Multimarket Facility Network Design with Offshoring Applications

MANUFACTURING & SERVICEOPERATIONS MANAGEMENT

Vol. 11, No. 1, Winter 2009, pp. 90–108issn 1523-4614 �eissn 1526-5498 �09 �1101 �0090

informs ®

doi 10.1287/msom.1070.0198©2009 INFORMS

Multimarket Facility Network Design withOffshoring Applications

Lauren Xiaoyuan LuKenan-Flagler Business School, University of North Carolina at Chapel Hill,

Chapel Hill, North Carolina 27599, [email protected]

Jan A. Van MieghemKellogg School of Management, Northwestern University, Evanston, Illinois 60208,

[email protected]

Moving production to low-wage countries may reduce manufacturing costs, but it increases logistics costsand is subject to foreign trade barriers, among others. This paper studies a manufacturer’s multimarket

facility network design problem and investigates the offshoring decision from a network capacity investmentperspective. We analyze a firm that manufactures two products to serve two geographically separated marketsusing a common component and two localized final assemblies. The common part can be transported betweenthe two markets that have different economic and demand characteristics. Two strategic network design ques-tions arise naturally: (1) Should the common part be produced centrally or in two local facilities? (2) If acentralization strategy is adopted, in which market should the facility be located? We present a transporta-tion cost threshold that captures costs, revenues, and demand risks, and below which centralization is optimal.The optimal location of commonality crucially depends on the relative magnitude of price and manufacturingcost differentials but also on demand size and uncertainty. Incorporating scale economies further enlarges thecentralization’s optimality region.

Key words : capacity investment; newsvendor network; location; transshipment; commonalityHistory : Received: October 17, 2005; accepted: July 23, 2007. Published online in Articles in Advance

April 17, 2008.

1. IntroductionGlobal manufacturing firms often have productionfacilities around the world that serve each majormarket. Moving production facilities to low-wagecountries provides an opportunity for labor costreduction. However, this offshore manufacturingstrategy increases logistics costs and is subject to for-eign trade barriers, among others. Capturing thesedecision factors, this paper studies a manufacturer’smultimarket facility network design problem andinvestigates the value of offshoring from a networkcapacity investment perspective.Specifically, we examine the operations strategy of

a firm that manufactures two products to serve twogeographically separated markets using a commoncomponent and two localized final assemblies. Thecommon part can be transported between the twomarkets that have different economic and demandcharacteristics. The associated transportation costs

account for shipping the common parts (intermediategoods) between the two markets, as well as for for-eign trade barriers such as tariffs and duties. For our2-product 2-market model with commonality, foursupply network strategies are possible, as illustratedin Figure 1. The U.S. market boasts higher sale priceswhile the other market, Asia, enjoys lower manu-facturing costs. A multinational car manufacturer isa motivating example for our model when localizedcar models serve local markets but share a commonengine. For example, Toyota recently started to pro-duce 2.4-liter engines in its joint venture in Chinaand planned to export two-thirds of the output toJapan and the U.S. The engines are shared by Camryssold in China, Japan, and the U.S., and also by mini-vans sold in Europe and Japan. Toyota plans to investas much as $2.5 billion in China by 2010 and cur-rently has no plans to export cars from China becauseof enormous local demand (Webb 2004, Webb and

90

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Lu and Van Mieghem: Multimarket Facility Network Design with Offshoring ApplicationsManufacturing & Service Operations Management 11(1), pp. 90–108, © 2009 INFORMS 91

Figure 1 Four Possible Configurations of a Multimarket Facility Network

USA

Asia

Plant 1

Finalassembly 1

Plant 2

Commoncomponent

1. Hybrid

2. Market focused

Plant 1

Plant 2

USA

Asia

Plant 1

Plant 2

Commoncomponent

Finalassembly 1

Finalassembly 2

3. Centralization in USA (Onshore)

USA

Asia

4. Centralization in Asia (offshore)

Plant 1

USA

Asia

Plant 2

Commoncomponent

Commoncomponent

Commoncomponent

Commoncomponent

Finalassembly 2

Finalassembly 1

Finalassembly 2

Finalassembly 1

Finalassembly 2

Treece 2004). We are interested in understanding howthe economic and demand characteristics drive thestrategic facility decision of engine production.As shown in Figure 1, the hybrid (Strategy 1) and

the market-focused (Strategy 2) configurations sourcethe common component locally, while the other twoconfigurations (Strategy 3 and 4) centralize it in a sin-gle market. Obviously, the market-focused configu-ration can be replicated, and thus is dominated bythe hybrid configuration. For the common compo-nent, we restrict attention to the two geographicallyseparated markets as the only location options. Thisrestriction highlights the key trade-offs in the loca-tion decision but precludes some interesting questionssuch as whether it is better to locate the common com-ponent at a hub, which can economically supply bothmarkets. The network design problem comes down totwo strategic questions: The first is whether the com-mon parts should be produced in a single facility orin two local facilities. If a centralized facility strategyis adopted for the common component, the secondquestion is where should such a facility be located?We use newsvendor network methodology to ana-

lyze the model under both deterministic and stochas-tic demand. Our main findings are as follows. Inthe simple base case of deterministic demand, thecentralization decision solely depends on transporta-

tion and manufacturing costs. If the unit transporta-tion cost is higher than the unit manufacturing costdifferential between the two markets, it is optimal toadopt the market-focused configuration and producecommon parts in both markets. Otherwise, it is opti-mal to centralize commonality in Asia to save manu-facturing costs.In the more realistic case that demand is uncer-

tain during network planning, centralization becomesmore attractive due to the benefits of demand pool-ing and the embedded ex-post revenue maximizationoption to allocate capacity to the more profitable mar-ket. Even centralization in the United States mayemerge as the optimal configuration when pricedifferential and demand uncertainty are high. Thisfinding underscores the importance of analyzing thenetwork design problem under stochastic demand:Not only do optimal network configurations changeunder stochastic demand, but the transportation costthreshold is refined to capture demand uncertainty inaddition to economic characteristics.The changes in network strategy due to demand

uncertainty can be explained by two factors: differ-ences in transportation costs and the value of therevenue maximization option. We show that trans-portation costs are typically lowest with local sourcingand decrease in demand correlation. However, when

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Lu and Van Mieghem: Multimarket Facility Network Design with Offshoring Applications92 Manufacturing & Service Operations Management 11(1), pp. 90–108, © 2009 INFORMS

market prices differ substantially, U.S. centralizationcan become optimal because its transportation costscan be lower than those of the hybrid network, whichmust invoke transshipment to satisfy U.S. demand toreap higher profits in addition to local sourcing.We also find that revenue maximization benefits are

typically equivalent under hybrid, U.S.-centralization,and Asia-centralization. The equivalence holds whenmarket prices differ substantially and transportationis inexpensive. Then U.S. demand has priority overAsia and cheap transshipment allows hybrid andAsia-centralization to satisfy as much U.S. demandas U.S.-centralization does. However, when marketprices are similar or transportation is expensive,local demand takes priority. Because the U.S. mar-ket still has an (albeit small) price advantage, U.S.-centralization enjoys larger revenue benefits, whichincreases in demand correlation. Differences in trans-portation costs and revenue maximization benefitsthus explain why and when the less intuitive U.S.-centralization can be optimal. An example in §4.2 willfurther illustrate this.In contrast to much of the related facility network

design literature, the contributions of this paper mustbe found in refining network design strategies to cap-ture uncertain demand and the revenue effect, i.e.,the option to maximize revenue by contingent capac-ity allocation to the high-price market. Strengthen-ing the results from previous literature,1 we provideanalytical conditions under which the centralizationand market-focused configurations arise as bound-ary solutions of the facility planning problem. Specif-ically, we prove that U.S.-centralization, or onshoring,can become optimal when markets have substantialprice differences and highly correlated demands. Inaddition, the hybrid configuration may outperformcentralization and market-focused configurations. Webelieve that providing the ex-post transshipmentoption to both locations is important to the flexibil-ity of the manufacturing network, as demonstratedby the concept of “chaining” in Jordan and Graves(1995). Eliminating one transshipment activity breaksthe chain and can significantly lower network flexibil-ity. Furthermore, the generality of our model encom-passes all possible configurations of the multimarket

1 See our literature review for detailed discussions on a closelyrelated paper, Kulkarni et al. (2005).

facility network formulated here and allows for ana-lyzing the location decision of commonality. Finally,our coverage of stochastic demand ordering andeconomies of scale (EoS) through fixed capacity costsseem to be novel analytical techniques in a newsven-dor network.

