufficiently high. When demands are perfectly positively correlated, general results on how capacity changes with demand variability are hard to establish. 3.5.2.3

Summary

The authors build an analytical model to study the global facility network design problem. The global firm has the flexibility to determine where to locate facilities that produce common parts. The model focuses on three key factors in facility network planning, cost, revenue, and demand. The optimal strategy is composed of four patterns, namely, hybrid, market-focused, centralization in USA (Onshore), and centralization in Asia (Offshore). After applying newsvendor network methodology under both deterministic and stochastic demand, they generate the following managerial insights on offshoring: (1) when the manufacturing cost reductions of offshoring outweigh transportation costs, centralizing the common component in low-wage countries is optimal. Otherwise, the optimal strategy is more complex and depends on price ratios as well as cost, market size, and uncertainty. (2) When demand is uncertain, centralization becomes more attractive due to the benefits of


85

demand pooling and embedded ex-post revenue maximization option to allocate capacity to the more profitable market. Even centralization in the United States (onshore) may emerge as the optimal configuration when the price advantage and demand uncertainty is high. (3) They derive the transportation thresholds to indicate the attractiveness of centralization. These thresholds are determined by price and cost differentials, capacity investment cost and demand distribution.

3.5.3

Global Capacity Investment Strategies for Product Variants

Biller and Xiang [4] study the capacity investment decision for a global firm that has to customize its non-modular product to meet special requirements in two different markets. In contrast to modular products whose customization can be decoupled from the base production process, and postponed until the latest possible point in the supply network if there is cost benefit, non-modular products have to be customized during the production process, and it is infeasible to delay the customization to a later point. The firm installs two different types of capacity under demand uncertainty: base capacity for producing the common features of the product, and customizing capacity for fulfilling the markets’ specific requirements. The firm is an expected-profit maximizer by determining capacity investment strategy in base and customizing capacity under demand uncertainty. The following four investment patterns emerge as a result of profit maximizing with different level of system flexibility (see Figure 3.3): (i) the local production pattern, in which the manufacturing facilities serve only their local markets; (ii) the one-way export pattern, in which the manufacturing facilities serve their local markets, while there is customizing capacity in the manufacturing facility of market A for the market B variant; (iii) the single plant pattern, in which demands for both markets are satisfied by the production only in market A; (iv) the two-way export pattern, in which every manufacturing facilities serves its local market, as well as the other market.

86


Fig. 3.3 Four patterns of the optimal capacity investment portfolio.

3.5.3.1

Model Formulation

As in Lu and Van Mieghem [28], they develop a two-stage stochastic programming model to derive the optimality conditions for all of the investment patterns of interest. Demand process D is modeled as a monotone transformation of a Gaussian base process. The firm is a price taker, thus the unit price of the product sold in market i (pi ) is given. In the first stage, the firm makes its capacity investment decision for base capacities K = (KA , KB )0 (Ki at unit capacity investment cost bi , i = A, B), and customizing capacities C = (CA[A] , CB[B] , CA[B] , CB[A] )0 (Ci[j] at unit capacity investment cost ci[j] , i, j = A, B) to maximize its expected profit under multivariate demand uncertainty, where Ci[j] is the capacity in market j for the customization of the variant that will be sold to market i. ri is the unit production cost via base capacity Ki . si[j] is the unit production cost via customizing capacity Ci[j] . t is the unit transportation cost. They assume all the costs are linear and their analytical results also hold to any convex cost functions. In the second stage, the demand di , i = A, B, is realized. The global firm maximizes its revenue through capacity allocation, constrained by the capacity in place at


87

Fig. 3.4 Basic and customizing capacities: Graphical representation of newsvendor network with activity decisions.

stage 1. They denote the capacity allocation vector of the second stage as y = (yA[A] , yB[B] , yA[B] , yB[A] ), where yi[j] is the quantity produced in market j that will be sold in market i. As displayed in Figure 3.4, the amount of production that goes through base capacity Ki is given by yi[i] + yj[i] , where yi[i] units go through local customizing capacity Ci[i] and yj[i] units go through local customizing capacity Cj[i] . Similar to Lu and Van Mieghem [28], they make assumptions on costs and prices to rule out triviality. Without loss of generality, market A is the one where the more profitable variant of the product is sold. The two-stage decision problem is formulated as follows: Stage 1 Problem: V ∗ (K, C) = maxV (K, C) K,C

= E[Θ∗ (K, C, D)] −

X i=A,B

bi K i −

X

X

i=A,B; j=A,B

ci[j] Ci[j]

88


subject to

Ki ≥ 0, i = A, B Ci[j] ≥ 0 i, j = A, B

Stage 2 Problem: Θ∗ (K, C, d) = maxΘ(K, C, d) y X X = Ri[i] yi[i] + i=A,B

subject to

yi[j] yi[i] + yj[i] yi[i] + yi[j] yi[j]

X

Ri[j] yi[j]

i=A,B; i6=j,j=A,B

≤ ≤ ≤ ≥

Ci[j] , i = A, B Ki , i = A, B, i 6= j, j = A, B di , i = A, B, i 6= j, j = A, B 0, i, j = A, B

(3.29)

where Ri[i] = pi − ri − si[i] when i = j, and Ri[j] = pi − rj − si[j] − t when i 6= j. To reduce the number of parameters, they assume that bA = bB . Similarly, si[i] = si[j] = si , and ci[i] = si[j] = ci , which implies the cost of customization is dependent on the variant, instead of location. They use ∆p, ∆r, and ∆s to denote the price differential (pA − pB ), the unit base production cost differential (rA − rB ), and the unit customization cost differential (sA − sB ). Their model assumption leads to the condition ∆p − ∆s ≥ ∆r ≥ 0. Adopting the classic newsvendor network approach, they find that the optimal capacity investment strategy takes four different forms: (i) the local production pattern (no system flexibility, similar to “market-focused strategy” in Lu and Van Mieghem [28]), in which ∗ = the manufacturing facilities serve only their local markets (KA ∗ ∗ = C∗ ∗ ∗ CA[A] , KB B[B] , and CA[B] = CB[A] = 0); (ii) the one-way export pattern (partial system flexibility), in which the manufacturing facilities serve their local markets, while there is customizing capacity in the manufacturing facility of only one of the markets for the variant of the ∗ ∗ other (CA[B] , or CB[A] = 0); (iii) the single plant pattern (“centralization” of both basic and customizing capacities), in which demands for both markets are satisfied by the production only in one of the mar∗ = C∗ ∗ ∗ ∗ ∗ kets (KA A[A] = CB[A] = 0, or KB = CB[B] = CA[B] = 0); and (iv) the two-way export pattern (complete system flexibility, “hybrid strategy” in Lu and Van Mieghem [28]), in which every manufacturing facility serves its local market as well as the other market.


89

Additionally, they find that the optimal strategy follows a thresholdbased structure, and thresholds on the unit profit achieved via the customization of the market A variant in market B (πA[B] ), and unit profit achieved via the customization of the market B variant in market A (πB[A] ), govern the transition from one pattern of optimal strategies to another. Thresholds are determined by product prices, production, transportation, and investment costs, and the characteristics of the multivariate demand distributions such as variability and distribution. 3.5.3.2

Managerial Insights

The threshold-based structure can be depicted on a two-dimensional plot, whose axes correspond to the unit profit margins πA[B] and πB[A] . It helps managers intuitively judge the robustness of their capacity investment decisions. As illustrated in Figure 3.5, the structure of the optimal investment strategy is divided into four different areas. Suppose values of πA[B] and πB[A] computed using the model parameters fall in the upper right corner, which indicates that the two-way export pattern is optimal. Managers observe how close the unit profit margins are to the thresholds conditions, and investigate whether a model parameter fastens or delays the transitions among the patterns of the

Fig. 3.5 The structure of the optimal investment strategy: A two-dimensional plot.

90


optimal capacity investment portfolio. For example, the two-way export pattern is considered as a more robust decision for the optimal solution corresponding to point sol1 than corresponding to point sol2 . Suppose that the optimal solution corresponds to point sol3 in Figure 3.5. If the manager expects changes in the model parameters that would decrease only πA[B] , then the manager should consider the selection of the oneway export pattern even though it is sub-optimal in the current problem setting. 3.5.3.3

Impact of Demand Correlation

The authors explore how the optimal investment strategy changes when the variant demands are perfectly positively correlated and perfectly negatively correlated. The capacity investment model of Van Mieghem [34] concludes that there is still a benefit in investing into flexible capacity when demands are perfectly positively correlated as long as a positive price differential exist. Biller and Xiang [4] generalize the insights provided in the literature to non-homogeneous markets with nonnegligible transportation cost. They show that there exists a benefit in investing in not only partial system flexibility, but also in complete system flexibility, depending on the impact of transportation cost on the order of contribution margins. The two-way export pattern with complete system flexibility in a global setting allows the exploitation of both the risk pooling benefit and the contribution margin differences even under perfectly positively correlated demands. On the other hand, in the case of perfect negative demand correlation, it allows the firm to take advantage of the risk pooling benefit to its fullest extent. However, the existence of non-homogeneous markets might diminish the significance of the risk pooling benefit and results in overinvest∗ + K ∗ > d), despite the fact that total ment in base capacity (KA B demand is known at the time of capacity investment decision. They find that all of the investment patterns of the optimal capacity portfolio can be optimal. Thus, it is possible that the local production pattern with no system flexibility is an optimal strategy, in which case the benefits of customizing capacities are dominated by the cost of transportation.


3.5.3.4

91

Conclusion

Biller and Xiang [4] extend the capacity investment literature by considering the capacity investment problem faced by a global firm selling to two non-homogenous markets. They characterize the structure of the optimal investment strategy as functions of the demand parameters, the variant prices, and the production, transportation, and investment costs. The optimal investment strategy follows a threshold-based structure with thresholds on governing the transitions among the four patterns of optimal strategies in different level of system flexibilities, namely, the local production pattern, the one-way export pattern, the single plant pattern, and the two-way export pattern. They also illustrate the structure of the optimal investment portfolio on a twodimensional plot, which enables managers to investigate the robustness of their capacity decisions with respect to the price and cost parameters. As a result of investigating the demand correlation, perfectly positively correlated demands and perfectly negatively correlated demands, they generalize some of the classical results in capacity investment literature to the global context serving two non-homogeneous markets with different production costs and nonnegligible transportation cost.

