European Journal of Operational Research 207 (2010) 725–735

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European Journal of Operational Research

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Production, Manufacturing and Logistics

Ensuring responsive capacity: How to contract with backup suppliers

Fabian J. Sting a,*, Arnd Huchzermeier b,1

a INSEAD, Boulevard de Constance, 77 305 Fontainebleau Cedex, Franceb WHU – Otto Beisheim School of Management, Burgplatz 2, 56179 Vallendar, Germany

a r t i c l e i n f o

Article history:Received 28 October 2009Accepted 26 May 2010Available online 4 June 2010

Keywords:Responsive capacityDemand and supply uncertaintySupply chain contractingOperational hedgingBackup supplier

0377-2217/$ - see front matter � 2010 Elsevier B.V. Adoi:10.1016/j.ejor.2010.05.044

* Corresponding author. Tel.: +33 160729129; fax:E-mail addresses: fabian.sting@insead.edu (F.J. Stin

1 Tel.: +49 2616509380; fax: +49 2616509389.

a b s t r a c t

Firms that source from offshore plants frequently perceive the lack of reliability and flexibility to beamong the major drawbacks of their strategy. To mitigate against imminent mismatches of uncertainsupply and demand, establishing capacity hedges in the form of responsive backup suppliers is a wayout that many firms follow. This article analyzes how firms should contract with backup suppliers, induc-ing the latter to install responsive capacity. We show that supply options are appropriate to achievesourcing channel coordination under forced compliance, whereas any firm commitment contract imposesa deadweight loss on the system. Whereas price-only contracts are unable to coordinate the sourcingchannel under voluntary compliance, utilization-dependent price-only contracts are. Under the formercontract, a price-focused strategy on the part of the manufacturer turns out to diminish the system’s ser-vice level and possibly has negative implications on installed backup capacity, and not least on the man-ufacturer’s profit.

� 2010 Elsevier B.V. All rights reserved.

1. Introduction

Firms that offshore their sourcing activities typically face two potential drawbacks (Fraunhofer, 2008; PRTM, 2008). First, sourcing fromoffshore plants or suppliers curtails supply-side flexibility because the distance to supply sources increases either from a geographical,organizational, or cultural perspective. Long delivery times and lack of sourcing flexibility (PRTM, 2008), which is an antecedent of supplychain agility (Swafford et al., 2006), decreases one’s ability to respond to demand-side fluctuations (Christopher and Peck, 2004). Second,the comparatively low reliability of offshore plants in terms of delivery performance and product quality is an ongoing issue for a largenumber of supply chain or purchasing managers. Firms seek to balance the cost advantages that come with offshoring with the responsive-ness of backup supply bases close to their operating sites. Relying on backup suppliers is one major strategy to mitigate (Chopra and Sodhi,2004) against these diseconomies of vulnerability (Hayes et al., 2005). In other words, firms attempt to install operational hedges(Huchzermeier and Cohen, 1996) in the form of backup supply sources, enabling them to smooth out the two-sided supply and demanduncertainty they face.

However, being more costly, the responsive supplier is relegated to a backup role. He only comes into the operation if demand is greaterthan offshore supply. Provided that offshore sources are able to cover demand entirely, the manufacturer will give preference to the cheapoffshore alternative and avoid costly responsive production. If, on the other hand, offshore production capabilities do not suffice to servedemand, the manufacturer critically relies on her responsive supplier in order to save severe mismatch costs. The question that arises is:How can the manufacturer ensure responsive capacity, given that the backup supplier is aware of his replacement function.

While firms in numerous industries – such as automotive (Sheffi, 2005), pharmaceuticals (Chopra et al., 2007), and electronics (Tomlin,2006) – reap the benefits of responsive backup supply, little attention has been paid on how to contract for it. One contracting strategy is tocompensate for backup deliveries with high prices upon large deliveries, as is practiced in the following example. Kolbus, a leading man-ufacturer of bookbinding machinery relies on a network of small suppliers located within 20 kilometre of its headquarters in Germany.Kolbus’s customers in the print industry demand quick delivery times of about 6 weeks; high service levels are among the most importantsales points for this complex project business. The majority of parts are produced or purchased on a make-to-stock basis through in-houseproduction or from offshore suppliers, respectively. In addition, for 70% of its purchased parts, Kolbus is connected to one alternative back-up supplier close to its plant. Kolbus’s COO, states that ‘‘if we actually need the local suppliers as an extended workbench on a full scale, we

ll rights reserved.