2. Literature Review2.1. Operations StrategyConfiguring the right multiplant facility networkplays an important role in a firm’s operations strat-egy. Hayes and Wheelwright (1984) illustrate fourapproaches for formulating a multiplant facility strat-egy: physical facilities analysis, geographical networkanalysis, functional needs and corporate philoso-phy analysis, and product-process focus analysis.They argue that these approaches represent differ-ent perspectives and should be used in a propercombination. Our analysis combines the geographi-cal network and product-process focus approaches.The geographical network analysis is often observedwhen transportation costs constitute a significant por-tion of total production cost. This paper illustratesthe pivoting role of transportation cost in choos-ing centralized versus localized commonality strat-egy. The product-process focus approach is based onthe concept of operational focus proposed by Skinner(2006) and recently modeled by Van Mieghem (2008).Firms may choose to focus their facilities according tovolumes, product, process, or service. Similar in spirit,our model incorporates two products with differentdemand characteristics, two geographically separatedmarkets with distinct economic characteristics, andtwo processes with different purposes: common com-ponent manufacturing versus dedicated assembly. Weillustrate how these elements interact and drive theoptimal network decisions.

2.2. Facility Location and Network DesignOur research falls within the vast literature on facil-ity location and supply chain network design. Snyder(2006) presents a recent and broad review of facilitylocation research. Our paper follows the stream thatdeals with facility decisions in a global context. We cat-egorize and summarize the related literature into fourgroups of papers according to their research method-ologies (an extended review is in the online appendix).

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2.2.1. Mathematical Programming. One of theseminal papers that formulate global manufactur-ing strategic planning as a mathematical program-ming problem is Cohen and Lee (1989). Their modelcan capture a large number of factors affectingresource deployment decisions in a multicountrymodel, such as regional demand requirements, sourc-ing constraints, interplant transshipments, taxation,and tariffs. In a global setting, firms’ manufacturingdecisions are significantly affected by internationaltrade barriers and regulations, as demonstrated byArntzen et al. (1995), Munson and Rosenblatt (1997),and Kouvelis et al. (2004). A common feature of thesemathematical programming formulations is that thedecision framework is deterministic, i.e., no demand,financial, production, or regulatory uncertainties.

2.2.2. Stochastic Programming. Some papersexplicitly model uncertainty in the global manufac-turing environment using a stochastic programmingapproach. Santoso et al. (2005) propose a model anda solution algorithm for solving large-scale stochasticsupply chain design problems. Others specificallyevaluate the benefit of operational flexibility embod-ied in owning international operations, e.g., Kogutand Kulatilaka (1994), Huchzermeier and Cohen(1996), Kouvelis et al. (2001), and Kazaz et al. (2005).

2.2.3. Newsvendor Networks. This stream ofpapers use parsimonious newsvendor models to gen-erate managerial insights pertaining to demand riskin general and specifically the value of transship-ment, e.g., Robinson (1990) and Rudi et al. (2001).Van Mieghem and Rudi (2002) present a systematicapproach to study network design in a newsven-dor setting, which was adopted by Kulkarni et al.(2004, 2005). The latter is closely related to ourmodel and numerically determines the better of twopredetermined network configurations for a multi-plant network with commonality: process plant (cor-responding to our U.S.-centralization) and productplant (corresponding to our market-focused config-uration). Four major distinctions separate our workfrom Kulkarni et al. (2005). First, we enlarge thefeasible configuration set and endogenize the loca-tion of common component by incorporating Asia-centralization and the most general configuration,i.e., the hybrid. Second, we let the optimal network

configuration emerge from optimization and pro-vide analytical optimality conditions. Third, insteadof using numerical sensitivity analysis, we ana-lytically demonstrate the impact of economic anddemand characteristics on optimal network configu-rations. Last, we explain how differences in trans-portation costs and revenue maximization benefitsdetermine optimal network design under demanduncertainty and demonstrate how this can even leadU.S.-centralization to be optimal.

2.2.4. Conceptual and Empirical Approaches.A group of papers draw on extensive interviews andcase studies to examine the strategies and trendsin facility location selections: Schmenner (1979),Bartmess and Cerny (1993), Bartmess (1994), MacCor-mack et al. (1994). Other papers conduct empiricalstudies on facility strategies of large manufacturingfirms, e.g., Schmenner (1982) and Brush et al. (1999).

2.3. Commonality, Dual Sourcing, and OffshoringLiterature

This is also relevant to our work. Commonalityis about assembling multiple products from com-mon components and product-specific components,according to Van Mieghem (2004). Multiproduct firmsoften use commonality to add flexibility to their exist-ing production networks. Kulkarni et al. (2005) exam-ine the trade-offs between risk pooling and logisticscost for two extreme configurations (process versusproduct) of commonality in a multiplant network. Incontrast to Kulkarni et al. (2005), we endogenize thelocation decision of commonality and allow differ-ent centralization configurations to arise from opti-mization. Our work also studies the choice betweensingle sourcing (centralization) and dual sourcing(hybrid) strategies for commonality. Other sourcingstrategies are studied by Anupindi and Akella (1993),Yazlali and Erhun (2004), Tomlin and Wang (2005),and Tomlin (2006). Finally, our research belongs to thegrowing literature on offshoring. Related literatureis mostly found in the international business andpopular management journals, e.g., Ferdows (1997),Markides and Berg (1988), Farrell (2004, 2005). Relatedeconomics literature focuses on the impact of off-shoring on domestic labor markets (Feenstra andHanson 1996, Baily and Lawrence 2004).

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3. ModelConsider a firm that uses four resources to producetwo products. In the capacity portfolio K = �K1�K2�

K3�K4��Ki captures end-product localization capacityin market i = 1�2 while Ki+2 represents common com-ponent capacity in market i. Thus, Resources 1 and 2are product-dedicated while transshipment allowsResources 3 and 4 to be shared by the two productswith demand vector D ∈ �2

+. The firm sells a singleproduct in each geographically separated market andhas the option to configure its production network asillustrated in Figure 2. The dedicated resources areexogenously chosen to be located in the market theyserve. Transshipment of common parts between thetwo markets is available at a positive cost. (Though itcan be easily incorporated into the model, we assumethat dedicated component manufacturing is costlessfor the convenience of notation.)Following the convention set by Van Mieghem and

Rudi (2002), we let p = �p1� p2� where pi is the per unitsale price of product i; cM = �cM�1� cM�2� where cM� i

is the per unit common component manufacturingcost in market i; cT = �cT �1� cT �2� where cT � i is thetotal transportation cost of one unit of common partfrom market i to market j including associated tariffsand duties; cK = �cK�1� cK�2� cK�3� cK�3� is the constantmarginal capacity investment cost. For expositionalsimplicity, we assume common component capacitycost is identical for both markets, but relax this later.We also assume that any currency exchange rates are

Figure 2 Graphical Representation of Our Newsvendor Network withVolume Decisions (Capacity K and Allocation x) and Data(Unit Capacity Costs cK , Net Values v , and Demand D)

D2

D1

Plant 2

x1

K3 K1

K4 K2

Plant 1

v1

x3

v3

x4

v4

x2

v2

cK, 3 cK, 1

cK, 3 cK, 2

fixed, so that all prices and costs can be denominatedin a single currency. Three price and cost differentialsarise naturally

�p = p1 − p2� �cM = cM�1 − cM�2�

�cT = cT �1 − cT �2�

The processing network of Figure 2 has four contin-gent activities: xi is the number of common parts usedlocally in market i, while xi+2 is the number of com-mon parts transshipped from market i. The net valuesof 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, we assume positive net val-ues so that production and transshipment are ex-postprofitable. In addition, it is economically justified toproduce both end products, which means investmentin the dedicated resources is always positive.The firm is an expected profit optimizer so that

the optimal capacity strategy K and contingent activ-ities x�K�D� emerge from a two-stage optimizationproblem. Let V �K� denote the expected firm valuegiven capacity investment K. The optimal expectedfirm value is

V ∗ =maxK∈�4+

Ɛ��K�D� − C�K��

where the optimal operating profit is

��K�D� =maxx∈�4+

v′x

subject to Ax ≤ K� RDx ≤ D�

where primes denote transposes and the consumptionand output matrices are

A =

⎛⎜⎜⎜⎜⎜⎜⎝

1 0 0 1

0 1 1 0

1 0 1 0

0 1 0 1

⎞⎟⎟⎟⎟⎟⎟⎠ � RD =

(1 0 0 1

0 1 1 0

)�

We first assume the capacity cost function is linear,i.e., C�K� = c′

KK, but later add a fixed cost to studyEoS. Finally, to compare the optimal value of the fournetwork configurations, we denote• Vhyb = optimal value of the hybrid configuration,

which is the most general and hence optimal strategy:Vhyb = V ∗;

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• Vmkt = optimal value of the market-focused con-figuration, where x3 = x4 ≡ 0;

• Von = optimal value of the configuration central-izing commonality in Market 1, where K4 ≡ 0;• Voff = optimal value of the configuration central-

izing commonality in Market 2, where K3 ≡ 0.In general, V ∗ = Vhyb ≥ max�Vmkt�Von�Voff with

equality meaning that a boundary solution is optimal.In this way, the optimal network strategy emergesfrom optimization. Finally, all proofs are in the onlineappendix.