4 Importance and Implications of Global Factors on Network Design

4.1

Risk Considerations in Facility Location under Uncertainty

In this section, we focus on modeling and decision support approaches that explicitly deal with global factors dominating the supply chain design of global firms. These factors are: fluctuating exchange rates, price uncertainties (both of inputs and outputs), investment financing decisions of global facilities, regional trade agreement complexities and local content rules, international taxation complexities and transfer pricing schemes. We also include the stream of research of applying option valuation approach to value the operational flexibility under exchange rate uncertainty. 4.1.1

Financial Market Approaches to Facility Location under Uncertainty

Hodder [15] applies financial market approaches as advocated by the Capital Asset Pricing Model (CAPM) to facility location problems under uncertainty and risk aversion with a profit maximization. CAPM is an approach that values risky investments focusing on the 93

94

Importance and Implications of Global Factors on Network Design

use of financial markets, based on the assumption that the financial markets provide diversification opportunities for investors and the only risks to be rewarded above a risk-free return level are nondiversifiable market correlated risks. Compared to mean variance objective function, the financial market approach yields simpler procedures and is able to handle more complex problems. The mean–variance approach incorporates risk aversion in an objective function of the form Z = E(R) − λVar(R), where R denotes the random payoff and λ is a measure of risk aversion. Thus, in the mean–variance objective expected returns are weighted (through the mean–variance return parameter λ) against corresponding total risks captured through a variance term. Model 1: Deterministic Model. In the absence of uncertainty and with a profit maximization objective, the problem can be formulated as in Table 4.1: XX X Max π = (Pj − cij )Xij − Fi Yi (4.1) i

j

i

Subject to 0 ≤ Xij ≤ Yi Dj

for all i and j

Yi = 0, 1

for all i

≤ Dj

for all j

P

i Xij

This formulation is a standard, variant of an uncapacitated plant location problem with a profit maximization objective, and can be readily solved using branch-and-bound techniques proposed in Efroymson and Ray [11] or Khumawala [20]. Model 2: Mean–Variance Approach. The mean–variance approach in the form of Z = E(R) − λVar(R) is one way to incorporate risk aversion Table 4.1 Notation: Deterministic model. Pj = the market price for output in market j, Xij = the quantity shipped from plant i to market j, cij = the unit cost of supplying market j from plant i, Dj = the target demand in the jth market, Yi = a zero–one variable to indicate whether plant i is open, Fi = the fixed cost of opening the ith plant.

4.1 Risk Considerations in Facility Location under Uncertainty

95

in facility location decisions. Although the mean–variance approach is criticized for its ignorance of the effects of skewness, it is still considered as a good model of risk preference if the distribution of random payoffs is reasonably symmetric. For facility location decisions, Hodder [15] models a quantity setting firm whose demand uncertainty is manifested in a random selling price Pj . The model can also be applied when cij and Fj are random. For simplification, the author assumes Xij is determined ex ante and does not respond to price or cost changes during the period. In the absence of the capacity constraints, the problem is formulated as follows: " # XX X Max Z = E (Pj − cij )Xij − Fi Yi i

j

i

" − λVar

# XX i

(Pj − cij )Xij −

j

Subject to 0 ≤ Xij ≤ Yi Dj Yi = 0, 1 P X i ij ≤ Dj

X

Fi Yi

(4.2)

i

for all i and j for all i for all j

The resulting problem is mixed-integer quadratic and can prove to be computationally difficult for problems of moderate-to-hedge sizes. In certain special cases, Problem (4.2) can be solved fairly easily. However, there are limitations on the form of uncertainty, and solution techniques require “dominance” (each market is served by at most one plant), and thus cannot handle capacity constraints. A “dominant” plant is formally defined in Section 4.1.2. Model 3: CAPM Approach. A different approach of evaluating risk is a financial market approach with an objective function based on the CAPM. For purposes of illustration, the review used the simple CAPM model, assuming that the risk associated with each plan is linear in its own production. However, the results carry over to more complex and sophisticated financial market models. The CAPM approach (formulated in (4.3)) is equivalent to Model 1 (formulated in (4.1)) from computational perspective. It becomes possible to solve the problem

96


with capacity constraints. Let ZM = E(π) − λM cov(π, VM ). With Pj , cij and Fi random, ("

# XX

cov(π, VM ) = cov

i

(Pj − cij )Xij −

X

j

)

Fi Yi , VM

i

Then, ZM =

XX i

(P j − cij )Xij −

j

X

F i Yi

i

" −λM

XX i

Xij cov(Pj , VM ) −

XX

j

i

Xij cov(cij , VM )

j

# −

X

Yi cov(Fi , VM )

i

=

XX i

j

−

X

{[P j − λM cov(Pj , VM )] − [cij − λM cov(cij , VM )]}Xij

Yi [F i − λM cov(Fi , VM )].

i

Use Pˆj = P j − λM cov(Pj , VM ), cîj = cij − λM cov(cij , VM ), and Fî = F i − λM cov(Fi , VM ). Then this problem can be stated as follows: ZM =

XX i

Subject to

(Pˆj − cîj )Xij −

j

0 ≤ Xij ≤ Yi Dj X Yi = 0, 1 Xij ≤ Dj

X

Fî Yi

(4.3)

i


i

The financial market approach permits a more general form of demand uncertainty in the uncapacitated problem. If all plants face the same demand curve in market j with no capacity constraints, constant marginal costs guarantee a least cost (dominant) plant for supplying the market. Let Zij denote the contribution to profit and fixed cost


97

if plant i were dominant for market j. Zîj = E(Zij ) − λm cov(Zij , Vm ). Then the location problem can be formulated as XX X max Zm = Zîj yij − Fî Yi i

Subject to

X

j

i

yij ≤ 1

for all j

i

yij , Yi = 0, 1 yij ≤ Yi

for all i and j for all i and j

The financial market approach (CAPM) has its own drawbacks in two main issues. First, CAPM makes extreme assumptions on risk diversification. It assumes that investors can easily diversify their security portfolios in the financial market, which is not always true for owners who hold a large percentage of the shares, or owners of closely held firms. Second, it is more appropriate to evaluate investment projects using both CAPM and total variance approaches such as mean–variance approach under circumstances where the probability of financial distress or bankruptcy is significant. However, financial market approaches are much simpler for computation and have greater modeling flexibility than the mean–variance approach of facility location under uncertainty. 4.1.2

International Plant Location under Price and Exchange Rate Uncertainty

Hodder and Jucker [18] developed a model that explicitly incorporated price and exchange rate uncertainty in international plant location decisions for a risk averse firm. They assume that the decision maker has a mean–variance attitude. They formulate the problem into a mixedinteger quadratic programming problem and provide efficient computational procedures to the problem when plant location decisions are given. The authors consider a multinational firm that seeks to maximize its mean–variance objective concerning the total profit in terms of its home country currency in a single-period model. There are J national markets (indexed by j) with I potential plant location countries (indexed with i). The home country is designated with the subscript 1. e1j represents exchange rate, defined as units of currency 1

98


per unit of currency j. The market price for the good in country j is denoted by Pj , with Xij being the quantity shipped from plant i to market j. Thus per unit revenue (in the numeraire currency) for sales from plant i to market j is Pj e1j . cij is the transfer price expressed in the numeraire currency, for sales from plant i to market j. δij cij represents the marginal profit recorded by plant i for each unit shipped to market j. Ti is the effective tax rate in country i, and Tj the tax rate in country j. They use Dj to indicate potential demand in the jth market, Fi the cost (in the numeraire currency) of opening the ith plant, and Yi a zero– one variable to indicate whether plant i is open. The firm’s total profit is denoted as: π=

XX i

[(Pj e1j − cij )Xij (1 − Tj ) + δij cij Xij (1 − Ti )] −

j

X

Fi Yi .

i

Assume that the random terms are prices in each market and exchange rates between markets, and many of these random variables will be correlated. The Law of One Price (LOP) says that arbitrage forces will tend to equalize prices for identical commodities selling in different national markets. If LOP holds perfectly, P1 = e1j Pj . Lots of factors such as import tariffs and transportation costs all lead to deviations from LOP. They model the price randomness as follows: Pj e1j = bj (P1 + j ), where bj is the coefficient and j is an independently distributed random error term, with mean zero and variance σj2 . The random price has mean P 1 and variance σp2 . The decision maker is to maximize an objective function of the form: V = E(π) − λVar(π) Max V =

XX i

j

−

X

[(bj P 1 − cij )Xij (1 − Tj ) + δij cij Xij (1 − Ti )]

 2 XX Fi Yi − λ  Xij bj (1 − Tj ) σP2

i

i

−λ

X X j

j

#2

" i

Xij bj (1 − Tj )

σj2

(4.4)


99

Subject to Xij X Yi Xij i X Xij

≥0 = 0, 1 ≤ Dj ≤ Yi


P

j Dj

for all i

j

Problem (4.4) is amenable to solution by dominance for a given integer solution, i.e., for a given set of open plants. The authors introduce the notion of the dominant plant. Each market will be served from at most one plant, and it is called its dominant plant. “Consistent dominance” refers to the property that the dominant plant is conditional on the set of open plants but not dependent on production levels at that or any other plant in the open set. Simple dominance requires for some feasible V (X11 , . . . , Xmn ): ∂V ∂V ≥ ∂Xhk ∂Xf k

for all f ∈ M ,

(4.5)

where M is the set of open plants and h is the dominant plant for market k conditional on M . Consistent dominance requires that (4.5) holds for all feasible V . For a dominant plant, Xjd denotes shipments to market j from its dominant plant. For a given set of open plants, M , Problem (4.4) can be rewritten as the so called Nodal Problem: Max V M =

X

[(bj P i − cdj )Xjd (1 − Tj )] + δjd cdj Xjd (1 − Tjd )]

j

#2

" −

X i∈M

Fi − λ

X

Xjd bj (1

− Tj )

σj2

j

X −λ Xjd bj (1 − Tj )2 σj2 j

Subject to 0 ≤ Xjd ≤ Dj

for all j

(4.6)

100


At optimality, M C = M Rk , where X M C = 2λσi2 Xjd bj (1 − Tj ) j

M Rk = P i −

cdk δ d cd (1 − Tkd ) − 2λXkd bk (1 − Tk )σk2 + k k bk bk (1 − Tk )

The authors apply a procedure developed in their earlier work (Hodder and Jucker [17]) to solve the Nodal problem. The branch-and-bound techniques solving Problem 4.4 coupled with the nodal algorithm provides efficient solutions to the original problem. 4.1.3

Financing Decisions and the International Plant Location Problem

Hodder and Dincer [16] incorporates financing decisions into the international plant location problem under exchange rate and price uncertainties. Subsidized financing as well as favorable tax rates utilized by local governments, can be influential factors on plant location choices. Use of global financial portfolios, by borrowing and/or being long on certain currencies, can often prove to be effective financial hedges against uncertain price and exchange rate movements. Different from Hodder and Jucker [18], location and financing decisions are simultaneously made in their model. The authors consider a multinational firm which maximizes its mean–variance objective in terms of the firm’s home currency in a single period model. They follow the notation used in Hodder and Jucker [18]. There are J national markets (indexed by j) with I potential plant location countries (indexed with i). A plant can be financed by borrowing in several currencies from a set K, with Zik the amount borrowed in currency k at an interest rate rik . The per-period financing cost is random due to the exchange rate uncertainty. ek represents a fractional change from the initial exchange rate eok , defined as units of the numeraire per unit of currency k. One period financing cost for P plant i is k Zik eok (rik + ek ). To fully finance the plant, it needs to satP isfy k Zik eok = Mi , where Mi represents the cost including a provision for working capital of plant i.