+33 160729240.g), ah@whu.edu (A. Huchzermeier).

726 F.J. Sting, A. Huchzermeier / European Journal of Operational Research 207 (2010) 725–735

compensate them for their deliveries generously. And they are prepared, still knowing that they cannot reckon on us for steadily incomingorders”.

In this article we analyze how a manufacturer should contract with her backup supplier to ensure responsive capacity and, at the sametime, benefit from offshore sourcing. We investigate how the manufacturer can obtain a responsive capacity hedge against two-sided sup-ply and demand uncertainty to achieve Pareto efficient alignment of the manufacturer’s offshore capacity and the backup supplier’sresponsive capacity investments via contracting mechanisms. We consider several types of contracts that reflect different degrees of flex-ibility, including firm commitments, supply options, price-only strategies, and utilization-dependent price-only strategies. Designing acontract requires the manufacturer to account for the backup supplier’s awareness of his backup role. Being conscious about the manufac-turer’s offshore investment option, the backup supplier has to decide on a relationship-specific investment (Williamson, 1985), that is, theinstallment of dedicated responsive capacity, before demand and offshore supply uncertainty materializes.

The remainder of this article is structured as follows. We review the literature in Section 2 and present our model in Section 3. The back-up and offshore capacity investment and contracting games under both forced compliance and voluntary compliance regimes are studiedin Section 4 for firm commitments, supply options, and price-only contracts. We present a simple utilization-dependent contract that coor-dinates the decentralized system under voluntary compliance in Section 5. We present our conclusions in Section 6.

2. Literature review

The research presented in this article is particularly connected to works in the fields of capacity contracting and random yield manage-ment. Cachon (2003) reviews the substantial literature on supply chain contracting. From the contracting point of view, our model is closelyrelated to the models of Cachon and Lariviere (2001) and Van Mieghem (1999). In both models, the downstream firm, referred to as themanufacturer, relies on capacity investments of an upstream firm, referred to as the supplier. Cachon and Lariviere (2001) consider a supplychain situation in which a manufacturer offers her single supplier a take-it-or-leave-it contract under two contract compliance regimes.Under forced compliance, the supplier has little room for manoeuver, whereas under voluntary compliance, he has substantial flexibilityin his choice of capacity. We adopt their classification to study the efficiency of contracts as well as their relatively general contractual de-sign consisting of firm commitments and supply options. Van Mieghem (1999) examines, in the terminology of Cachon and Lariviere(2001), a supply chain comprising a manufacturer and a subcontractor under voluntary compliance. In this model, a manufacturer anda subcontractor each face a stochastic demand. Apart from relying on her own capacity, the manufacturer may also process units of thesubcontractor’s production. Our model is methodically similar to Van Mieghem (1999), and extends on the newsvendor competition underrandom demand that was introduced by Parlar (1988) and generalized by Lippman and McCardle (1997) and uses a modification of themultidimensional newsvendor model developed by Van Mieghem (1998).

Our model differs from the contracting papers mentioned previously along two dimensions: (1) the type of the prevailing uncertaintyand (2) the supplier’s role. A manufacturer who faces supply and demand uncertainty seeks to hedge her offshore activities by inducing thesupplier to install reliable and flexible (i.e., responsive) capacity. The supplier, in turn, finds himself relegated to a backup role because hisproduction will be substituted for offshore production only if there is a mismatch between offshore supply and demand, that is, only ifoffshore supply underscores demand.