4. Optimal Network ConfigurationsWe focus on two key components of the optimal solu-tion to the network design problem. First, is it opti-mal for the firm to adopt a centralization strategy forthe common component? Second, if centralization ofcommonality is optimal, in which market should thefacility be located? To highlight the first-order costdrivers, we start with the deterministic demand set-ting before tackling the stochastic model.

4.1. Deterministic DemandBecause the common component capacity cost isidentical for both locations, the investment decisioncomes down to evaluating the economic attractive-ness of the alternative processing activities for eachproduct. Without imposing any assumption, thereare 24 (=4!) possible orderings of the four net val-ues, but their definitions imply an interdependence,v4 ≥ v1 ⇒ v2 ≥ v3, which eliminates 6 orderings. Theremaining 18 are divided into two groups, one ofwhich is the mirror image of the other. Due to sym-metry in results, our subsequent analysis focuses onthe 9 orderings displayed in Table 1. The four pro-cessing activities are categorized into basic and “dis-cretionary,” as described by Van Mieghem and Rudi(2002). The discretionary processing activities are onlyused in stochastic settings to deal with deviationsfrom the expected scenario. Proposition 1 provides theconditions under which each of the 9 cases occurs andthe corresponding optimal network configuration.

Proposition 1 (Deterministic Demand). If cT �1 ≤−�cM , centralizing commonality in Market 1 is optimalwith capacity investment K∗ = �D1�D2�D1 + D2�0�′. IfcT �2 ≤ �cM , centralizing commonality in Market 2 is opti-mal with capacity investment K∗ = �D1�D2�0�D1 + D2�

′.

Table 1 Optimal Network Configurations Under Deterministic Demand

Net value Basic Discretionary Optimal networkordering Conditions activities activities configuration (K ∗)

v1 ≥ v4 ≥ v2 ≥ v3 cT �1 ≥ −�cM x1, x2 x3, x4 Market-focusedv1 ≥ v2 ≥ v4 ≥ v3 cT �2 ≥ �cM �D1� D2� D1� D2�

v2 ≥ v1 ≥ v4 ≥ v3

v1 ≥ v3 ≥ v4 ≥ v2 cT �1 ≤ −�cM x1, x3 x2, x4 Centralization: Market 1v1 ≥ v4 ≥ v3 ≥ v2 (D1� D2� D1 + D2�0�v3 ≥ v1 ≥ v4 ≥ v2

v2 ≥ v4 ≥ v1 ≥ v3 cT �2 ≤ �cM x2, x4 x1, x3 Centralization: Market 2v4 ≥ v1 ≥ v2 ≥ v3 (D1� D2�0� D1 + D2)v4 ≥ v2 ≥ v1 ≥ v3

Otherwise, a market-focused configuration is optimal withcapacity investment K∗ = �D1�D2�D1�D2�

′.

Proposition 1 demonstrates that it is optimal tocentralize commonality in the low-cost market when-ever the manufacturing cost advantage outweighs thetransportation cost of centralization. Lemma 1 furthercharacterizes the three net value orderings that giverise to the market-focused configuration. These threecases will become the center of our analysis understochastic demand.

Lemma 1. If cT �1 > −�cM and cT �2 > �cM , three casesare possible:(i) High price differential, meaning �p ≥ cT �2 and thus

v1 > v4 ≥ v2 > v3.(ii) Medium price differential, meaning max��cM�

−�cM − �cT � < �p < cT �2 and thus v1 > v2 > v4 > v3.(iii) Low price differential, meaning −�cM − �cT ≤

�p ≤ �cM and thus v2 ≥ v1 > v4 ≥ v3.

4.2. Stochastic DemandThough demand uncertainty complicates the networkdesign problem, it is straightforward to show thatthe conditions for centralization to be optimal underdeterministic demand extend to stochastic demand asstated in Proposition 2:

Proposition 2 (Stochastic Demand). If cT � i ≤�−1�i�cM , centralizing commonality in market i isoptimal, where i ∈ �1�2.

This also implies that the common component thatonly provides discretionary activities remains value-less under demand uncertainty. While Proposition 2is sufficient for our purpose, it also simplifies find-ing the specific optimal capacity levels when cT � i ≤

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�−1�i�cM : set Kj+2 = 0 (where j = i) and solve thethree-dimensional optimal capacity problem.For the remainder, we will focus on the less obvi-

ous cases illustrated in Lemma 1. Without loss ofgenerality, we label Market 1 the high-price market,i.e., p1 ≥ p2. To cast the model in the context of off-shoring, we further assume that Market 1 has highermanufacturing costs, i.e., cM�1 ≥ cM�2, and call Mar-ket 2 the low-cost market. These two assumptions alsoensure that the three interesting cases in Lemma 1 arenonempty sets.With uncertainty, even expensive transshipment

has an option value because it reduces ex postsupply-demand mismatch costs and can increaserevenues. Our analytic model is designed to increaseunderstanding of this option value. Before delvinginto the general analysis, let us first consider asimple example to generate some intuition on therole of the three drivers in this network design:revenue maximization option, transshipment option,and manufacturing costs. Two three-point discretedemand distributions are sufficient for our purpose.When demand is perfectly negatively correlated, therealizations are (1+ �1− ), (1�1), (1− �1+ )each with probability 1

3 , where ∈ �0�1� is a measureof demand volatility. When demand is perfectly pos-itively correlated, the realizations are (1+ �1+ ),(1�1), (1− �1− ) each with probability 1

3 . Assumesymmetric transportation costs for simplicity, i.e.,cT �1 = cT �2 = cT , and consider three networks: Hybridwith capacity (1 + z�1 + z�0�5�1 + z��

0�5�1 + z�), Onshore with capacity (1 + z�1 + z�

1+ z�0), and Offshore with capacity (1+ z�1+ z�

0�1+z), where z ∈ �0�1� is a measure of service prob-ability. It is reasonable to assume that total commoncomponent investment is higher than the lowest totaldemand, i.e., 1 + z > 2�1 − � so that �2+ z� > 1.We keep investment in dedicated and commoncomponents equal across the three networks to focusattention on the impact of common component allo-cation. Table 2 shows the resulting expected revenues,transportation costs, and manufacturing costs.With high �p, expected revenues are identical

across the three networks because cheap transship-ment allows the high-price U.S. demand to be satis-fied as much as possible. In contrast, with mediumto low �p, Onshore has the highest revenues while

Offshore has the lowest. Moreover, the revenueadvantage of Onshore is higher when demand is pos-itively correlated and less volatile: Indeed, �R

on-hyb =1 =

13�p > �R

on-hyb =−1 = 1

6 �3 − �2 + z��p, indicating thevalue of revenue maximization of onshoring increasesin demand correlation while larger demand volatil-ity decreases that revenue advantage. This patternalso holds if we compare Onshore against Offshore.Hybrid achieves the lowest transportation costs in

general with one surprising exception: Onshore incurseven lower transportation costs than Hybrid whenthe price differential is high and demand is positivelycorrelated (notice that �TCon-hyb

=1 = − 13�1− z�cT ).

Substantial price difference induces the network toprioritize satisfying the demand of the high-pricemarket. When this price priority is coupled withpositive demand correlation, the service level of theother market is relatively low, letting Onshore savetransportation costs. Further, the cost savings increasewhen demand volatility rises. Similarly, the trans-portation cost advantage of Onshore over Offshoreincreases in demand correlation. However, the costsavings decrease in demand volatility.Finally as expected, Offshore incurs the lowest

manufacturing costs while Onshore incurs the high-est. The cost savings are higher under negatively cor-related demand (notice that �MCon-off

=−1 = �1+z��cM >

�MCon-off =1 = 2

3 �2− +z��cM�. The cost savings of off-shoring increase (decrease) in demand volatility whendemand correlation is negative (positive).In summary, this example illustrates that the rev-

enue maximization advantage and transportation costsavings of onshoring increase in demand correla-tion while the manufacturing cost savings of off-shoring decrease in demand correlation. The impactof demand volatility depends on both network con-figuration and demand correlation. Next we formal-ize the intuition derived from this example by solvingthe stochastic capacity investment problem using thenewsvendor network approach and assuming a ran-dom demand vector D with continuous bivariate dis-tribution F . (We will use Fi to denote the marginaldistribution of market i demand.)

Lemma 2. If cT �1 > −�cM and cT �2 > �cM , the optimalcapacity investment vector satisfies K∗

i ≥ K∗i+2. Moreover,

K∗i+2 = 0 implies K∗

j = K∗j+2, where i, j ∈ �1�2 and i = j .