101

Basic model. Similar to Hodder and Jucker [18], price uncertainty is modeled through demand uncertainty. Let di = Fi /Mi , " # X X o πi = Pij Xij − Fi − Zik ek (rik + ek ) (1 − Ti ) j

=

k

" X X i

# Pij Xij −

j

X

Zik eok (di + rik + ek ) (1 − Ti )

k

The decision maker seeks to maximize a mean–variance function by making financing decisions Zik and plant location decisions. Max V (π) = E(π) − λvar(π)

(4.7)

Subject to Xij ≥ 0, 0 Yi = 1 J X j=1 I X

j = 1, . . . , J if plant i is closed , if plant i is open

i = 1, . . . , I

Xij ≤ Ri Yi ,

i = 1, . . . , I

Xij ≤ Dj ,

j = 1, . . . , J i = 1, . . . , I k = 1, . . . , K

i=1

Zik ≥ 0, K X

( i = 1, . . . , I

Zik eok = Mi Yi

i = 1, . . . , I

k=1

where Pij is a random variable, and represents the unit selling price in market j less unit production and transportation costs as well as any adjustments for import tariffs or export taxes of plant i. The constraint PJ j=1 Xij ≤ Ri Yi , where Ri represents a potential capacity constraint on plant size, requires that there be no shipments from a closed plant. The solution of this formulation requires to simultaneously solve three interrelated problems: the optimal configurations of plants, shipment quantities, and financing pattern. Due to the mean–variance objective,

102


it results in a mixed-integer quadratic programming problem, with a large variance–covariance matrix. Solving the above formulation turns out to be computationally infeasible unless that matrix has a special form (e.g., diagonal). They propose an approximation procedure to be able to solve problems of larger size. A multifactor model. The main computational difficulty lies in the calculation of the variance term Var(π). They simplify decision variables in dimension as follows. Use g = (i − 1)J + j and h = (i − 1)K + k. Then Xg replaces Xij , where g = 1, . . . , G with G = IJ. Zh replaces Zik eok with h = 1, . . . , H and H = IK. Also, Pg = Pij (1 − Ti ) and Bh = (di + rik + ek )(1 − Ti ). Then, profit function is simplified as π=

X

X g Pg −

g

X

Zh Bh ,

h

where Pg and Bh are random variables. If Pg and Bh can be expressed as a linear combination of a reasonable number of orthogonal factors plus unique error terms, the variance–covariance matrix can be dramatically simplified. Assume Pg = ag0 + ag1 W1 + ag2 W2 + · · · + agN WN + ug

for all g

Bh = bh0 + bh1 W1 + bh2 W2 + · · · + bhN WN + vh

for all h,

where, W1 , W2 , and W3 are random, and ug and vh denote zero error terms uncorrelated with the factors and with each other. agn and bgn , n = 0, 1, 2, . . . , N are constant coefficients. Then the original mean– variance objective can be formulated as follows: Max V =

G X

ag0 Xg +

g=1

N X

XG+n E(Wn ) −

n=1

H X

bh0 Zh −

N X

ZH+n E(Wn )

n=1

h=1

 G H X X 2  −λ Xg var(ug ) + Zh2 var(vh ) g=1

+

N X n=1

h=1

# (XG+n − ZH+n )2 var(Wn ) .

(4.8)

4.2 Valuing Operational Flexibility Under Exchange Rate Risk

103

Subject to Xg ≥ 0, XG+n =

G X

g = 1, . . . , G agh Xg ,

n = 1, . . . , N

g=1

Zh ≥ 0, ZH+n =

H X

h = 1, . . . , H bhn Zh ,

n = 1, . . . , N

h=1

Yi = 0, 1, ji X

Xg < Ri Yi ,

g=J(i−1)+j I X

XJ(i−1)+j ≤ Dj ,

i = 1, . . . , I i = 1, . . . , I

j = 1, . . . , J

i=1 Ki X

Zh = Mi Yi ,

i = 1, . . . , I

h=K(i−1)+1

PH P where XG+i = G h=1 bhn Zh . g=1 agi Xg , and ZH+n = To solve (4.8), they apply a branch-and-bound procedure coupled with a quadratic programming (QP) procedure. For solving the QP the authors suggest using the existing QP package of LINDO for small size problems, and a gradient search procedure, for larger problems. The presented branch-and-bound procedures can solve problems of moderate-to-large size, adequate for most corporate application, with relatively modest computational times.

4.2 4.2.1

Valuing Operational Flexibility Under Exchange Rate Risk Designing Global Strategies: Profiting from Operational Flexibility

Kogut [21] argues that the benefit of being a multinational firm lies in the construction of operational flexibility, which allows the firm to exploit the fluctuations in exchange rates in global competition.

104


There are many sources of volatility in the world market, such as new product entries, new government policies, or new international competitors, which affect both the firm’s cost structure and its choice of technology along the value chain. Kogut focuses on a major source of uncertainty in international markets, the volatility in exchange rates, and explores how firm’s real cost of labor and the sourcing decisions are affected. According to Kogut, a firm’s global sourcing decisions influence the risk borne. Three types of risk policies, namely, the speculative, the hedged, and the flexible, are discussed. The speculative consists of betting on one sourcing site. The hedged policy refers to the strategy that a firm can reduce its risk exposure by sourcing from multiple locations. A hedged position can lead to a flexible strategy that permits the firm to exploit valuable options. One option is to invest in excess capacity in plants in multiple countries. Another option is to invest in flexible technologies that increase capital leverage but permit firms to tailor products to other markets when the production cost is relatively lower resulted from fluctuations of exchange rates. In response to exchange rates uncertainty, the multinational firm can exercise two kinds of strategic flexibility: one is the arbitrage of market imperfections, the second is leverage, by which a firm’s position in one national market is enhanced by its position in a second. Arbitrage is to exploit differences in the price of an asset, product or factor of production between markets. There are four kinds of arbitrage opportunities in global markets. They include production shifting, tax minimization, financial markets, and information arbitrage. Production shifting permits the firm to respond to movements in exchange rates. Tax minimization refers to the ability of the multinational corporation to minimize its tax bill through thoughtful adjustments of transfer prices and choice of remittance channels. Production shifting and tax minimization represent factor market and institutional arbitrage. Arbitrage in financial markets represents a combination of the two. Information arbitrage concerns arbitraging informational imperfections in product markets and transferring new product and process developments from one location to the next. Different from arbitrage, leverage is to create market or bargaining power, and enhance the strategic gaming position because of the


105

global position of the firm. There are two points of leverage gained by being global, one is through the global coordination, for example, the global firm has the ability to differentiate prices according to its world competitive posture. The second is the bargaining power captured by operating dispersed operations. To exploit these forms of operational flexibility, a firm has to create the corresponding centralized organizational structures, which is responsible for the coordination of the international activities of the firm. Centralization is constrained by the need to maintain a careful balance between local subsidiary responsiveness and the coordination of these global benefits. From this perspective, the structural configuration of dispersed investment location and market penetration is a prerequisite to the operational flexibility to respond to changes in the international environment.

4.2.2

Operational Flexibility, Global Manufacturing, and the Option Value of a Multinational Network

Kogut and Kulatilaka [22], to the best of our knowledge, were the first researchers to develop a stochastic T-period dynamic programming formulation to value the option of shifting production between two plants located in two different countries as exchange rates move. They conclude that the optimal policy displays hysteresis effects when switching is costly. The firm is subject to production cost uncertainties due to variations in exchange rate, and there is no uncertainty in output price and demand. The firm’s objective is to minimize total costs by choosing between the production locations over T periods in response to fluctuations in exchange rates. A stochastic dynamic programming model is used to evaluate the real options of owning two plants in different countries with excess capacity over the single-location alternative. The production cost in home country is normalized as 1 and the cost function of the foreign country is denoted as ψ(θ), where θ is the exchange rate. Exchange rate is modeled as a discrete variable which has the mean preserving property. The discretetime mean reverting stochastic process for the exchange rate is stated

106


as follows: ∆θt = λ(θ¯ − θt )∆t + σθt ∆Zθ , where ∆Zθ are the increments of a discrete-time Wiener process and are normally distributed with mean 0 and variance ∆t. σθt is the standard deviation of θ per unit of time, and λ is the mean reverting parameter, measuring the speed that random shock that affects the real exchange rate would be corrected. 4.2.2.1

Costless Switching

If switching between locations is costless, at the ending horizon time T , the firm chooses the location with the minimum costs over the last time period. F(θT ) = min[1, ψ(θT −1 )]. At any previous time t, F(θt ) = min[1, ψ(θt )] + ρEt F(θt+1 ),

t = 0, . . . , T

where Et is the expectation operation, and ρ is the one-period risk-free discount factor. If switching is costless, then the optimal strategy is to choose in each period the location that has the minimum production cost in that period. There exists a unique optimal threshold for exchange rate, at which the firm switches production. 4.2.2.2

Costly Switching

When switching is costly, there is a cost to switch from location i to j, as κij . If the firm operated at location 1 during the period t − 1, then the value function at t is given by F(θt , 1) = min {[1 + ρEt F(θt+1 , 1)], [−κ12 + ψ(θt ) + ρEt F(θt+1 , 2)]} , where F(θt , l) is the value of the flexible project at time t (when θt is realized), when the location l was in operation during the period t − 1. The first term inside the minimum operator is the cost if firm continues using location 1 for period t. The second term gives the cost when the firm switches to employ location 2 and incurs a cost κ12 .


107

Similarly, the value of the project when operating in location 2 during the previous period is F(θt , 2) = min {[1 − κ21 + ρEt F(θt+1 , 1)], [ψ(θt ) + ρEt F(θt+1 , 2)]} . The first term is the cost if switching to location 1 and the second term is the cost of continuing using location 2. If switching costs are zero (i.e., let κ12 = κ21 = 0), the value function F is independent of the current operating mode. Therefore, the optimal exchange rate that triggers the production switching is independent of the current operating mode. At this threshold exchange rate, the value of the two cost functions are identical. If switching is costly, a firm’s switching decision is affected by the probability distribution of future real exchange rates. A firm may decline to switch locations if it anticipates the possibility of a reversal in the relative cost advantage due to subsequent exchange rate movements. This phenomenon is called a condition of hysteresis. The hysteresis band, which measures the inertia associated with declining to switch locations, widens with the degree of uncertainty and switching costs. They generalize the formulation to more than two plants, however the model becomes intractable for multiple-exchange rate processes.