Typically, managing random yield requires determining optimal lot sizes when there is uncertainty about the quantity that actually willbe delivered by an unreliable source. The extensive body of work on random yield management has been reviewed by Porteus (1990), Yanoand Lee (1995), and Minner (2003) with a focus on multiple-supplier sourcing. One may classify this research into single- or multiple-sup-plier models, according to the random yield or supply uncertainty construct applied and the time horizons of the models. The random yieldconstruct applied to the unreliable source in this article is the concept of ‘‘random capacity” which is featured in the models of Ciarallo et al.(1994, 2002) and Dada et al. (2007); it is referred to as ‘‘exogenous supply uncertainty” in the latter. Our adaptation generalizes the randomcapacity construct in two directions. First, we do not rule out the stochastic dependence of supply and demand uncertainty; that is, weallow supply and demand to be interrelated. Second, supply disruption type of events are captured because the construct allows us to rep-resent complete shutdowns of the unreliable source.

The trade-offs analyzed in Tomlin (2005, 2006) and Chopra et al. (2007) also arise in our model in that two combinable sourcing alter-natives are considered: a responsive but more expensive supply source and an unreliable but inexpensive supply source. The backup sup-plier, as he is modeled in this article, conforms to the ‘‘flexible and reliable supplier” of Chopra et al. (2007) or the ‘‘contingent supplier” ofTomlin (2005): responsive supply has zero lead time which enables the manufacturer to initiate responsive production accounting for thethen-materialized supply and demand states. This article differs from the backup supply models mentioned previously primarily in termsof the backup supplier’s capacity: it is endogenous. To our knowledge, although backup suppliers’ price decisions have been incorporated inmodels (e.g., Babich, 2006), the backup capacity installment, which is of paramount importance for the manufacturer’s risk management,has not been investigated as a decision variable beyond the manufacturer’s boundaries and control.

3. The model

Our contracting model considers a supply chain comprising a manufacturer and a backup supplier who both seek to maximize theirexpected profit. The timing of events is depicted in Fig. 1, notation is summarized in Table 1. The manufacturer offers a contract to theresponsive backup supplier, who may accept or reject the offer. Reflecting the market power of the manufacturer, the offer has a take-it-or-leave-it character. The supplier’s reservation profit is normalized to zero. Thus, he will accept any contract with an expected profitno lower than zero. If the contract is rejected, the game stops, and the manufacturer is left with a single offshore sourcing decision. Other-wise, the game continues and both the manufacturer and the supplier make their capacity decisions. The manufacturer incurs a constantcost cM > 0 for each unit of offshore capacity QM installed. Likewise, the supplier bears constant capacity cost cB > 0 for the amount QB P 0 ofresponsive capacity installed. Let Q = (QM,QB)0 summarize both agents’ decisions. The responsive capacity’s only purpose is to provide abackup for the manufacturer. However, positive constant residual values vB > 0 for unused backup capacity can be incorporated into themodel by deflating the backup capacity costs to cB � vB. Before uncertainties materialize, the manufacturer decides on the quantity of

Manufactureroffers contract

to supplier

Backupsupplier may

accept or reject the offer

Manufacturerinstalls/procures

offshore capacity QM

Backupsupplier installs

responsivecapacity QB

Manufacturerplaces order with offshore

source

Demand and supply states are realized

Manufacturer places order

with responsive Supplier

Demand that can be met is fulfilled,

unused quantitiessalvaged

Backup supplierinitiates and

delivers responsive production

time

Fig. 1. Sequence of events.

Table 1Notation summary.

cB Marginal capacity cost of the backup suppliercM Marginal capacity cost of the manufacturer’s (unreliable) offshore resourceD Random demandf Bivariate joint probability density function of supply and demand uncertainty induced by Pg Goodwill loss for units of unsatisfied demandK Random potential production capability of the manufacturer’s offshore resourcel Firm commitments quantitymB Marginal production costs of the backup suppliermM Marginal production costs for successfully delivered units of the manufacturer’s offshore resourceXn Element of the state space partition defined in Table 2 and illustrated in Fig. 2, n = 1, . . . ,6o Supply options quantity/B Critical fractile of backup supplier’s responsive resourcePcen Expected supply chain profitPB Expected profit of the backup supplierPM Expected profit of the manufacturerpcen Operating supply chain profitpM Operating profit of the manufacturerpB Operating profit of the backup supplierP Probability measure of bivariate supply and demand uncertaintyQ Vector of installed responsive and offshore capacitiesQB Backup supplier’s responsive capacity installmentQM Manufacturer’s offshore capacity installmentqB Responsive production in the integrated systemqe Exercise of responsive production under forced complianceqt Responsive production transfer under voluntary compliancer Retail price for finished goodsS Random offshore supplyv Salvage value for overage supply