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Table 2 Expected Revenues (R), Transportation Costs (TC), and Manufacturing Costs (MC) of the Three Networks Depend onPrice Differential �p (H: High, M: Medium, L: Low) and Demand Correlation � for the Simple Example

�p Hybrid Onshore Offshore

� = −1 H R3− � + z�

3p1 + � + 2z�

3p2 Same as left Same as left

M/L1+ z�

2�p1 + p2� Same as above

� + 2z�

3p1 + 3− � + z�

3p2

H TC0�5+ � + 0�5z�

3cT

� + 2z�

3cT

3− � + z�

3cT

M/L−1+ 2� + z�

3cT Same as above Same as left

H/M/L MC1+ z�

2�cM�1 + cM�2� �1+ z� �cM�1 �1+ z� �cM�2

� = 1 H R3− � + z�

3p1 + 1− � + z�

3p2 Same as left Same as left

M/L2− � + z�

3�p1 + p2� Same as above

1− � + z�

3p1 + 3− � + z�

3p2

H TC13

cT

1− � + z�

3cT

3− � + z�

3cT

M/L Same as above Same as left

H/M/L MC2− � + z�

3�cM�1 + cM�2�

2�2− � + z� �

3cM�1

2�2− � + z� �

3cM�2

Lemma 2 says that investment in the common com-ponent is weakly less than in the dedicated compo-nent in both markets. Van Mieghem (2007) providestwo explanations: “excess” downstream capacity pro-vides a “switching option” that requires an unbal-anced capacity portfolio, and the resource poolingbenefit (here brought by the ex post transshipmentoption). As common parts can be shared across mar-kets, the need to invest in the common componentin both markets is reduced. Moreover, Lemma 2 pro-vides a simplification property for analyzing the cen-tralization configurations, i.e., equal investment in thecommon and dedicated components.As illustrated in Figure 1, two centralization strate-

gies are possible: centralization in Market 1 and inMarket 2. Given the equal investment property statedin Lemma 2, let the two boundary solutions �K =� �K1� �K2� �K1�0� and K = �K1�K2�0�K2� represent thetwo centralization configurations, respectively. Withdemand uncertainty, both strategies may become opti-

mal under certain conditions that hinge on the pricedifferential and demand volatility. Different central-ization configurations may arise for the three casesin Lemma 1. To specify the optimal strategies for thehigh and medium �p cases, it is useful to introducethe following transportation cost threshold defined bythe “upper” boundary solution �K

c̄T = �p �P3 − �cM − cK�1

1− �P3

� (1)

where �P3 = Pr�D1 > �K1�. (The online appendix showsits derivation.) Proposition 3 states the optimal net-work configuration for the high and medium �p

cases.

Proposition 3. For the high and medium price dif-ferential cases, the optimal investment strategy dependson cT �1:(i) If cT �1 < c̄T , it is optimal to centralize commonality

in Market 1;

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(ii) If cT �1 ≥ c̄T , it is optimal to invest in commonalityin both markets;(iii) Market-focused configuration is a special case of (ii)

in which activities x3 and x4 are identically zero, andits capacity vector �K = � �K1� �K2� �K1� �K2� is optimal if andonly if

Pr�D1 > �K1�D2 > �K2�

>max{

a∗(

cK�1+cK�3

v1− cK�1

v4

)�cK�2+cK�3

v2− cK�2

v3

}�

where

�K1=F −11

(v1−cK�1−cK�3

v1

)� �K2=F −1

2

(v2−cK�2−cK�3

v2

)�

a = v4

v2(or 1� for high (or medium) �p�

Under deterministic demand, onshoring can neverbe optimal because cT �1 ≤ −�cM can never be satis-fied. In contrast, demand uncertainty makes central-ization in the high-price market more attractive underthe conditions given in Proposition 3. Also notice thatwith medium to high price differentials, Proposition 3implies that it is never optimal to centralize common-ality in the low-cost market. Further, the high andmedium �p cases share the same set of strategiesand transportation cost threshold (though the deriva-tions are different as shown in the proof). The market-focused configuration may arise, but only as a subsetsolution of the hybrid strategy, depending on howlikely the capacity constraint �K is reached simultane-ously for both products. When the likelihood is suf-ficiently large, the value of the transshipment optionto alleviate the ex post demand-capacity mismatchdecreases to zero and thus the market-focused con-figuration becomes optimal. To specify the optimalstrategies when the price differential is low, we needanother transportation cost threshold defined by the“lower” boundary solution K

cT = �cM − �pP3 − cK�2

1− P3� (2)

where P3 = Pr�D2 > K2�.

Proposition 4. For the low price differential case, theoptimal investment strategy depends on cT �2:

(i) If cT �2 < cT , it is optimal to centralize commonalityin Market 2.

(ii) If cT �2 ≥ cT , it is optimal to invest in commonalityin both markets.(iii) Market-focused configuration is a special case of (ii)

in which activities x3 and x4 are identically zero, and itscapacity vector �K = � �K1� �K2� �K1� �K2� is optimal if andonly if

Pr�D1 > �K1�D2 > �K2�

>max{

cK�1 + cK�3

v1− cK�1

v4�

cK�2 + cK�3

v2− cK�2

v3

}�

where

�K1=F −11

(v1−cK�1−cK�3

v1

)� �K2=F −1

2

(v2−cK�2−cK�3

v2

)�

Together Propositions 3 and 4 highlight the impor-tance of capturing the revenue impact in stochasticnetwork planning: A substantial price difference cou-pled with demand uncertainty are the key conditions toargue against offshoring. Notice that a common featureshared by the two propositions is that the transporta-tion cost thresholds depend on demand distributionsand thus the optimality of centralization depends ondemand volatility. Moreover, notice that a positivetransportation cost threshold requires either �p > �cM

in the case of c̄T , or �p < �cM in the case of cT . Thesetwo opposite conditions underscore the pivotal role ofthe price differential in network decisions: When thetransportation cost is relatively inexpensive, depend-ing on the price differential it may be optimal to cen-tralize common component in either the high-pricemarket or in the low-cost market, but not both.

5. Impact of Costs and Prices5.1. Impact of Costs and Prices on the Optimal

Network ConfigurationThe previous two propositions identify the transporta-tion cost thresholds below which centralization strate-gies are optimal. Next we analyze how economiccharacteristics such as price, manufacturing cost, andcapacity investment cost, affect network decisions. Thepivotal role of the price differential in network deci-sions is manifested in its association with the specificcentralization strategy as shown earlier. Here we alsoanswer other interesting questions: (1) Does central-ization in the high-price market become more attrac-tive when the price differential increases? (2) Does

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centralization in the low-cost market become moreattractive when the manufacturing cost differentialincreases? (3) How does the optimal network con-figuration change with the capacity investment cost?Since the transportation cost thresholds determine theoptimal network configuration, we can answer thesequestions by finding out how c̄T and cT are affectedby a change in any of the economic characteristics.We will focus on c̄T (the analysis on cT is similar).

The change of c̄T w.r.t. parameter y is given by thetotal derivative

dc̄T

dy= �c̄T

�y︸︷︷︸Direct Effect

+ �c̄T

� �P3

d �P3

dy︸︷︷︸Indirect Effect

�

Decomposing the total effect of parameter y on c̄T

enables a better understanding of the countervailingforces that affect the attractiveness of centralization.Determining the sign of �c̄T /�y is straightforward.However,

sign(

�c̄T

� �P3

d �P3

dy

)

= sign(

�c̄T

� �P3

)× sign

(d �P3

d �K1

)× sign

(d �K1

dy

)�

where

sign(

�c̄T

� �P3

)= 1� sign

(d �P3

d �K1

)= −1�

Therefore determining the sign of the indirect effectcomes down to determining the sign of d �K1/dy, whichis derived analytically in the online appendix. Thesigns of direct, indirect, and total effects of all the eco-nomic parameters are summarized in Table 3.We selectively discuss the effects of some parame-

ters. For example, the third column in Table 3 showshow the costs and prices may impact the decision tomaintain U.S.-centralization, indicated by the changeof c̄T . An increase in Asian price decreases c̄T andthus the attractiveness of onshoring. In contrast, anincrease in Asian manufacturing or dedicated com-ponent investment cost enhances the attractivenessof centralization in the United States, as manifestedby the increase of c̄T . The same holds true for thecommon component investment cost. The other three

Table 3 Impact of Costs and Prices on the Transportation CostThresholds

c̄T cT

Parameter Direct Indirect Total Direct Indirect Total

p1 + − +/− − − −p2 − − − + − +/−cM�1 − + +/− + 0 +cM�2 + 0 + − + +/−cK�1 − + +/− 0 + +cK�2 0 + + − + +/−cK�3 0 + + 0 + +

changes, i.e., U.S. price, manufacturing cost, or ded-icated component investment cost, lead to ambigu-ous change in c̄T . This ambiguity reflects the inherenttrade-offs in centralization. For example, in the caseof p1, the positive direct effect is induced by increasedservice level of the U.S. market. The negative indirecteffect is caused by the decreased service level of theAsian market, which can be shown from the optimal-ity conditions.Our result on the investment cost of the common

component confirms and generalizes that of Kulkarniet al. (2005, §4.2, Figure 5) i.e., centralization strategyremains optimal for larger values of transportationcosts when the investment cost of common compo-nent increases. Kulkarni et al. (2005) base their resulton observations from numerical analysis assuminguniform demand distributions and comparing processplant (corresponding to our centralization) with prod-uct plant (corresponding to our market-focused) con-figuration. Ours is a general analytical result for theless restrictive model formulated here.