4.2.3

Valuing Operational Flexibility under Exchange Rate Risk

Huchzermeier and Cohen [19] extend the work of Cohen and Lee [7] by taking into account exchange rate uncertainties. They integrate network flow models and option valuation models, the two fundamental streams of research in global manufacturing strategy planning. The multinational firm’s objective is to maximize its expected, discounted, global after-tax value. Their work allows more than one exchange rate process, which addresses the limitations in Kogut and Kulatilaka [22] and Dasu and Li [9]. They take a two-step approach: the first step is to use a multinomial approximation model of correlated exchange rates that generates a consistent and tractable lattice model of exchange rate scenarios and transition probabilities. The second step is to solve

108


a multi-period stochastic dynamic programming problem for the valuation of the global manufacturing strategy options with switching costs. 4.2.3.1

The Multi-Period, Stochastic Dynamic Programming Model

Similar to the previous work, the option valuation problem is formulated as a stochastic dynamic program. The firm’s objective is to maximize its expected, discounted, global after-tax value by selecting the global manufacturing strategy option O, which includes decisions on supplier selections, plant capacities, product allocations to market regions, and open supply linkages from plants to market regions within the firm’s global supply chain network. The formulation is as follows: ∗ ∗ Vt (eskt , Ot−1 ) = max Pt (eskt , Ot−1 , Ot ) + αEVt+1 (˜ et+1 , Ot ) Ot ∈Ωt

∗ = max Pt (eskt , Ot−1 , Ot ) Ot ∈Ωt X +α πk,k0 · Vt+1 (esk0 ,t+1 , Ot ) es 0 ,t+1 ∈succ(esk ) k t

VT (eskT −1 , OT∗ −1 ) = max PT (eskt ,T −1 , OT∗ −1 , OT ). OT ∈ΩT

In each time period, the firm maximizes its value by selecting the global manufacturing strategy option Ot from the set of available manufacturing strategy option Ωt given that the firm adopted ∗ option Ot−1 in the preceding period and the current exchange rate scenario is eskt . α is the discount factor, succeskt is the set of the successor states of exchange rate scenario eskt , and πk,k0 is the transition probability. The single-period profit Pt accounts for both the switching costs δ and the global, after-tax profit by optimizing the single-period subproblem SPt . ∗ ∗ Pt (eskt , Ot−1 , Ot ) = δ(Ot−1 , Ot ) + SPt (eskt , Ot ).

For any given exchange rate scenario eskt and manufacturing strategy option Ot in each period, they solve a mixed-integer program


109

(the subproblem SPt ) to determine the optimal production and distribution plan for the entire supply chain network that maximizes the global, after-tax profit expressed in the numeraire currency. The objective function of SPt subproblem determines the firm’s global, after-tax profit or loss, subject to the following constraints that account for country profit or loss, corporate tax payments based on country profit or loss; country profit or loss defined as the difference between revenues, variables and fixed manufacturing costs, distribution logistics costs, and raw material costs; supply availability of components at plants; capacity limits at plants; demand limits at market regions; availability of supplier-to-plant network linkages; availability of plant-to-market network linkages; nonnegativity of losses, profits, tax payments, and decision variables (the shipment of components from a supplier to a plant, and the shipment of finished product from a plant to a market region); and integrality of binary variables that describe a global manufacturing strategy option Ot . We refer the interested readers to the original paper for a more detailed formulation. 4.2.3.2

Exchange Rate Modeling

One important contribution of this review is that the authors propose a multinomial approximation model of correlated exchange rates so that (n − 1) stochastic processes can be approximated by an n-nomial process with one degree of freedom. Therefore, the proposed framework can account for multiple correlated exchange rate processes. To model the two-exchange rate case (indexed with i and j), they work with the trinomial approximation model. Define u and d as the size of the up- or down-movement of a particular exchange rate process. The trinomial approximation assume that for any exchange rate scenario eskt = (eikt , ejkt ) at time t, there are three successor scenarios at time t + 1, i.e., es1,t+1 = (ui eikt ; uj ejkt ), es2,t+1 = (di eikt ; uj ejkt ), and es2,t+1 = (di eikt ; dj ejkt ) with transition probabilities (1 − p), p(1 − ), and p, respectively. The size of the up- and down-movement as well as the transition probabilities can be solved through a set of equations using the mean (µi , µj ) and standard deviation (σi , σj ) of the

110


underlying stochastic processes. Let ρij denote the coefficient of correlation. The set of equation are as follows: pdi + (1 − p)ui (p)dj + (1 − p)µj pd2i + (1 − p)µ2i − [µi (∆t )]2 (p)d2j + (1 − p)µ2j − [µj (∆t )]2 (p)di dj + p(1 − )di uj + (1 − p)ui uj − [µi (∆t)][µj (∆t)]

= = = = =

µi (∆t ) µj (∆t ) σi2 ∆t σj2 ∆t ρij σi σj ∆t .

(4.9) Combined with an additional constraint, u = 1/d, which forces the upand down-movements to be symmetric, the probability can be uniquely determined. The authors generalize the approximation model to the (n − 1) exchange rate case. Similarly, the set of equations are formulated using n − 1 equations for the mean, (n − 1)+(n − 2) equations for the variance and co-variance terms of the exchange rate processes. The transition probabilities π1 through πn−1 can be solved and they are always positive. 4.2.3.3

Value of Operational Flexibility

They construct various numerical examples by considering 16 different supply chain network designs for an American firm operating in Asia, United States, and Europe. Each manufacturing strategy option specifies the location of the supply, production plants, and market distribution. Through these numerical examples, they demonstrate the value of operational flexibility that a multinational firm can switch to alternative manufacturing strategy options to respond to changes in exchange rates. The financial hedging with forward contracts protected the firm from downside risk, but the firm also loses the upside potential. Contrary to financial options, operational hedging resulted from the firm’s switching capability controls the downside risk, exploits the volatility of the firm’s cash flows, and increases the firm’s value. Furthermore, operational hedging can create an effective hedge in the long term, while financial hedging can be used to reduce the variability of the firm’s cash flows in the short term.


4.2.4

111

Optimal Operating Policies in the Presence of Exchange Rate Variability

Dasu and Li [9] generalize the work of Kogut and Kulatilaka [22] by having both plants to produce every period to satisfy demand. The multinational firm is obliged to meet a deterministic and stationary demand each period. The firm carries extra capacity in the network, and decides when and by how much to alter the magnitude of the production quantities to minimize total cost, which is composed of variable production costs and switch-over costs. They study the structure of the optimal production allocation policies. They build a two-plant, two-country model. Let Ki be the capacity of the plant in country i, i = 1, 2. At each period, the firm meets a demand of D units. The firm keeps surplus capacity S in the network, i.e., K1 + K2 = D + S, and has the option of shifting production volumes to minimize its total cost in response to the exchange rate movement. Each plant must produce at least Ki − S units, and the firm’s decision is to determine how the S units of excess capacity are to be allocated between the plants. Let α denote the risk-free discount factor, the operating problem as the following infinite horizon stochastic dynamic program: ( ) X 0 V (θ, y) = min φ(θ, x) + s(y, x) + α Pθ,θ0 V (θ , i) , 0≤x≤S

θ0

where V (θ, y) is the lowest expected cost over the infinite horizon given that plant 1 produced K1 − S + y units in the previous period and the prevailing exchange rate is θ. The exchange rate is modeled as a discrete time Markov process θt . The transition probabilities are denoted by the matrix P , where Pθ,θ0 represents the probability that the exchange rate changes from θ to θ0 in the next period. φ(θ, x) is the total single period production cost with plant 1 producing K1 − S + x units and plant 2 K2 − x units. Production shifting from one plant to the other is costly, and s(y, x) is the switch-over cost from production allocation y to allocation x. When the switch-over costs are linear or step functions, they show that the optimal policy is a barrier policy for concave or piece-wise

112


linear convex variable production costs. The optimal barriers can be determined by linear programming techniques. The expected costs in the infinite-horizon problem can be obtained by solving a system of linear equations. 4.2.4.1

Concave Production Costs

If both the production cost φ(θ, ·) and switch-over cost δ(·) are concave, the structure of the optimal allocation policy is such that depending on the initial allocation, x may never be changed from its initial level. If the allocation level is ever changed from the initial levels, then there exists an optimal solution in which x is always either 0 or S. If in some period the allocation variable x equals 0 or S, then from then on, x can be restricted to the set {0, S}. Under certain assumptions on the production cost function and transition matrix, the optimal policy is a monotone two-barrier policy. Denote the optimal barriers by L∗ and U ∗ . The barrier size increases in the switch-over cost, volatility of the exchange rate, decreases in the discount factor, and is also affected by the production costs structures. 4.2.4.2

Convex Production Costs

If production can be switched between plants with no cost, it is optimal for plant 1 to produce K1 − S + x∗ (θ) for each period. Assuming production switching is costly, there exist two critical points x1 (θ) ≤ x∗ (θ) ≤ x2 (θ). The structure of the optimal policy is as follows: If the production in previous period is in the range of [x1 (θ), x2 (θ)], then no change is made so as to reduce any unnecessary switch-over cost. If the previous period’s production does not lie in the range [x1 (θ), x2 (θ)], then a partial adjustment is made to bring the production level back to x1 (θ) if the allocation in the previous period falls below the lower bound of the range, or to x2 (θ) if the allocation in the previous period exceeds the upper bound of the range. Under certain assumptions on the production cost function and transition matrix, the optimal policy is a monotone hysteretic policy. Furthermore, if they assume that the cost function is piece-wise linear and convex in x, and the switch-over cost is either linear or a step function, there is an optimal

4.3 Local Content Rules

113

policy in which the quantity produced at plant 1 belongs to the set: [K1 − S + βi ], where βi s are the boundaries of the piece-wise linear functions, partitioning the region [0, S] into m intervals [βi , βi+1 ] with 0 = β1 < β2 < · · · < βm+1 = S. Dasu and Li [9] extend their results to the multi-country, multimarket problem, the generalized problem is formulated with the following structure: ( ) X v(θ, j) = min φ(θ, i) + s(j, i) + α Pθ,θ0 v(θ, i) . i∈{1,...,m}

θ0

The optimal policy is still a barrier policy, and the firm has to choose from a finite set of options.