A1 mM 6 v < mB

A2 cM < (r + g �mM)P(D > 0,K > 0) + (v �mM)P(D = 0,K > 0)A3 cB < (r + g �mB)P(D > 0)

F.J. Sting, A. Huchzermeier / European Journal of Operational Research 207 (2010) 725–735 727

offshore production. This decision, however, collapses economically with the capacity investment decision of the offshore source becausethe manufacturer’s state of information has not changed. The lack of flexibility on the part of the offshore supply rules out any updating ofinformation. The technology of the responsive supplier, on the other hand, allows for production contingent on the state of the world. Thus,the manufacturer may call off an order from the supplier after observing the offshore resource’s potential production capability K, receivingoffshore supply min{QM,K}, and recording demand D. Offshore deliveries cost the manufacturer mM per unit, and the supplier incurs a con-stant cost mB for each unit of responsive production. The manufacturer then turns total supply into finished products and receives a con-stant price r for each unit of satisfied demand. Unsatisfied demand causes a unit loss of goodwill g, overage supply units can be salvaged atv. The backup supplier receives compensation by the manufacturer in fulfillment of the contract, whose various forms are to be specified inthe following paragraphs.

The states of the world are specified by the bivariate random variable X ¼ X1

X2

� �: ðX;F; PÞ ! ðR2;B2Þ which obeys the finite, contin-

uous and widely known probability measure P. Let f : R2 ! R denote the joint probability density function induced by P, which is assumedto be positive over its support. The random demand and supply states are given by D � Xþ1 and K � Xþ2 , respectively. The way random off-shore supply S = min{QM,K} materializes in our model follows the construct of random capacity (Ciarallo et al., 1994), also referred to asexogenous supply uncertainty (Dada et al., 2007), in that a random variable which is independent of the amount of capacity installed,places an upper bound on the quantity delivered. The fact that we do not restrict X to be positive has the following implications: Because

728 F.J. Sting, A. Huchzermeier / European Journal of Operational Research 207 (2010) 725–735

we allow P(X2 < 0) > 0, supply disruption type of events can occur with positive probability, that is, P(K = 0) > 0. Likewise, disruptions indemand can occur because we allow for P(X1 < 0) = P(D = 0) > 0.

We make the following assumptions. The marginal cost for successfully delivered offshore units is assumed to be low, that ismM 6 v < mB (A1), capturing the costliness of responsive production. The two supply sources should be viable on their own; that is, a centraldecision maker would invest in each type of source, provided it is the only sourcing option available. Therefore, we assume that marginalexpected returns for the first single investment unit of either type of capacity are positive, that is, cM < (r + g �mM)P(D > 0,K > 0) +(v �mM)P(D = 0,K > 0) (A2) and cB < (r + g �mB) P(D > 0) (A3).

The integrated solution of the game assumes that there is a single decision maker who seeks to find a responsive production and capac-ity investment policy that achieves channel-wide optimal expected profit. To establish a reference point for decentralized supply chainmodel, we briefly summarize the optimal strategy of a single decision maker, which has been derived by Sting and Huchzermeier(2009). To solve the two-stage dynamic problem, we work backwards, starting with the second-stage problem in which the central decisionmaker determines her maximum operating profit pcen(Q,D,K) by choosing the optimal level of responsive production qB contingent on thesupply and demand states:

pcenðQ ;D;KÞ ¼ maxqB2Rþ

rðqM þ qBÞ � gðD� qM � qBÞ þ ðv � rÞðqM � DÞþ �mMqM �mBqB ð1aÞ

subject to qB 6 minfQ B; ðD� qMÞþg; qM ¼ S: ð1bÞ

For any ðD;KÞ0 2 R2þ and QM ;QB 2 Rþ, the optimal responsive production of the centralized system is given by

qcenB ¼

QB; if D� S > Q B;

D� S; if Q B P D� S > 0;

0; if D� S 6 0;

8><>: ð2Þ

or, in abbreviated form, qcenB ¼minfðD� SÞþ;QBg.