5.2. Impact of Costs and Prices on the OptimalValue and Capacity Investment

Now we study the impact of the economic parameterson optimal network value and capacity investment.The total capacity investment in common componentis denoted by Kcom = K3 + K4.

Property 1. The optimal expected firm value V ∗ isa nonincreasing convex function of cK with gradient�cK

V ∗ = −�K∗1�K∗

2�K∗3�K∗

4 �′ ≤ 0. Moreover, the optimal

value V ∗ is an increasing convex function of p with gradi-ent �pV

∗ = Ɛ�x∗1 + x∗

4�x∗2 + x∗

3�′ > 0.

The sensitivity terms of K∗ on any of the economicparameters can be calculated following the approach

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in Van Mieghem (1998). (Calculation of those sensitiv-ity terms are available upon request.) Here we employa different approach to characterize the impact, draw-ing on the concepts of supermodularity and increas-ing differences.

Property 2. The expected firm value V �K� is super-modular in (K1�K2�K3�Kcom) and has increasing differ-ences in (K1�K2�K3�Kcom�y), where y = −cK or p1.Moreover, the expected firm value is supermodularin (K1�K2�K4�Kcom) and has increasing differences in(K1�K2�K4�Kcom�y), where y = −cK or p2.

Complementarity among K1, K2, and Kcom is notsurprising given that the network is a connected“chain” so that a capacity increase in one type ofresource should be accompanied by an increase in anyother type of resource within the network. However,the supermodularity property cannot be establishedfor �K1, K2, K3, K4) because of the substitution effectbetween K3 and K4. When perturbed by a change inthe economic environment, the system needs to beadjusted towards optimality, and the adjustment maynot be monotone at all facilities. Nevertheless, somemonotonicities can be established.

Property 3. K∗1 , K∗

2 , K∗3 , and K∗

4 are monotone decreas-ing in any marginal capacity cost cK� i, i = 1, 2, 3. K∗

1 , K∗2 ,

K∗com are monotone increasing in pi, i = 1, 2. K∗

3 is mono-tone increasing in p1. K∗

4 is monotone increasing in p2.

The monotonicity of K∗1 , K∗

2 , K∗com in both cK and p

is not surprising due to the complementarity prop-erty stated in Property 2. However, K∗

3 and K∗4 may

be increasing or decreasing in p2 and p1, respectively.When p2 increases, the incentive to invest more inK2 obviously increases. What is less obvious is theincreased incentive to invest more in K3 because someof the capacity can be used towards the productionof Product 2 ex post. However, if p2 becomes largeenough so that �p becomes less than �cM , centraliza-tion in Asia will become more attractive as demon-strated earlier, thus leading to a decrease in K3.Not only do economic characteristics impact net-

work decisions, demand characteristics also interactwith economic characteristics in determining the opti-mal network configurations. We discuss the impact ofdemand characteristics in the next section.

6. Impact of Demand Size andUncertainty

We have shown that the optimality of centralization isindependent of demand uncertainty when the trans-portation cost is lower than the manufacturing costdifferential. However, the dependence emerges whentransportation is more expensive. For this case, weanalyze the impact of demand size, volatility and cor-relation on the optimal network configuration.

6.1. Demand SizeWhen centralizing commonality in market i is opti-mal for a given demand size, we expect it to remainoptimal when market i grows. The less obvious caseis when the demand size of the other market changes.The next proposition illustrate how these changesaffect the optimal network configuration.

Proposition 5. Suppose market demands are indepen-dent and have a finite mean. Let Di and D′

i denotetwo demand distributions of market i. Suppose D′

i hasfirst-order stochastic dominance over Di (i.e., FD′

i�·� ≤

FDi�·��.(i) If centralization of commonality in Market 1 (or 2)

is optimal for (D1�D2), it remains optimal for (D′1�D2)

(or (D1�D′2)).

(ii) If centralization of commonality in Market 1 (or 2)is optimal for (D1�D′

2) (or �D′1�D2�), it remains optimal

for (D1�D2).(iii) If centralization of commonality in Market 1 (or

2) is optimal for (D1�D2), there exists a �̄2 (or �̄1) suchthat when Ɛ�D′

2� > �̄2 (or Ɛ�D′1� > �̄1) the centralization

strategy is never optimal for (D1, D′2) (or (D

′1, D2)).

The insight from the propositions is that, in con-trast to the deterministic case, market size matters innetwork design under demand uncertainty. Becauseevery unit of deterministic demand can be satis-fied, increasing demand size scales up the networkproportionally and thus has no impact on the opti-mal network configuration. However, when demandsare stochastic, demand-capacity mismatch causes theoptimal network value to be nonlinear in demand sizebecause of risk pooling and the revenue maximiza-tion option. Indeed, the trade-off between the revenuemaximization benefits, transportation costs, and man-ufacturing costs is affected by demand size. Specifi-cally, suppose centralizing commonality in market i

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is optimal for a given demand size. When the sizeof market j increases, centralization in market i

remains optimal until market j grows so large thatthe expected transportation costs outweigh either thebenefits of revenue maximization or manufacturingcost reduction, making the hybrid strategy dominantamong the centralization strategies.Relating the result to the context of offshoring, sup-

pose centralization in Asia is optimal given currentglobal demand. If Asian demand grows larger, ceterisparibus, centralization in Asia stays optimal. If weinstead suppose centralization in the United Statesis optimal given current global demand, when Asiandemand grows larger, localization of commonalitybecomes optimal. Therefore, given the likelihood thatgrowth rates in Asia will continue to surpass those inthe United States, we expect to see configurations thatcentralize commonality in the United States graduallydisappear, while more configurations arise that local-ize commonality or centralize commonality in Asia.

6.2. Demand Volatility and CorrelationOur stochastic analysis highlights the fact that thefacility network design decision not only dependson the relative demand size, but also on volatilityand correlation. Van Mieghem and Rudi (2002) provethat for bivariate normally distributed demands D theoptimal value V ∗ is increasing in the mean � anddecreasing in any variance term �ii. In other words,for normally distributed demands, because its capac-ity is capped from above, demand volatility degradesthe expected value of a network. Further, if ��K�D� issubmodular in D, then V ∗ is decreasing in any covari-ance term �ij . Submodularity of � in D can be estab-lished for the high �p case.

Property 4. For the high �p case, the operating profit��K�D� is submodular in D.

Property 4 implies that increased market correla-tion decreases the network value when market 1’sprice is substantially higher than Market 2. This resultis specific to normal demand distributions. Now weanalyze general continuous demand distributions.

Proposition 6. Let product demands be perfectly neg-atively correlated: P��D1 + D2 = k > 0� = 1.

(i) For the high and medium �p cases,

c̄T = cT �1

{1+ �v1 − v3��cK�2 + cK�3 − v2�

v1 − �cK�1 + cK�2 + cK�3�

}�

Moreover, it is optimal to centralize commonality in mar-ket 1 if and only if v1 > cK�1 + cK�2 + cK�3 and v2 <cK�2 + cK�3.(ii) For the low �p case,

cT = cT �2

{1+ �v2 − v4��cK�1 + cK�3 − v1�

v2 − �cK�1 + cK�2 + cK�3�

}�

Moreover, it is optimal to centralize commonality in mar-ket 2 if and only if v2 > cK�1 + cK�2 + cK�3 and v1 <cK�1 + cK�3.

This proposition highlights the nonobvious role ofprice and manufacturing cost differentials in deter-mining the optimal network configuration. Noticethat the sufficient and necessary conditions for theoptimality of centralization imply that v1 − v2 > cK�1

and v2 − v1 > cK�2 for (i) and (ii), respectively. Thissuggests that centralization becomes dominant onlywhen the profit advantage of the centralizing marketis sufficiently high.When demands are perfectly positively correlated,

a closed-form expression for the transportation costthresholds is not obtainable. Nevertheless, some struc-tural properties of the optimal capacity vector exist.