4.3

Local Content Rules

Many governments (or regional trade agreements, like NAFTA) have set local content rules for companies that wish to operate in their country (or within the protected region by the trade agreement). Local content rules require manufacturers to purchase a certain amount of components from suppliers located in that country (or the protected region). Munson and Rosenblatt [29] develop models to design global sourcing networks satisfying local content rules. Local content is defined either in volume or value terms. A physical content protection scheme requires a fraction of the total number of components or raw materials used to produce the final good to be of domestic origin. A value-based content protection scheme requires the value of locally manufactured components to be at least as large as a specified percentage of either the value of all purchased parts or of the final good’s value. 4.3.1

Single-Plant Model: The Value-Based Local Content Rule

First, the authors consider a single-plant model to illustrate the financial impact of a local content rule on a single plant under no supplier capacity constraints. The key decisions are to determine the set of suppliers and the percentage of each component’s total demand that each

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Table 4.2 Notation for single-plant model. i = a component used in the production of the final product, i = 1, . . . , I, k = a potential supplier, k = 1, . . . , K, Cik = delivered unit purchase cost of component i sourced from supplier k, R = periodic demand for the final product, Mi = number of units of component i used to produce one final product, L(i) = the set of local suppliers that can supply component i, α = the local content percentage, xik = amount of component i sourced from supplier k.

supplier provides. (Notation is provided in Table 4.2). XX Minimize Cik Xik i

(Single-Plant)

k

Subject to X

∀i

Xik = RMi

k

X X

Cik Xik ≥ α

P P i

k Cik Xik

i k∈L(i)

Xik ≥ 0

∀i, k,

Let h(i) represent the supplier in the host country offering the cheapest delivered price and let g(i) represent the cheapest global supplier. Define new decision variables Zik as the percentage of component i that is sourced from supplier k. For notational convenience, the subscript ih(i) and ig(i) have been written as ih and ig. Zih is the percentage of component i sourced from the cheapest local supplier, and Zig is the percentage of component i sourced from the cheapest global supplier, respectively. Note that Xik = Zik RMi , and Zih = 1 − Zig . X X Maximize (Cih Zih + Cig Zig )RMi = RMi (Cih − Cig )Zig i

i

(Capacited Single-Plant) Subject to X

Mi [(1 − α)Cih + αCig ]Zig ≤ (1 − α)

i

X

Mi Cih

i

0 ≤ Zig ≤ 1

∀i


115

The optimal solution to this type of knapsack problem can be solved efficiently via pseudopolynomial algorithms. Recall the general form of a knap-sack problem is as follows: X Maximize ci Zig (Knapsack) i

Subject to

X

ai Zig ≤ b

i

0 ≤ Zig ≤ 1

for i = 1, . . . , I,

where ci , ai , and b are constants. When ai > 0 and ci ≥ 0, knapsack problem can be solved as follows. First, rank the items in a nonincreasing order of the efficiency ratio ci /ai . Brackets are used to denote the position in this ranking. [1] represents the item with the largest value of ci /ai , and [I] represents the item with the smallest value of ci /ai . Next, P define p as the smallest integer (0 ≤ p ≤ I) such that [i]≤p a[i] ≥ b. Then,   [i] < p  1 if P Z[i]g = (b − [q]
p and the percentage allocated to the cheapest local supplier is Z[i]h = 1 − Z[i]g . The solution to the single plant model is obtained by (1) ranking the components in a nonincreasing order of the effective ratio Cih /Cig , P (2) computing p as the smallest integer such that [i]≤p M[i] [(1 − P α)C[i]h + αC[i]g ] ≥ (1 − α) i Mi Cih , and (3) computing Z[i]g and Z[i]h as defined above. Properties of the Single Plant Model: (1) There is at most one component that will be sourced from two suppliers. (2) The ranking of the components is based only on the relative “cost penalty” of using the cheapest delivered local supplier versus the cheapest delivered worldwide supplier. (3) The optimal percentage of demand to be purchased locally for each component are independent of the demand for the final product at the plant.

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4.3.2

Other Local Content Rules

Other local content rules can easily be incorporated into the model. We label Rule 1 as the one described in Section 4.3.1. Rule 1 is the value-based scheme where the value of local purchases must be at least as large as a percentage of values of total purchases. Rule 2 is the value-based scheme where the value of local purchases must be at least as large as a percentage of the final product’s value, P P that is, Rule 2 results in the following constraint i k∈L(i) Cik Xik ≥ P P α(P + i k Cik Xik ), where P represents the final product’s unit production cost (net of component purchasing costs). Rule 3 is the physical content protection scheme, that is, Rule 3 results in the folP P P P lowing constraint i k∈L(i) Xik ≥ α i k Xik . Table 4.3 summarizes the single plant solution parameters for the three local content rules. Key observations from comparisons of the three rules: (1) For Rule 2, if the value of b in Table 4.3 is negative, then with even 100% locally purchased parts, the local content rules will still be violated. (2) For the same percentage requirement α, Rule 2 requires a higher number of locally procured components than Rule 1. (3) For Rule 3, the ranking is based on absolute, not the relative “cost penalty” of purchasing from the cheapest local supplier as opposed to the cheapest worldwide supplier. 4.3.3

Multi-Plant Models and Local Content Rules

For the multi-plant model, Munson and Rosenblatt [29] relax the assumption of no supplier capacity constraints. Each potential country of production has its own local content percentage. For simplicity, they assume that at most one plant will be located in each country. The Table 4.3 The single plant solution parameters for the three local content rules. Rule 1 Rule 2 Rule 3

ai Mi [(1 − α)Cih + αCig ] Mi [(1 − α)Cih + αCig ] Mi

P P P

b (1 − α) i Mi Cih (1 − α) i Mi Cih − αP (1 − α) i Mi

Ranking formula Cih /Cig Cih /Cig Cih − Cig


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Table 4.4 Notation for multi-plant model. j = a potential country of production of the final product, j = 1, . . . , J, l = a customer, l = 1, . . . , L, Sil = amount of final product produced in country j and shipped to customer l, Tjl = unit transportation cost of the product from the plant in country j to customer l, Xijk = amount of component i used for production in country j sourced from supplier k, Cijk = delivered purchase cost of component i used in country j sourced from supplier k, Pj = final product’s unit production cost (net of component purchasing costs) in country j, Fj = periodic fixed cost associated with opening and operating a plant in country j, Dl = periodic demand of customer l for the final product, Kik = periodic demand of supplier k for the production of component i, L(i, j) = the set of local suppliers k for the production of component i, αj = country j 0 s local content percentage, Yj = 1 if a plant is built in country j and 0 otherwise.

problem is formulated as follows: (Notation is provided in Table 4.4.) " # X XX X Minimize Cijk Xijk + (Pj + Tjl )Sjl + Fj Yj j

i

k

l

(Multi-Plant) Subject to X

∀l

Sjl = Dl

j

X

Xijk = Mi

X

k

∀i, j

Sjl

l

X

Xijk ≤ Kik

∀i, k

j

X

Sjl ≤ Yj

l

X X

X

∀j

Dl

l

Cijk Xijk ≥ αj

i k∈L(i,j)

XX i

Sjl , Xijk ≥ 0 Yj = {0, 1}

Cijk Xijk

∀j

k

∀i, j, k, l ∀j

118


Although the elegant knapsack solution structure is lost, the managerial insights of single-plant model still apply to the multi-plant model. For a value-based content rule, firms will choose local suppliers with small per-unit cost penalties. Two special cases of multi-plant model with local content rules can be solved efficiently: Special Case 1: Plant location with local content requirements. Assume there exist no supplier capacity constraints, then the problem formulated in (Multi-Plant) turns into a plant location problem with the supplier selection alternatives for each component to satisfy local content rules. According to the third property of (Single-Plant) model in Section 4.3.1, the supplier selection decision at a given plant is independent of demand for the final product at that plant. Therefore, we can calculate the unit variable cost per unit at each plant j with no information on the demand that will be allocated to that plant, which equals P Pj + i Mi [Cijg + Zijh (Cijh − Cijg )], where Zijh is the percentage of component i used for production in country j sourced from the cheapest supplier in the host country. Then use the fast single plant solution method for each plant separately to determine the value of each Zijh variable. Finally use the average variable cost per unit at each plant as defined above for solving the plant location model with the efficient algorithm in Efroymson and Ray [11]. Special Case 2: Predetermined plant locations. In this case, the binary variables Yj are predetermined and the original problem shrinks to be a linear program with no integer restrictions, and it can be solved efficiently for large problems. 4.3.4

Managerial Insights

In their numerical studies, the authors consider a single-plant producing with several components under local content constraints. As local

4.4 Transfer Pricing Schemes

119

content percentage goes up, the plant increasingly prefers sourcing from local suppliers and the changes become much greater for high values of the local content percentage. On the other hand, when government sets too high a local content percentage, it may cause companies to shift production to other countries and eventually become detrimental to local suppliers rather than helpful and lead to a reduced production investment in the country.

4.4

Transfer Pricing Schemes

Transfer pricing schemes play a very important role in global supply chain coordination and management, as pointed out in Cohen and Lee [7] (see Section 2.4). In our further discussion, we use the “transfer price” definition given in Villegas and Ouenniche [41]: a “transfer price” is the price used for intra-firm trade of resources, goods, and services between subsidiaries or divisions of a multinational firm. Global firms can, and often do, manipulate taxes by transfer pricing schemes, e.g., the right transfer price can be applied to redistribute resources and profits, so that most of the profit is made in a country with low taxes. On the other hand, governments try to prevent such transfer price “manipulation” by imposing penalties and setting regulatory control polices, because transfer pricing may have adverse effects on employment levels, consumer prices, factor incomes and the balance of payments. Therefore, multinationals must optimally set the transfer pricing scheme within the government’s control. Villegas and Ouenniche [41] present an unconstrained mathematical programming model to help managers of multinationals understand the transfer pricing decisions as well as decisions on trade quantities and transportation cost allocation. To explore the decision making process, we have to first understand the relationship between a division and the headquarter of a multinational firm. They are tied up in two ways: a division may be entirely owned by the corporation, then it is called unincorporated, and is considered for tax purposes as the same legal entity as the headquarters. The earnings of an unincorporated division are fully repatriated by the headquarters after taxes. If a division is a

120


separate legal entity, then it is called incorporated and a different tax scheme is used. The repatriation of earnings from the incorporated division to the headquarter is achieved by paying royalties and dividends, which are taxable by the home country but may or may not be taxable by the host country depending on the treaty between the two countries. 4.4.1

Detailed Model Formulation

The multinational firm’s goal is to maximize repatriated earnings from the corporate headquarter’s perspective by making decisions on trade quantities, transfer pricing, and transportation cost allocation. The authors present a comprehensive model that takes into account production costs, transportation costs, import tariff, duty drawback, royalties and dividends, exchange rate risk exposure, illegal manipulation of transfer prices related penalties, percentage of headquarters ownership of a division, income tax and withholding tax rates, and the difference between importing and exporting decisions. From the corporate headquarters’ perspective, the objective function is formulated as follows: CE(Corporate earnings) = After tax earnings from unincorporated divisions + After tax earnings from incorporated divisions + Repatriated royalties after withholding taxes + Tax difference/deficit to pay to the home country where divisional earnings paid to the host country are DE(Divisional earnings) = (1 − Tax Rate)(Total Divisional Revenue −Total Divisional Cost) Total Divisional Revenue (TDR) includes sales in intra-firm markets and sales in external markets. Total Divisional Cost (TDC) includes production and purchase costs, import tariffs, transportation costs, duty drawbacks, cost of currency fluctuations and penalty costs.