In the first-stage problem, the central decision maker seeks to maximize her expected profit by deciding on the optimal capacity vectorQcen. To determine the optimal integrated profit, she seeks to maximize the following program:

maxQ

PcenðQ Þ ¼maxQ

E pcenðQ ;D;KÞ½ � � ðcM; cBÞ � Q ð3aÞ

subject to Q P 0: ð3bÞ

The nonlinear program (3) can be solved uniquely by considering the dual variables kcenM ðQ ;D;KÞ and kcen

B ðQ ;D;KÞ of the linear program(1) w.r.t. the offshore capacity QM and backup capacity QB. These dual variables can be understood as shadow prices for the capacities; thatis, they reflect the marginal increase in operating profit by having an additional unit of offshore or responsive capacity given a specific stateof the world. We can partition the supply and demand state space such that the shadow prices are constant over each domain of the par-tition, which is formulated in Table 2 and illustrated in Fig. 2. Defining the 2 � 6 shadow matrix of the centralized problem as

Kcen � KcenM

KcenB

!�

kcenM ðQ ;XjðQ ÞÞ

kcenB ðQ ;XjðQ ÞÞ

!j¼1;...;6

�0 0 0 v �mM mB �mM r þ g �mM

r þ g �mB 0 0 0 0 r þ g �mB

� �

and denoting the vector of domain probability masses by PðQ Þ � ðPðXjðQ ÞÞÞj¼1;...;6 2 R6þ we can state the sufficient and necessary optimality

conditions for the centralized system:

Proposition 1.

(i) The capacity vector Q cen 2 R2þ is optimal for the centralized system if and only if there exists a l 2 R2

þ such that

KcenPðQ cenÞ ¼

cM

cB

� �� l; l0Q cen ¼ 0: ð4Þ

(ii) The channel optimal capacity vector Q cen 2 R2þ is unique.

The optimal strategy of the centralized system can be written out explicitly, depending on capacity cost threshold levels, which indicatewhether the resource types should be activated.

Theorem 1. Define the capacity cost thresholds as

�cM ¼ KcenM P

0Q B

� �and �cB ¼ Kcen

B PQ M

0

!; ð5Þ

where QM and QB are optimal single sourcing solutions to

cM ¼ KcenM P

QM

0

!and cB ¼ Kcen

B P0

Q B

� �: ð6Þ

The optimal strategy has one of three distinct forms, depending on the marginal costs for offshore capacity and responsive capacity:

(i) It is optimal to invest solely in offshore capacity Q cen ¼ ðQM ;0Þ0 if and only if cB P �cB.(ii) It is optimal to invest solely in responsive capacity Q cen ¼ ð0;Q BÞ0 if and only if cM P �cM.

Table 2State contingent shadow prices for offshore and responsive capacity in the centralized problem.

Domain kcenM ðQ ;D;KÞ kcen

B ðQ ;D;KÞ

X1ðQ Þ ¼ fðD;KÞ0 2 R2þjK 6 QM ; K þ QB 6 Dg 0 r + g �mB

X2ðQ Þ ¼ fðD;KÞ0 2 R2þjK 6 QM ; K 6 D < K þ QBg 0 0

X3ðQ Þ ¼ fðD;KÞ0 2 R2þjK 6 QM ; D 6 Kg 0 0

X4ðQ Þ ¼ fðD;KÞ0 2 R2þjK > QM ; D 6 QMg v �mM 0

X5ðQ Þ ¼ fðD;KÞ0 2 R2þjK > QM ; QM 6 D < QM þ QBg mB �mM 0

X6ðQ Þ ¼ fðD;KÞ0 2 R2þjK > QM ; QM þ QB < Dg r + g �mM r + g �mB

Fig. 2. Supply and demand state space of the centralized problem.