Proposition 7. Let demands be perfectly positivelycorrelated: P��D1 = D2� = 1. For the medium and low �pcases, if �cK�1 + cK�3�/v1 < �cK�2 + cK�3�/v2, then 0≤ K∗

4 ≤K∗

2 < K∗3 = K∗

1 ; if �cK�1 + cK�3�/v1 = �cK�2 + cK�3�/v2, thenK∗

1 = K∗2 = K∗

3 = K∗4 ; if �cK�1 + cK�3�/v1 > �cK�2 + cK�3�/v2,

then 0≤ K∗3 ≤ K∗

1 < K∗4 = K∗

2 .

The structural properties of the optimal capacityvector indicate a weakened value of the ex post trans-shipment option. Notice that K∗

i = K∗i+2 holds for

either i = 1�2, or both. It follows that all units of prod-uct i are produced locally at market i even thoughcommon component capacity at market j could bepositive.It is well known that the newsvendor critical fractile

solution crucially depends on the distribution overthe entire support and that the optimal capacity levelcan be below, at, or above the mean of the demand.Hence, general results on how capacity changes withdemand variability are hard to establish. We usenumerical analysis to illustrate the impact of demandvolatility and correlation on capacity investment.

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Figure 3 Optimal Network Configurations Under Deterministic and Stochastic Demand for p1 = 20, cM�1 = 1, cT = 0�5, cK = �0�5�0�5�13�5�13�5�, = �1�0�1�, = 1, � = 1

cMcM

0 0.1 0.2 0.3 0.40

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

p

0.5 0.6 0.7 0.8 0.90 0.1 0.2 0.3 0.40

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0.5 0.6 0.7 0.8 0.9

p

(a) Deterministicdemand (b) Stochastic demand

Marketfocused Offshore

Onshore

Hybrid

Offshore

cT cT

1.0 1.0

��

��

7. Numerical AnalysisThe analysis in the previous sections illustrates howthe optimal network configuration is impacted by eco-nomic and demand characteristics but has two limita-tions. First, we are only able to determine the signs ofthe effects rather than their magnitude. Second, unlikenetwork values, we cannot draw a general conclu-sion on how demand volatility affects network con-figuration and capacities. To strengthen our analysisin these two aspects, we present numerical exam-ples using optimization with simulated bivariate nor-mal demands with means � = ��1��2) and covariancematrix

� = �

(21 12

12 22

)�

where i = �iCVi and CVi is the coefficient of vari-ation of demand i, � is a standard deviation mul-tiplier, and is the correlation coefficient. We setCV = �0�3�0�4� as constant for all subsequent exam-ples but may vary �, �, and . For simplicity, weassume cT �1 = cT �2 and use cT to denote the trans-portation cost. To compare the performance of thefour network configurations described in the intro-duction, we define relative lost value of onshore

production= �V ∗ − Von�/Von; relative lost value of off-shore production = �V ∗ − Voff�/Voff; relative value oftransshipment= �V ∗ − Vmkt�/Vmkt.

Figure 3 illustrates how optimal network config-urations change under demand uncertainty in thecomplete space of price and manufacturing cost dif-ferentials.2 In the deterministic case, network deci-sions are solely driven by cost considerations (i.e.,offshoring is optimal when the transportation costis lower than the manufacturing cost differential)and only market-focused and offshoring may becomeoptimal. In contrast, onshoring may become optimalunder stochastic demand, as illustrated in the rightpanel of the figure. Demand uncertainty makesonshoring more attractive when the price differenceis substantial and the manufacturing cost difference issmall.Offshoring decisions are often driven by significant

labor cost advantages in the foreign market. Figure 4shows that for a high �p case, an increase in the man-ufacturing cost in the foreign market, as measured

2 We hold p1 and cM�1 fixed and vary p2 and cM�2. This ensuresmonotonic changes in the attractiveness of the network configura-tions. Recall that c̄T is monotone decreasing in p2 and monotoneincreasing in cM�2.

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Figure 4 Network Values as a Function of Manufacturing Cost Ratio

0 0.2 0.4 0.6 0.8 1.0 0.8 1.00

5

10

15

20

25

Relative lost value of onshore production

0 0.2 0.4 0.6 0.8 1.00 0.2 0.4 0.60

5

10

15

20

25

Relative lost value of offshore production

0

5

10

15

20

25

Relative value of transshipment

cM, 2/cM, 1 cM, 2/cM, 1 cM, 2/cM, 1

ρ = –1ρ = –1

ρ = –1

ρ = +1

ρ = +1

ρ = +1

(%)

(%)

(%)

Note. Parameterized by correlation for p = �20�14�, cM�1 = 1, cT = 1�5, cK = �1�1�10�10�, = �1�0�2�, = 1.

by the ratio cM�2/cM�1, increases the attractiveness ofonshoring, which becomes optimal when the correla-tion of demands approaches 1. The impact of this costchange on the value of transshipment is rather flat,meaning a similar impact on both market-focused andhybrid configurations. Notice that Figure 4 assumesa large high-price market: �1 = 5�2. The hybrid con-figuration remains optimal, however, even whencM�2/cM�1 = 1 if �1 = �2 = 1 (not shown). Therefore,low volume in the low-cost market contributes to theattractiveness of onshoring.Figure 5 shows the impact of transportation cost

on the network values for the same parameter val-

Figure 5 Network Values as a Function of Transportation Cost

0 1 2 3 4 50

1

2

3

4

5

0 1 2 3 4 50

50

100

150

200

0 1 2 3 4 50

5

10

15

20

cT cT cT

Relative lost value of onshore production Relative lost value of offshore production Relative value of transshipment

ρ = –1

ρ = –1

ρ = –1

ρ = +1

ρ = +1

ρ = +1

(%)

(%)

(%)

Note. Parameterized by correlation for p = �20�14�, cM = �1�1�, cK = �1�1�10�10�, = �1�0�2�, = 1.

ues of Figure 4 except that we now fix cM�2/cM�1 = 1but vary cT . As expected, more expensive trans-portation leads to lower value of centralization andtransshipment.

7.1. Demand CorrelationIn Figures 4 and 5, the value of transshipmentdecreases in demand correlation, which implies thatthe hybrid configuration incurs lower transportationcosts as demand correlation increases. Consistent withour example in §4.2, the two figures also illustratethat the attractiveness of onshoring (embodied inthe revenue maximization option and transportation

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Figure 6 Network Capacity Investment as a Function of Correlation

–1 0 10.5

1.0

1.5

0.5

1.0

1.5

0.5

1.0

1.5

0.5

1.0

1.5

Correlation coefficient–1 0 1




Correlation coefficient

K1 K2 K3 K4

0.5

1.0

1.5Kcommon/Kdedicated

–1 0 10.5

1.0

1.5

0.5

1.0

1.5

0.5

1.0

1.5

0.5

1.0

1.5





Correlation coefficient

K1 K2 K3 K4

0.5

1.0

1.5Kcommon/Kdedicated

γ = 0%

γ = 0% γ = 0%

γ = 0%

γ = 0%

γ = 0%

γ = 100%

γ = 100%

γ = 100%γ = 100%

γ = 100%

γ = 100%

γ = 100%

γ = 100%γ = 100%

γ = 100%

γ = 0% γ = 0% γ = 0% γ = 0%

Notes. Parameterized by standard deviation multiplier for p1 = 20, cM = �1�0�, cT = 1�3, cK = �1�1�10�10�, = �1�1�. (top) high �p� p2 = 14; (bottom)low �p� p2 = 20.

cost savings) increases in correlation while that ofoffshoring (embodied in manufacturing cost savings)decreases in correlation.Figure 6 details the impact of correlation and

volatility on network investment for high and low�p. Demand sizes are kept equal for the two mar-kets to illustrate that similar forces are at playas in the previous two examples even though inthis example the hybrid configuration always domi-nates the others. Except K3, all capacities decrease indemand correlation, consistent with the notion thatthe value of network production (i.e., demand pool-ing) decreases in demand correlation. Under high�p, increasing K3 enhances the revenue maximizationbenefit, which increases in demand correlation. Underlow �p, increasing K3 is also profitable, but for a dif-ferent reason: The manufacturing cost savings from

investing in K4 decreases in demand correlation. Theinvestment in K2 and K4 is impacted differently bydemand volatility in the two cases: Under high �p,there exists a correlation coefficient threshold abovewhich K2 and K4 decrease in demand volatility, whileunder low �p they almost always increase in demandvolatility. In the former case, because of the high pricein Market 1, the revenue maximization effect domi-nates, making investment in Market 1 more profitableas demand volatility increases. In the latter case, noprice advantage is present and thus the manufactur-ing cost effect dominates, making investment in Mar-ket 2 more attractive as demand volatility goes up.Finally, in both cases of Figure 6, total investment

in the common component increases in demand cor-relation compared to that in dedicated components.Under low �p, the capacity ratio of common compo-

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nent to dedicated component even increases to 1 andthus operational hedging through capacity imbalancedisappears. This is consistent with Van Mieghem(2007) and reflects that the risk pooling benefit ofcommonality decreases to zero as demand correlationapproaches 1 in the absence of the revenue maximiza-tion option.