4.4 Transfer Pricing Schemes

121

In the literature, a common treatment of transportation cost is to model it as a part of purchase price or transfer price and assumed that it is paid by the buyer. The authors’ treatment of transportation costs is to model it explicitly, and the firm makes decisions on whether to allocate the costs to the sender (division) or the buyer (division) based on the tax trade-offs. Importing goods and exporting goods have distinct effects on duty drawbacks. Let us examine how they model the duty drawbacks. Duty drawbacks are also explicitly defined and modeled by Arntzen et al. [2] (see Section 3.4). The amount of duty drawback depends on the value added locally for imports, and the value added abroad on exports for the proportion of imports that is exported. For example, the percentage of a certain importing goods that are exported is denoted as r. value of a product has been added locally by a percentage of the total value (v), and abroad by (1 − v). Therefore, duty drawbacks from imports are Tariff Rate·v, and duty drawbacks from exports are Tariff Rate·r(1 − v). Penalties are imposed by governments to avoid manipulations. The mechanism proposed in this work is implemented by a probabilistic function that measures the extent to which the transfer prices set by a multinational deviating from a preset range. No penalty cost on exports is imposed if the multinational sets the price higher than the predefined upper bound, a full penalty cost is imposed if the price is lower than the lower bound, and a partial penalty if the price falls in the range. Similarly, no penalty costs on imports are imposed if the price is set lower than the lower bound, a full penalty cost is imposed if the price is higher than the upper bound, and a partial penalty if the price falls in the range. Their model also incorporate the exchange rate risk associated with currency fluctuations. They assume part of the risk can be hedged at a hedging cost and the rest is a random variable which results in a currency fluctuation exposure cost. Another factor they take into account is the tax deficit cost that a headquarter is required to pay. This tax deficit cost is the tax difference between local and foreign income tax, when the foreign tax rate charged by the host country of a division is lower than that charged by the home country.

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4.4.2

Managerial Insights

The resulting nonlinear mathematical programming formulation is solved via the Karush–Kuhn–Tucker the KKT optimality conditions. The KKT optimality conditions lead to the following insights: First, when no exchange risks and penalty risks are considered, the optimal decisions have the following properties: (1) Transfer price for imports must be set at the lowest possible level due to the adverse effects of the tax differential rate. Transfer price for exports will be set at the upper bound if the tax differential rate is significantly favorable, (i.e., the tax differential between the parent country and the host country is high enough to compensate the increment on tariffs due to a higher export price and the cost of repatriate dividends from the foreign subsidiary), and will be set at the lower bound, otherwise. (2) Managers will fully allocate the transportation costs to the sender on imports and the receiver on exports, but never allocate between them. (3) Based on their formulation, transfer prices are independent of decisions of trade quantities or transportation costs, and transportation cost can be determined independently of decisions on trade quantities and transfer price. Second, when exchange risk and penalty risk are considered, the optimal decisions have the following properties: • Transfer prices of imports and exports may have interior solutions due to the new trade-offs brought by exchange risks and penalty risks. • Properties 2 and 3 in the first scenario do not hold in this scenario.

4.5

Taxation and Other Factors

Kouvelis et al. [25] focus on special cases of the model introduced in Section 3.1 to obtain useful insights on the nature of international

4.5 Taxation and Other Factors

123

facility networks for various environments. They demonstrate the dominating effects of financing, taxation, regional trading zones, and local content rules on the structure of global facility networks. The special cases are designed to simplify the settings. They relax the capacity constraints on plants and DCs and assume straight-line depreciation. They consider “identical time periods” and “identical countries” in the sense that the final product has the same demand and price of the final product, equal tax rates, and depreciation rate, in each country for any time period. The final product consists of “identical subassemblies,” in terms of revenue and cost parameters. Assume that only one plant of each subassembly type will be built. Also, there is no differentiation among subassembly plants or DCs. A trade tariff is charged on flows crossing their borders. 4.5.1

Base Case: Tariff and Transportation Costs

Kouvelis et al. [25] start with the base case in which they assume no financing and equal tax rates across countries. Without loss of generality, assume that a DC can be constructed in every market. The transportation costs within the countries are C per unit of final product. Transportation costs per unit of final product across borders equal C(1 + δ), δ > 0 taking into account the trade tariff. Assume that the transfer prices p are the same for all subassemblies. Construction of Plants and DCs: For the case of identical plants and identical countries, the authors conclude that it is preferable to build all plants in one country, and it is preferable to either build a single DC in the country where all plants are located or to construct DCs in all countries. The decision on how many DCs to build is to compare which one is more expensive, to transport the subassemblies individually or to transport the final product. When transportation of subassemblies is more expensive, firms prefer a single DC (i.e., a centralized manufacturing and distribution structure). When transportation of the final product is more expensive and there exists a substantial demand in foreign markets, it is preferable to open a DC in each one of the markets (i.e., a decentralized distribution structure) and transport subassemblies from

124


the subassembly manufacturing plants given a substantial demand in foreign markets. As the transportation cost element between countries and/or cross-border flow government imposed penalties increase firms tend to open DCs in markets away from the manufacturing facilities. 4.5.2

Government Incentives: Financing and Taxation

Then, the authors relax the assumptions of no financing and equal tax rates. They find that governments can attract DC investments in such environments by offering financing help through loans. Financing affects a firm’s facility investment as follows: For the case of identical plants and identical countries, if only one country offers attractive financing for facility construction with an attractive interest rate, then all plants and a DC will be built in that country. The level of the facility investment in the country by a firm is nondecreasing with the level of subsidized financing. To explore how tax rates affect a firm’s facility investment, the authors examine the situation where one country charges a lower tax rate than the rate of other countries. They conclude that if there is only one DC, the plants and the DC are located in the country with the lower tax rate. If more than one DC is open, the plants and the DC serving any market without a DC will be located in the country with the lower tax rate. For the case of identical plants and identical countries, if one country offers a lower tax rate than the rest, all plants will be built in that country. It is preferable to either build a single DC in the lower tax rate country or to construct DCs in all countries. According to their findings, a country can induce firms to invest in plants and/or DCs by lowering its tax rate. Further, the demand flowing through existing DCs in that country may increase. 4.5.3

Tariff Structure: Regional Trading Zones and Local Content Rules

Kouvelis et al. [25] also examine how tariff structure affects a firm’s global facility investment. Regional trading zones agreements allow for tariff-free trade among nations that belong to the pact. The authors

4.5 Taxation and Other Factors

125

conclude that if the firm’s sourcing countries belong to different tarifffree trade zones, then no more than one DC should be located in each trading zone, and all plants should be built in any of the countries that form the trading zone which contains the most countries. Further, with the existence of the regional trading zones, the centralization/decentralization distribution network configuration decision is more sensitive to the relative transportation costs of subassemblies and the final product, compared to the base case. That is, if it is more (less) expensive to transport the subassembly individually than to transport the final product, then a completely centralized distributed network, with only one DC, is more likely (less likely) to be optimal than for the case without tariff-free zones. With the existence of regional trading zones, when the transportation cost structure leads to a decentralized distribution network, the distribution network becomes decentralized over trading zones (instead of countries) but centralized within each trading zone (so called “regionalized”). On the other hand, when it leads to a centralized one, the existence of trading zones will more likely result in all facilities in one location. Therefore, trading zones that offer the best incentives have the potential to attract investments. Discussion on the effects of local content rules also appears in Kouvelis et al. [25]. We have introduced local content rules in Section 4.3. Consider a value-based local content rule that impose a tariff δ for domestic shipment from the DC if the local content rule is violated. The final product is treated as an imported goods if the firm cannot meet the value-based rule. Under the assumption of “identical” countries, if one government introduces a local content rule, then a DC and all plants will be diverted to that country. The authors examine the situation where there are two candidate countries to build plants and DCs, one of the countries, country A with a lower tax rate, and country B imposing a local content rule in order to attract investments. There are two possible outcomes: (1) if it is optimal to have a completely centralized distribution network, prior to the introduction of any local content rules, then country A will have all of the facilities according to previous analysis. The local content rule enforced by country B has no effect because the firm currently has no

126


DC in country B. (2) If it is optimal for each country to have a DC, and all plants are located in country A, prior to the introduction of the local content rule, country B will “force” some of the plants to move to that country by the local content rule. The number of the plants is the smallest number such that the firm still meets the local content requirement. The authors warn that if the local content percentage imposed by country B becomes too greedy, it will result in the closing of all plants and DCs in that country. This is in agreement with similar insights in the Munson and Rosenblatt [29] work.

5 Classification Scheme

We will first discuss previous research survey papers on the topic of the global supply chain design, for Global Supply Chain Design research, as each one of them allows us to examine the literature from different perspectives, and highlight different aspects and methodological or managerial insights. Our discussion will be highly selective in the summary of the results of those papers (as the reader should be referring to these originals for more detail), and it will only depict results of papers not previously discussed and relevant to the scope of our current paper.

5.1

Previous Research Surveys: Global Manufacturing Strategy Literature

Verter and Dincer [38] envision facility location, capacity acquisition, and technology selection decisions as building blocks for designing global manufacturing strategies. In literature, these three kinds of problems were dealt with separately. The authors recognize the technical feasibility for a synthesis approach and consider it important for the design of effective global manufacturing strategies to develop an integrated model. In their review on stochastic international plant 127

128

Classification Scheme

location problems, they indicate that import tariffs and quotas, differential tax rates and subsidized financing have a significant effect on internal manufacturing strategies. They highlight the models in the literature that integrate the international location and financing decisions, when firms face price uncertainty and exchange rate uncertainty. We have already summarized and presented most of the important results of this literature in Sections 3 and 4. Vidal and Goetschalckx [39] define three levels of supply chain planning, namely, strategic, tactical, and operational. The strategic level planning involves deciding the configuration of the network. The tactical level planning involves deciding the aggregate quantities and material flows for purchasing, processing, and distribution of products. The operational level planning involves short-term decisions and detailed arrangements. Their review focuses on the strategic global supply chain network design models. They summarized the optimization models, and especially reviewed the popular modeling approach widely used in production–distribution models, the mixed-integer programming technique. From an optimization modeling perspective, they summarize in a table for selected papers in the literature, the model characteristics, such as stochastic factors, objective functions, cost structures,constraints, and key decisions considered in each paper. Another classification effort presented in their paper is to categorize the selected papers by the main international issues considered in their models. One of the future research they suggest is to examine important stochastic aspects of a global supply chain, such as customer service level and lead times. Both of their classifications are insightful, and we refer the reader to the original paper for their review.