F.J. Sting, A. Huchzermeier / European Journal of Operational Research 207 (2010) 725–735 729

(iii) Otherwise, if cB < �cB and cM < �cM, dual (offshore sourcing and responsive sourcing) is optimal; Qcen solves optimality condition (4) withl = 0.

So far, we have characterized the optimal sourcing portfolio of a central decision maker. In what follows, we study systems whoseinvestment and production decisions are simultaneously made by two decentralized decision makers. For the analysis of decentralized sys-tems, we are interested in the case in which the entire system benefits from having both offshore capacity and responsive capacity, that is,the channel optimal sourcing portfolio consists of both types of capacities. Consequently, to confine our attention to this case, we assumethat Qcen

M ;QcenB > 0 or, equivalently, that cM < �cM and cB < �cB. Interestingly, in this case, the overall system’s service level (i.e., the probability

that demand is no greater than total supply) will be set by the characteristics of the backup supplier’s capacity.

Corollary 1. The centralized system’s service level resulting from strategy Q is given by PS5

i¼2XiðQ Þ� �

. Let 1B � rþg�mB�cBrþg�mB

denote the critical

fractile of responsive capacity. The system’s service level is determined exclusively by the critical fractile of the backup supplier. Thus,

P[5i¼2

XiðQ cenÞ !

¼ 1B: ð7Þ

In terms of Fig. 2, the previous statement implies that investment in responsive capacity balances the thick line, which can be referred toas the system’s service profile, such that the system’s service profile equals the backup supplier’s critical fractile.

4. Firm commitments, supply options, and price-only contracts

In this section, we extend the ‘‘full information scenario” of Cachon and Lariviere (2001) by endowing the manufacturer with a (cheap)offshore supply alternative; this relegates her responsive supplier to a backup role. The contract the manufacturer offers the backup sup-plier is assumed to consist of a number l P 0 of firm commitments and a number o P 0 of options. This combined contract type allows us tocapture several other contract schemes such as buy-back contracts (Pasternack, 1985) and quantity flexibility contracts (Tsay, 1999) asshown by Cachon and Lariviere (2001). For purchasing options and firm commitment quantities, the manufacturer has to pay the supplierwl per firm commitment and wo per option. Option units, as their name suggests, provide the manufacturer with the right, but not the obli-gation to call off responsive production after supply and demand states are observed. The manufacturer has to pay the supplier we P 0 forevery option unit exercised. In advance, we limit our attention to wl 6 wo + we and wl P we; only supply option quantities or firm commit-ment quantities would be relevant if either the first or the second inequality does not hold, respectively. Furthermore, assuming that

730 F.J. Sting, A. Huchzermeier / European Journal of Operational Research 207 (2010) 725–735

r + g > wl P cB + mB and r + g > wo + we P cB + mB ensures that both agents would have an incentive to engage in trade based on the partic-ular contractual components.

4.1. Forced compliance regime

Under forced compliance, the capacity installments are observable and enforceable by a court of law. The supplier’s capacity decisionmust conform to the quantity specified in the contract. He has to be prepared to cover the manufacturer’s largest possible order. Hence, thesupplier’s problem is reduced to either accepting or rejecting the manufacturer’s offer; there is no room for him to make a decision at eitherthe production or the capacity investment stage. Provided the supplier accepts the offer, he has to install capacity QB = l + o. Likewise, themanufacturer must adhere to any offshore capacity agreements that may be written in the contract. Working backwards, we begin by for-mulating the manufacturer’s problem at the production stage in which she decides on the call-off quantity qe for responsive delivery asfollows:

pMðQ M; l; o;D;KÞ ¼maxqe2Rþ

rðSþ lþ qeÞ þ ðv � rÞðqM þ l� DÞþ � gðD� S� qeÞ �mMS�weqe ð8aÞ

subject to qe 6 minfo; ðD� S� lÞþg: ð8bÞ

The manufacturer’s optimal call-off quantity is qe = min{o, (D � S � l)+}, because by assumption, we have that r + g > we. At this stage,nothing else remains to be done by the supplier but to produce l + qe. Note that the state-dependent responsive production quantityl + min{(D � S)+,o} may, in general, deviate from the channel optimal production min{(D � S)+,QB} of (2). The supplier’s expected profit func-tion at the capacity investment stage can be formulated as