8. ExtensionsWe consider two extensions: (1) generalizing ourmodel to asymmetric capacity cost of common com-ponent; and (2) exploring the impact of EoS by incor-porating fixed cost of investment.

8.1. Asymmetric Capacity Cost ofCommon Component

Until now we have assumed that the capacity costs ofthe common component in both markets are identical.The difference in real estate, labor costs, and exchangerates, however, can lead to asymmetric capacity costof common component in geographically separatedmarkets. To generalize our results, we derive struc-tural properties assuming cK�3 = cK�4. It is useful todefine �cK = cK�3 − cK�4.

Proposition 8. Under deterministic demand,(i) If cT �1 ≤ −�cM−�cK , centralizing commonality in

Market 1 is optimal;(ii) If cT �2 ≤ �cM + �cK , centralizing commonality in

Market 2 is optimal;(iii) Otherwise, the market-focused configuration is

optimal.

Table 4 Optimal Network Configurations Depend on Net Values and Capacity Costs of the Common Component

Ordering cK�3 = cK�4 cK�3 > cK�4 cK�3 < cK�4

v1 ≥ v4 ≥ v2 ≥ v3 K ∗i ≥ K ∗

i+2 K ∗1 ≥ K ∗

3 K ∗2 ≥ K ∗

4

v1 ≥ v2 ≥ v4 ≥ v3 K ∗i+2 = 0⇒ K ∗

j = K ∗j+2 K ∗

4 = 0⇒ K ∗1 = K ∗

3 K ∗3 = 0⇒ K ∗

2 = K ∗4

v2 ≥ v1 ≥ v4 ≥ v3 i� j ∈ �1�2 � i = j

v1 ≥ v3 ≥ v4 ≥ v2 Centralization: Market 1 See Proposition 8 Centralization: Market 1v1 ≥ v4 ≥ v3 ≥ v2v3 ≥ v1 ≥ v4 ≥ v2

v2 ≥ v4 ≥ v1 ≥ v3 Centralization: Market 2 Centralization: Market 2 See Proposition 8v4 ≥ v1 ≥ v2 ≥ v3v4 ≥ v2 ≥ v1 ≥ v3

Under stochastic demand,(i) If cT �1 ≤ −�cM−�cK and �cK ≤ 0, centralizing com-

monality in Market 1 is optimal;(ii) If cT �2 ≤ �cM + �cK and �cK ≥ 0 centralizing com-

monality in Market 2 is optimal.

Proposition 8 states the conditions under whichthe centralization configurations are optimal underdeterministic and stochastic demand. The resultsare rather general and cover previous results (set-ting �cK = 0 reduces Proposition 8 to Propositions 1and 2). Notice that the optimality condition understochastic demand requires lower common compo-nent capacity cost in the centralizing market. Considerthe condition cT �1 ≤ −�cM−�cK , which is equivalentto v2 − v3 ≤ −�cK . When �cK ≤ 0, v2 − v3 is the upperbound of profit gain of moving one unit of commoncomponent from Markets 1 to 2 while −�cK is theassociated capacity cost increase. The inequality con-dition implies that investing in any amount of com-mon component in Market 2 would be suboptimal. If,however, �cK ≥ 0, the optimal network configurationbecomes less obvious and depends on the demanddistribution and thus has to be solved from optimiza-tion. This is because even though the profit gain ofmoving one unit of common component from Mar-ket 2 to 1, as measured by v3 − v2, is greater than thecapacity cost increase �cK , the expected profit gainmay be lower than �cK , making investment in Mar-ket 2 common component profitable.Table 4 applies Proposition 8 to the nine cases of

net value ordering. The top three cases central to ourprevious analysis share similar structural properties

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as before, yet are less restrictive. The behavior ofthe remaining six cases depends on which markethas the capacity cost advantage. On the one hand,the results under the symmetric cost assumption arecarried over under the asymmetric cost assumptionwhen the centralizing market has cost advantage incapacity investment. For example, when Market 2 haslower capacity cost (i.e., cK�3 > cK�4), centralization inMarket 2 remains optimal. On the other hand, cer-tain configurations may become optimal even thoughthey are never optimal under the symmetric costassumption. For example, when Market 2 has suffi-ciently high investment cost (i.e., cT �1 ≤ −�cM−�cK)and sufficiently low manufacturing cost (i.e., cT �2 ≤�cM ), centralization in Market 1 becomes optimal forthe bottom three cases in Table 4, which only giverise to centralization in Market 2 when both marketshave identical capacity cost of the common compo-nent. This implies that when the common componentcapacity cost increases in the low-wage countries theoptimality region of onshoring is enlarged.

8.2. Fixed Cost of InvestmentOur analysis until now has focused on the risk pool-ing and revenue maximization benefits of central-ization. We now examine a third benefit: EoS, animportant driver in investment decisions that, simi-lar to demand volatility, increases the value of cen-tralization. To analyze EoS in our model, we use theconcave affine cost function C�K� = c01�K>0 + c′

KK. Weonly add a fixed cost to the common component asthe capacity decision hinges on whether to invest thisresource in both markets. Although the inclusion offixed cost makes the cost function discontinuous atzero and complicates first-order conditions, we iden-tified a simple condition to check whether centraliza-tion is optimal.Let Vcen = max�Von�Voff). If there is no fixed cost,

the optimization problem remains the same as before.When the fixed cost increases, the marginal invest-ment decision remains unchanged for a range offixed cost, in other words, the optimal capacity vec-tor is determined by the same first-order conditionsas before. But the optimal values of the centraliza-tion and hybrid configurations decrease at differ-ent rates. Vhyb decreases with slope −2 while Vcen

decreases with slope −1 because the decentralized

network has two common component facilities whilethe centralized network has only one. When the fixedcost is sufficiently high, the benefit of scale economiesbecomes dominant and makes centralization optimal.The outer envelope of the two downward-slopinglines in Figure 7 represents how the optimal networkvalue changes with the fixed cost. It follows from thegraph that the fixed cost threshold, denoted by c0(where the kink is located) is exactly the differencebetween Vhyb and Vcen.Given an affine concave cost structure, we can

decompose the optimization problem with EoS intothree: one with the hybrid and two with the central-ized configurations. The latter two problems can besolved using the newsvendor network approach illus-trated earlier but with reduced dimensionality. Fur-ther, our intuition is confirmed that EoS only increasesthe optimality region of centralization: if centraliza-tion is optimal without EoS, the optimal configura-tion remains after EoS is incorporated. If, however,centralization is suboptimal, the hybrid configurationremains optimal as long as the fixed cost is smallerthan the threshold c0.

It is important to point out that the optimal loca-tion of centralized commonality becomes dependenton demand characteristics in the presence of EoS.Recall that, without EoS, the potential optimal loca-tion of centralization is determined solely by therelative magnitude of price and manufacturing costdifferentials (under symmetric capacity cost of com-mon component). High and medium �p cases sup-

Figure 7 Impact of Fixed Cost on Optimal Network Values

c0 = Vhyb−Vcen

Fixed cost c0c0

Vhyb

Vcen Slope = –2

Slope = –1

Valueunder EoS

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port centralization in the high-price market whilelow �p puts centralization in the low-cost market. Ina more realistic situation where capacity investmentinvolves a significant fixed cost, the performance ofboth centralized configurations need to be evaluatedagainst the hybrid configuration. Since Von and Voff

are impacted by demand size and volatility, the opti-mal location of centralization is impacted by thosedemand characteristics as well.