5.2

Stochastic Global Facility Location Models

As identified in the literature, uncertainty plays a key role in design of the global supply chain structure. In this section, we will briefly review some latest papers that model uncertainties within a global facility location or supply chain design context. Snyder [32] presents a comprehensive review of the literature that incorporates uncertainty into the facility location models. The author

5.2 Stochastic Global Facility Location Models

129

reviews stochastic and robust location models. Stochastic optimization models work with uncertain parameters whose values follow a known probability distributions. Robust optimization models work with parameters that are uncertain and no probabilistic information is available. The author illustrates the applications of these two types of models in the facility location literature. The presented taxonomy is based on types of uncertainties under consideration and measures of optimality (objectives) under uncertainty. The review makes us aware that very few of the models have been applied to real-world problems due to the cumbersome data requirements of many of the stochastic models. To reduce the data and computational burden, the author identified four fruitful research avenues by applying today’s available OR (Operations Research) technology: (1) exact algorithms for minimax problems; (2) multi-echelon models; (3) Stochastic programming technology; and (4) Meta-heuristics for general problems. 5.2.1

Risk Measures

As summarized in Snyder [32], there are a rich variety of approaches to measure the optimality under uncertainty. Velarde and Laguna [36] present a formulation and a solution procedure of the robust international sourcing problem when suppliers have capacity constraints and face demand and exchange rate uncertainty. Their work is heavily based on, and extends, the work of Gutierrez and Kouvelis [14](see Section 3.3) by modeling uncertainty via a bigger set of scenarios and using an objective function that combines the total expected cost and a measure of downside risk (only penalizing undesirable deviations). This approach is different from measuring the total risk done by the mean–variance approach proposed in Hodder and Jucker [18] and Hodder and Dincer [16] (see Section 4.1). The authors propose a heuristic based on Benders decomposition and tabu search, which yields acceptable solutions. Butler et al. [5] present a robust optimization approach for a supply chain design of new products, constrained by the manufacturer’s long term financial viability, under the situation where the supply chain is exposed to uncertainty in demand, selling price, fixed facility

130


costs, production costs, transportation costs, and capacity. The authors divide robust supply chain models into two categories: regret models (e.g., Gutierrez and Kouvelis [14] in Section 3.3) and variability models (e.g., Hodder and Jucker [18] in Section 4.1). Regret models measure the difference between the cost of the chosen solution and the cost of the optimal solution for a certain scenario. Variability models control the spread of the costs by adding standard deviation, variance, or other measures to the objective function. The authors take the regret approach to avoid penalizing firms for their upside potential and driving all solutions toward the average outcome. Similar to Velarde and Laguna [36], their approach (called “Robust Lagrangian” model) is to optimize an objective that combines the expected profit and a weighted penalty for the unfavorable regret. The authors claim that their model generalizes many of the previous robust optimization models in the literature, including both worst-case and expected value models, and both regret and variability models. Recent work of Chen et al. [6] on strategic facility location design under uncertainty is another example of regret model. They present a new risk measure called α-reliable Mean-excess regret in the context of stochastic p-median problem, and the firm’s objective is to minimize the expected regret with respect to an endogenously selected subset of worst-case scenarios whose collective probability of occurrence is no more than 1 − α. The classical deterministic p-median problem is to minimize the sum of demand weighted distance between demand nodes and facilities by locating p facilities relative to a set of demand nodes. In the stochastic version of p-median problem considered in their work, demands at the demand nodes are uncertain and the distances between demand nodes and facilities are stochastic. The uncertainty is modeled via a set of scenarios with probabilities. α-reliable Mean-excess regret model improves the previously proposed risk measure called the α-reliable Minimax regret by Dskin et al. [8], both applying to p-median problem. In this earlier approach, the maximum regret is computed over an endogenously selected subset of scenarios, called the reliability set, whose collective probability of occurrence is at least α. Therefore, the firm is 100α% confident that the regret realized will be no more than that found by the model. Clearly, the α-reliable Minimax


131

regret model ignores the possibility that the regrets associated with the scenarios that are not included in the α-reliable set are much higher than the α-reliable maximum regret. The new approach α-reliable Mean-excess regret accounts for the magnitude of regrets in the worst-case scenarios, and minimizes the expectation of the regrets associated with the scenarios in the tail, which has a collective probability of 1 − α. Moreover, the mean-excess risk measure is coherent and computationally efficient. Their computational experiments show that the α-reliable Mean-excess measure matches the α-reliable Minimax criterion closely. Therefore, the α-reliable Mean-excess criterion can be used to obtain an approximate solution to the α-reliable Minimax criterion.

5.2.2

Two-Stage Stochastic Programs for Global Supply Chain Planning

Alonso-Ayuso et al. [1] present a general framework for global supply chain strategic planning, which emphasizes the design of the sourcing and production stages (see Figure 2.1) of the global supply chains under uncertainty. The uncertainty is in product price and demand, raw material cost and production costs. Uncertain parameters are modeled by a set of scenarios, each assigned with the weight representing the likelihood that a certain scenario happens. They propose a two-stage stochastic 0–1 program: At Stage 1, the firm makes strategic decisions in the form of binary variables, deciding the supply chain topology before uncertainties are resolved. At Stage 2, after observing the uncertainties, the firm makes tactical decisions on utilizing the resources invested at Stage 1, such that constraints, for example, demand requirements and material flow constraints, are met at minimum cost. Their objective is to maximize the expected profit over the time horizon minus the investment depreciation and operation costs. They propose a two-stage version of a Brand and Fix Coordination (BFC) algorithmic approach to solve the two-stage problem. Computational results for very large instances (involving 6 plants, 12 products, 24 markets, and 23 scenarios) are reported. In contrast to the scenario-based analysis in Alonso-Ayuso et al. [1], Santoso et al. [30] model uncertainties continuously, with a known joint

132


distribution. They also propose a two-stage stochastic programming model for global supply chain network design, under uncertainty in costs, demands, supplies, and capacities. The firm’s objective is to minimize the total investment costs, expected future operational costs, and demand shortage penalty, by making strategic level decisions in the supply chain configuration (decisions on which of the processing centers to build and which of the machines to procure) and tactical level decisions based on the configuration for each realized scenario. The continuous randomness results in an infinite number of scenarios, which represent a solution challenge to solve based on the available algorithms in the literature often viable for a modest number of scenarios. By integrating a sampling strategy with an accelerated Benders decomposition algorithm, the authors solve supply chain network design problems of realistic size through the use of the sample average approximation (SAA) scheme. The effectiveness of the proposed solution strategy is highlighted by their computational study. Vidal and Goetschalckx [40] highlight the importance of modeling the uncertainties in the design of global supply chain, and discuss the limitations of the mixed-integer programming techniques when the underlying system experiences significant variability. The authors provide mechanisms in modeling the supplier reliability and international transportation lead times. They develop a simple MIP model, and demonstrate how the global supply chain design is affected by uncertainty in exchange rates, changing demand, supplier reliability, and international transportation lead times, through extensive sensitivity analysis.

5.2.3

Supply Chain Network Design Model on Strategic Level with Demand Choice Flexibility

Shen [31] also presents a supply chain configuration model from the strategic point of view. A profit-maximizing firm can set different sales prices for different region to choose whether to satisfy a customer’s demand. The firm makes decisions not only on location and customer-DC (Distribution Center) assignment, but also production and inventory related decisions within a supply chain network. Given a


133

production site, a set of customers and a set of candidate DC locations, the decision maker wants to determine (i) the number and locations of the DCs, (ii) the assignments of customers to DCs, (iii) the inventory replenishment strategy at each DC, and (iv) the inventory replenishment strategy at each region associated with a particular DC. The profit equals to the revenue minus the total cost, which includes the DC location cost, inventory holding cost at DCs, and delivery cost to DCs. A delivery cost will also be charged to a customer based on the distance between the customer and the DC that serves the customer. Each customer has a reserve price, and if the actual price charged by the firm is higher than the reserve price, the firm will lose this customer to competition. The problem is formulated as a set-covering program,1 and a branch-and-price algorithm — a variant of branch-and-bound in which the nodes are processed by solving linear-programming relaxations via column-generation — is presented to solve this model. Their numerical study shows that allowing flexibility on satisfying customer demands results higher profit compared with the “serve-all model” (a traditional supply chain design model in which all customers’ demands have to be satisfied). The model is also generalized to deal with random customer demand. They assume that the mean and variance of the demand are known, and inventory is managed through a continuous review policy (R, Q), where an order of size Q (Economic Order Quantity) is placed whenever the inventory level reaches R. They are able to solve this problem efficiently as in the deterministic demand case. 5.2.4

Computational Improvements for Global Logistic Models

Heavy computational burden prevents the wide applications of robust optimization models in practice. In an effort to bridge this gap in the literature, Yu and Li [43] proposed an improved method to solve stochastic optimization problems using the robust programming 1 The

set covering problem is a classical question in computer science and complexity theory. As input you are given several sets. They may have some elements in common. You must select a minimum number of these sets so that the sets you have picked contain all the elements that are contained in any of the sets in the input. It was one of Karp’s 21 NP-complete problems shown to be NP-complete in 1972. (Source: Wikipedia)

134


approach. They consider a large-scale logistics model with scenariobased data having the probability of occurrence. The objective function is formulated as follows: minimize E[cost] + λVar[cost] + ω[feasibility penalty], where feasibility penalty is imposed due to the violations of the control constraints. To enhance the computational efficiency, their approach is to add n + m artificial variables (where n and m are the number of scenarios and total control constraints, respectively) to transform the problem into a linear program. The proposed robust programming method improves the methods existing in literature, which require adding 2n + 2m variables. There are two limitations with the newly proposed method: it requires linear objective function under each scenario, and all coefficients in the objectives and constraints are neat and clear-cut.

5.3


We classify the papers by their optimization objectives, the stochastic and global factors that are taken into account, and key decisions at which stages of a supply chain (supply, production, or distribution) each paper discusses. In the papers we have discussed, the decision maker is either a profit maximizer or a cost minimizer. A variant form of profit/cost optimization is to include a term that represents regretbased penalty or model robustness when dealing with uncertain factors. The effects of uncertainty receive increasing attention in the global supply chain design modeling. There exist different approaches in handing the uncertainty proposed in these papers (see Snyder [32]). Major uncertain factors considered include uncertainties in capacity, cost, demand, exchange rate, inflation rate, and suppliers reliability. Another important shared feature of the papers is that they formulate the supply chain design problem in the global framework. Global factors that affect firms’ decisions on global supply chain design include local content rule, macroeconomic factors (exchange rate, inflation values), offset trade requirements, subsidized financing, taxes and duties, and transfer pricing. Table 5.1 summarizes the papers we have discussed.

1989

2006

1997 1997 1995

Chen et al.

Dasu and Li

Ferdows

Gutierrez and Kouvelis

2004

Min–Max regret (p-robustness)

N/A

Min total cost

Min the α-reliable Mean-excess regret

Min a weighted combination of total cost and activity time Max expected profit Max (expected profit — regret-based penalty) Max after-tax profit

1995

2006

Objective Max expected profit

Year 2003

Cohen and Lee

Biller and Xiang Butler et al.

Author(s) AlonsoAyuso et al. Arntzen et al.

Table 5.1 Classification scheme.