9. Conclusions, Managerial Insights,and Limitations

We have presented an analytic model to study sourc-ing and location decisions of commonality in multi-market facility networks. As a special case, the modelallows us to analyze the offshoring decision from anetwork capacity investment perspective. The modelin this paper belongs to the broad class of newsvendornetworks but has a distinct focus on network designin the presence of interplant transshipment. Althoughthe model is kept simple for analytical tractability, itcaptures three key factors in facility network plan-ning: cost, revenue, and demand. Our main objectiveis to show how uncertainty may change the opera-tions network strategy relative to intuitive, determin-istic thinking based on cost only. We demonstrate thatcentralizing common component production in thehigh-price (but high-cost) market, or onshoring, canbe optimal under certain conditions.We translate our results into managerial insights on

offshoring: (1) When the manufacturing cost reduc-tions of offshoring outweigh transportation costs(including tariffs and duties), centralizing the com-mon component in low-wage countries is optimal,as expected. Otherwise, the optimal network strat-egy is more complex and depends on price ratios(revenue impact) as well as cost, market size anduncertainty. (2) Centralizing the common componentonshore becomes more attractive when the domes-tic price advantage outweighs the manufacturing costdisadvantage and when demand is positively corre-lated, i.e., high-price product with volatile correlateddemand. (3) Demand volatility affects the centraliza-tion versus localization decision, but the optimal loca-tion of centralization, in the absence of fixed costsof capacity investment, is independent of demand

characteristics. It is determined by the relative mag-nitude of the price and the manufacturing cost dif-ferential. (Recall that the high and medium pricedifferential cases only support onshoring while thelow price differential case only supports offshoring.)However, with the fixed costs, both decisions dependon demand characteristics of the two markets. (4) Weprovide the transportation cost thresholds to serve asan indicator of the attractiveness of centralization.Though commonality is a key component of our

model, it is worth noting that most of the managerialinsights hold for any flexible manufacturing system(no distinction between common component versusdedicated component). A simpler yet equally impor-tant network question is where flexible manufactur-ing system should be located. Our analysis can beapplied directly to answer this question. As telecom-munication and transportation costs decreased andinternational trade barriers were lifted over the lastdecade, many companies in developed countries havemoved production to low-wage countries. Our studyleads to insights that can guide managers in eval-uating the cost and benefit of offshoring. The keypoint is that it is crucial to incorporate the rev-enue effect and the global demand characteristics intotheir decision framework, in addition to understand-ing the cost structure of the global manufacturingnetwork.The limitation of our work lies in three aspects.

First, while we capture many relevant first-orderglobal parameters including exchange rates and tar-iffs, we focus on demand risk while keeping allother elements deterministic. The interaction betweenexchange rate risk and demand risk has been exploredin the literature. A recent paper by Ding et al. (2007)shows that buying financial option contracts on thecurrency exchange rate impacts not only the magni-tude of capacity levels but also the desired locationand number of production facilities. Second, leadtimeis not captured because our model has no explicit timedimension. In reality, capacity investment is followedby many demand and production periods. Significanttransshipment leadtimes may increase the the implieddemand volatility, making transshipment a less effec-tive operational hedge. The conjectured result is thatlocalization and even onshoring may then becomemore attractive. Last, transshipment of end product is

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not considered, yet that is not restrictive when local-ized end products are not substitutable.

Electronic CompanionAn electronic companion to this paper is available onthe Manufacturing & Service Operations Management website(http://msom.pubs.informs.org/ecompanion.html).

ReferencesAnupindi, R., R. Akella. 1993. Diversification under supply uncer-

tainty. Management Sci. 39(8) 944–963.Arntzen, B. C., L. F. Escudero, T. P. Harrison, L. L. Trafton. 1995.

Global supply chain management at digital equipment corpo-ration. Interfaces 25 69–93.

Baily, M. N., R. Z. Lawrence. 2004. What happened to the greatU.S. job machine? The role of trade and electronic offshoring.Brookings Papers Econom. Activity 2 211–284.

Bartmess, A. 1994. The plant location puzzle. Harvard Bus. Rev.72(March–April) 20–22.

Bartmess, A., K. Cerny. 1993. Building competitive advantagethrough a global network of capabilities. California ManagementRev. 35 78–103.

Brush, T. H., C. A. Maritan, A. Karnani. 1999. The plant locationdecision in multinational manufacturing firms: An empiricalanalysis of international business and manufacturing strategyperspectives. Production Oper. Management 8(2) 109–132.

Cohen, M. A., H. L. Lee. 1989. Resource deployment analysis ofglobal manufacturing and distributions networks. J. Manufac-turing Oper. Management 2 81–104.

Ding, Q., L. Dong, P. Kouvelis. 2007. On the integration of pro-duction and financial hedging decisions in global markets.Oper. Res. 55(3) 470–489.

Farrell, D. 2004. Beyond offshoring: Assess your company’s globalpotential. Harvard Bus. Rev. 82 82–90.

Farrell, D. 2005. Offshoring: Value creation through economicchange. J. Management Stud. 42(3) 675–683.

Feenstra, R. C., G. H. Hanson. 1996. Globalization, outsourcing, andwage inequality. Amer. Econom. Rev. 86(2) 240–245.

Ferdows, K. 1997. Making the most of foreign factories. HarvardBus. Rev. 75 73–88.

Hayes, R. H., S. C. Wheelwright. 1984. Restoring Our CompetitiveEdge� Competing Through Manufacturing. John Wiley & Sons,New York.

Huchzermeier, A., M. A. Cohen. 1996. Valuing operational flexibil-ity under exchange rate risk. Oper. Res. 44(1) 100–113.

Jordan, W. C., S. C. Graves. 1995. Principles on the benefits of man-ufacturing process flexibility. Management Sci. 41(4) 577–594.

Kazaz, B., M. Dada, H. Moskowitz. 2005. Global production plan-ning under exchange-rate uncertainty. Management Sci. 51(7)1101–1119.

Kogut, B., N. Kulatilaka. 1994. Operating flexibility, global man-ufacturing, and the option value of a multinational network.Management Sci. 40(1) 123–139.

Kouvelis, P., K. Axarloglou, V. Sinha. 2001. Exchange rates and thechoice of ownership structure of production facilities. Manage-ment Sci. 47(8) 1063–1080.

Kouvelis, P., M. J. Rosenblatt, C. L. Munson. 2004. A mathematicalprogramming model for global plant location problems: Anal-ysis and insights. IIE Trans. 36 127–144.

Kulkarni, S., M. J. Magazine, A. S. Raturi. 2004. Risk pooling advan-tages of manufacturing network configuration. Production Oper.Management 13(2) 186–199.

Kulkarni, S., M. J. Magazine, A. S. Raturi. 2005. On the trade-offsbetween risk-pooling and logistics costs in a multi-plant net-work with commonality. IIE Trans. 37 247–265.

MacCormack, A. D., L. J. Newman III, D. B. Rosenfield. 1994.The new dynamics of global manufacturing site location. SloanManagement Rev. 35(Summer) 69–80.

Markides, C. C., N. Berg. 1988. Manufacturing offshore is bad busi-ness. Harvard Bus. Rev. 66(September–October) 113–120.

Munson, C. L., M. J. Rosenblatt. 1997. The impact of local contentrules on global sourcing decisions. Production Oper. Management6(3) 277–190.

Robinson, L. W. 1990. Optimal and approximate policies in mul-tiperiod, multilocation inventory models with transshipments.Oper. Res. 38(2) 278–295.

Rudi, N., S. Kapur, D. F. Pyke. 2001. A two-location inventorymodel with transshipment and local decision making. Manage-ment Sci. 47(12) 1668–1680.

Santoso, T., S. Ahmed, M. Goetschackx, A. Shapiro. 2005. A stochas-tic programming approach for supply chain network designunder uncertainty. Eur. J. Oper. Res. 167 96–115.

Schmenner, R. W. 1979. Look beyond the obvious in plant location.Harvard Bus. Rev. 57(January–February) 126–132.

Schmenner, R. W. 1982. Multiplant manufacturing strategies amongthe fortune 500. J. Oper. Management 2(2) 77–86.

Skinner, W. 1974. The focused factory. Harvard Bus. Rev. 52(3)113–121.

Snyder, L. V. 2006. Facility location under uncertainty: A review.IIE Trans. 38 537–554.

Tomlin, B. 2006. On the value of mitigation and contingency strate-gies for managing supply-chain disruption risks. ManagementSci. 52(5) 639–657.

Tomlin, B., Y. Wang. 2005. On the value of mix flexibility and dualsourcing in unreliable newsvendor networks. ManufacturingService Oper. Management 7(1) 37–57.

Van Mieghem, J. A. 1998. Investment strategies for flexible re-sources. Management Sci. 44(8) 1071–1078.

Van Mieghem, J. A. 2004. Note: Commonality strategies: Valuedrivers and equivalence with flexible capacity and inventorysubstitution. Management Sci. 50(3) 419–424.

Van Mieghem, J. A. 2007. Risk mitigation in newsvendor networks:Resource diversification, flexibility, sharing, and hedging. Man-agement Sci. 53(8) 1269–1288.

Van Mieghem, J. A. 2008. Operations Strategy� Principles and Practice.Dynamic Ideas, Belmont, MA.

Van Mieghem, J. A., N. Rudi. 2002. Newsvendor networks:Inventory management and capacity investment with discre-tionary activities. Manufacturing Service Oper. Management 4(4)313–335.

Webb, A. 2004. U.S. will get China engines. Automotive News79(6111) 16.

Webb, A., J. Treece. 2004. Toyotas sold in U.S. may get Chineseengine. Automotive News 78(6082) 6.

Yazlali, O., F. Erhun. 2004. Managing demand uncertainty withdual supply contracts. Working paper, Stanford University,Stanford, CA.

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Multimarket Facility Network Design with Offshoring Applications