Exchange rates, inflation rates, production cost

N/A

Demands, the distances between demand nodes and facilities Exchange rate

Supply

Production

Production

Supply– Production– Distribution Production

Production– Distribution

Capacity, demand, production cost, selling price Deterministic model

Production

Supply– Production– Distribution

Demand

Deterministic model

Stochastic factors Cost, demand, selling price

Decisions (Supply– Production– Distribution) Supply–Production

Exchange rate uncertainty Subsidized financing, Tax and duties Macroeconomic factors uncertainty (exchange rate, inflation values)

Offset trade require ments, taxes and duties, transfer pricing Implicity modeled

Implicitly modeled

Local content rule, offset trade requirements, taxes and duties

Key global factors Implicitly modeled

(Continued)

Chapter 3.3.1

Chapter 2.2

135

Chapter 4.2.4

Chapter 5.2.1

Chapter 2.4

Chapter 5.2.1

Chapter 3.5.3

Chapter 3.4

Chapter Chapter 5.2.2

5.3 Classification Scheme

Exchange rate Deterministic model Deterministic model

1994 Min total cost 2004 Max discounted after-tax profit 2004 Max discounted after-tax profit

Kogut and Kulatilaka Kouvelis and Munson Kouvelis et al.

2002 Min total cost 2007 Max expected profit 1997 Min total cost

Lowe et al.

Lu and Van Mieghem Munson and Rosenblatt

N/A

1985

Kogut

Deterministic model

Exchange rates, inflation rates Demand

Exchange rate

Exchange rate, selling price Exchange rate

1985 Max mean– variance profit 1996 Max discounted after-tax profit

Hodder and Jucker Huchzermeier and Cohen

Stochastic factors Cost, price Cost, exchange rate, selling price

Year Objective 1984 CAPM 1986 Max mean– variance profit

Author(s) Hodder Hodder and Dincer

Table 5.1 (Continued).

Supply

Production

Supply

Production

Production

Production

Supply– Production– Distribution Supply–Production

Production

Decisions (Supply– Production– Distribution) Production Production

Local content rule

Exchange rate uncertainty, tax and duties Exchange rate uncertainty Subsidized financing, taxes and trade tariffs Local content rule, subsidized financing, taxes and duties Macroeconomic factors uncertainty

Key global factors None Exchange rate uncertainty, subsidized financing, tax and duties Exchange rate uncertainty Exchange rate uncertainty

(Continued)

Chapter 4.3

Chapter 3.5.1

Chapter 3.3.2

Chapter 2.1 & Chapter 3.1 Chapter 4.5

Chapter 4.2.2

Chapter 4.2.1

Chapter 4.2.3

Chapter 4.1.2

Chapter Chapter 4.1.1 Chapter 4.1.3

136 Classification Scheme

Year 2005

2006 2001 2004

2006 2000

2005

2000

Author(s) Santoso et al.

Shen

Tsiakis et al.

Velarde and Laguna

Vereecke et al. Vidal and Goetschalckx

Villegas and Ouenniche

Yu and Li

Table 5.1 (Continued).

Min total cost (+ solution robustness and model robustness)

Max after-tax repatriated earnings

Min total cost (+ downside deviation penalty) N/A Min total cost (qualitative discussion)

Min total cost

Max profit

Objective Min total cost

Economic conditions: Cost, demand

N/A Demand, exchange rate, international transportation lead times, supplier reliability Exchange rate

Demand, exchange rate

Demand

Stochastic factors Capacities, demands, production costs, suppliers Demand

Any stage is possible (Supply, Production, or Distribution) Production– Distribution

Production Supply–Production

Production– Distribution Production– Distribution Supply

Decisions (Supply– Production– Distribution) Supply–Production

Implicitly modeled

Exchange rate uncertainty, tax and duties

N/A Exchange rate, international transportation lead times

Exchange rate uncertainty

None

None

Key global factors Implicitly modeled

Chapter 5.2.4

Chapter 4.4

Chapter 2.3 Chapter 5.2.2

Chapter 5.2.1

Chapter 3.2

Chapter 5.2.3

Chapter Chapter 5.2.2

5.3 Classification Scheme

137

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Biographies

Panos Kouvelis is the Emerson Distinguished Professor of Operations and Manufacturing Management at the Olin School of Business at Washington University in St. Louis, and he currently serves as the Area Chair of the Operations and Manufacturing Management(OMM) group at Olin. He also serves as the Director of the Boeing Center on Technology, Information and Manufacturing at Washington University. He has held visiting appointments with the Graduate School of Business, University of Chicago, where he taught in the executive programs in Barcelona, Chicago and Singapore, and Koblenz School of Management, Germany. He received his PhD in Industrial Engineering and Engineering Management at Stanford University, MBA and MS in Industrial and Systems Engineering at the University of Southern California, and a diploma in Mechanical Engineering at the National Technical University of Athens. He has previously taught at the Fuqua School of Business, Duke University and the Management Department of the University of Texas at Austin. He teaches courses in Information Technology and Supply Chain Management, Global Operations and Logistics, Global Business Process Outsourcing, Managing Technological Innovation, Operations Strategy and Operations 143

144

Biographies

Management. He has received numerous teaching awards, with the most recent ones being the EMBA Reid Teaching Award 2003, Executive Masters in Manufacturing Management (EM 3 ) Teaching Awards, 1998, 1999, 2000, and 2002; the MBA Reid Teaching Awards, 1998 and 2000 at Olin, and Faculty of the Term MBA Teaching Award, 1996 at Fuqua, Duke. He has been frequently mentioned as a top operations management professor in surveys of top MBA programs by Business Week (quoted as the most popular” business professor at Olin in the 1998 Business Week Survey). He often teaches in executive management programs and offers short customized courses to interested companies. He currently teaches in the EMBA program at the Olin School of Business and the joint Olin-Fudan EMBA program in Shanghai, China. He also recently developed an e-learning course on “Global Supply Chain Management” (currently sold by the Chicago based Learning Insights company). He is an accomplished and prolific researcher, ranked in the top ten operations management researchers in terms of research productivity and quality (recent survey in Journal of Operations Management). He received the 2000 IIE Transactions Award for the Best Paper in Operations Engineering Issue (awarded by the Institute of Industrial Engineers for the best research paper in the flagship journal of the field). His research interests include global supply chain management, implications of e-business for supply chain strategies, business process outsourcing and purchasing management, manufacturing strategy, technology management, the study of marketing/manufacturing interfaces, project management, e-procurement and other B2B applications, scheduling of operations, process management and reengineering, facilities location and layout design. He has published over 70 articles in Management Science, Operations Research, Manufacturing and Service Operations Management (M&SOM), Naval Research Logistics, IIE Transactions, Production and Operations Management (POM), Journal of Operations Management, European Journal of Operations Research, Operations Research Letters, Journal of Operational Research Society, and other high quality academic journals. He also frequently contributes chapters in edited books on global supply chain management and optimization issues. He currently serves as Department Editor of Supply Chains/Production-Inventory Systems

Biographies

145

of IIE Transactions (and in the past he served as Department Editor of Project Selection, Coordination and Management of the same journal), as senior editor of M&SOM, as Department Editor of POM in the area of Manufacturing Operations, and as associate editor of Operations Research and Decision Sciences. In the past he served as associate editor of Interdisciplinary Management Research and Applications of Management Science (and before that he was associate editor for Supply Chain Management in the same journal), and has been for many years on the editorial review board of POMS and MSOM. He has also edited special issues for the Journal of Global Optimization and the Journal of Intelligent Manufacturing. Kouvelis’ book on Robust Discrete Optimization was published in 1997 by Kluwer and his co-authored textbook on Global Operations and Logistics: Text and Cases was published by Wiley in 1998 (and has been translated in Chinese and Portuguese). He has served as President-Elect and President of the MSOM Society for 2002–2004. He has consulted with and/or taught executive programs for Emerson, IBM, Dell Computers, Boeing, Hanes, Duke Hospital, Solutia, Express Scripts, Spartech, MEMC, Ingram Micro, Smurt Stone, Reckitt & Colman, and Bunge on supply chain, inventory management, lean manufacturing, operations scheduling, and manufacturing system design issues. Ping Su is currently an assistant professor in Operations Management and Technology at SUNY New Paltz. She received her PhD in Operations Management at Washington University. She received her Bachelor in MIS from the School of Economics and Management, Tsinghua University, China. Her research interests include global supply chain management and the interface between Operations Management and Finance/Industrial Organization.

The Structure of Global Supply Chains

Handbook of Integrated Risk Management in Global Supply Chains

Supply Chains: A Manager's Guide

Supply Chains: A Manager's Guide

Risk Management of Supply and Cash Flows in Supply Chains

Freshwater Supply (Global Issues)

Supply Chain Redesign: Transforming Supply Chains into Integrated Value Systems

Steuerung von Supply Chains: Strategien - Methoden - Beispiele

Understanding Supply Chains: Concepts, Critiques, and Futures

Globalized Supply Chains and U.S. Policy

Global Integrated Supply Chain Systems

Analysis of Cooperation in Supply Chains Using Game Theory

Chains of the Sea

Chains of the Sea

The Extended Enterprise: Gaining Competitive Advantage through Collaborative Supply Chains

Chains of Darkness, Chains of Light

Enhancing the Role of SMEs in Global Value Chains

Chains of the Sea

Chains

Chains of Darkness, Chains of Light

Chains of Darkness, Chains of Light

Chains

Energy Supply and Renewable Resources (Global Issues)

Scheduling in supply chains using mixed integer programming

Strategic Planning Models for Reverse and Closed-Loop Supply Chains

Strategic Procurement: Organizing Suppliers and Supply Chains for Competitive Advantage

Scheduling in Supply Chains Using Mixed Integer Programming

Chains

The Structure of Global Supply Chains

Handbook of Integrated Risk Management in Global Supply Chains

Supply Chains: A Manager's Guide

Supply Chains: A Manager's Guide

Risk Management of Supply and Cash Flows in Supply Chains

Freshwater Supply (Global Issues)

Supply Chain Redesign: Transforming Supply Chains into Integrated Value Systems

Steuerung von Supply Chains: Strategien - Methoden - Beispiele

Understanding Supply Chains: Concepts, Critiques, and Futures

Globalized Supply Chains and U.S. Policy

Global Integrated Supply Chain Systems

Analysis of Cooperation in Supply Chains Using Game Theory

Chains of the Sea

Chains of the Sea

The Extended Enterprise: Gaining Competitive Advantage through Collaborative Supply Chains

Chains of Darkness, Chains of Light

Enhancing the Role of SMEs in Global Value Chains

Chains of the Sea

Chains

Chains of Darkness, Chains of Light

Chains of Darkness, Chains of Light

Chains

Energy Supply and Renewable Resources (Global Issues)

Scheduling in supply chains using mixed integer programming

Strategic Planning Models for Reverse and Closed-Loop Supply Chains

Strategic Procurement: Organizing Suppliers and Supply Chains for Competitive Advantage

Scheduling in Supply Chains Using Mixed Integer Programming

Chains

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