PBðQ M; l; oÞ ¼ E½pBðQ M; l; o;D;KÞ� þwllþwoo� cBQ B; ð9Þ

where

pBðQ M; l; o;D;KÞ ¼ weqe �mBðlþ qeÞ ð10Þ

is the backup supplier’s state-dependent operating profit at the responsive production stage. During the purchasing and investment stage,the manufacturer seeks to balance offshore capacity investments and optimal purchases of options and firm commitments by optimizing thefollowing problem:

maxQM ;l;o

PMðQ M; l; oÞ ¼maxQM ;l;o

E pMðQ M ; l; o;D;KÞ½ � �wll�woo� cMQ M ð11aÞ

subject to PBðQM ; l; oÞP 0; ð11bÞ

where constraint (11b) ensures the supplier’s participation. We start analyzing the contract’s implications for the supply chain with Lemma1, which confines our attention to options contracts, because contracts including firm commitment components do not coordinate respon-sive production.

Lemma 1. Any contract that includes firm commitments l > 0 is Pareto inefficient.

Pareto improvements can directly be achieved by transforming firm commitment quantities into supply options quantities and by set-ting the two-part option tariffs to we = mB and wo = wl �mB. The flexibility of the backup supplier should be accommodated in a flexiblecontract; firm commitments ignore this flexibility. Note that this result hinges on the assumption that firm commitments do not resultin lower production costs for the backup supplier, as is assumed in Donohue (2000). Responsive production is considered to rely on a singletechnology that entails timely but relatively costly one-mode production.

A contract consisting only of options imposes no loss on the decentralized system while guaranteeing the entire profit to the manufac-turer as shown in the following theorem.

Theorem 2. Suppose the manufacturer offers a contract consisting only of options (l = 0) with options quantity o ¼ QcenB and price terms

(wo,we) = (cB,mB). Then the supplier will accept the contract because he will earn his zero reservation profit. Responsive production and offshorecapacity investment are aligned Pareto efficiently, that is, responsive production and capacity investments conform to the centralized system. Themanufacturer captures the integrated system profit PcenðQcen

M ;QcenB Þ.

Note that Theorem 2 does not make any statement about the manufacturer’s capacity decision; only the supplier’s behavior is subject tothe forced-compliance regime and written in the contract. In fact, there is no need for a quantity commitment because the supplier willrightly believe that the manufacturer will choose the Pareto efficient offshore capacity Qcen

M as her best response. The manufacturer’s deci-sion problem under this contract perfectly duplicates the central decision maker’s capacity investment problem. Thus, only unilateral forcedcompliance is required; the manufacturer will self-select the channel optimal quantity. The following theorem establishes the existence of acontinuum of coordinating contracts opened up by the manufacturer’s commitment to the channel optimal offshore quantity Q cen

M .

Theorem 3. Suppose the manufacturer contractually commits herself to install the channel optimal offshore quantity Q cenM and purchases Qcen

Boptions. Let VðQM;QBÞ ¼ E½qe� ¼ E½minfðD� SÞþ;QBg� denote the expected responsive production quantity under an options-only contract.Offering the backup supplier an options contract with the following price terms:

wo ¼ cB � qV Q cen

M ;QcenB

� �Q cen

B

and we ¼ mB þ q; forq 2 �mB;min cBQ cen

B

V Q cenB ;Q cen

M

� � ; r þ g

( ) !

aligns production and capacity investment decisions Pareto efficiently, that is, production and capacity decisions equal those of the centralized sys-tem. The manufacturer earns the integrated system’s expected profit PcenðQcen

M ;QcenB Þ, whereas the backup supplier defrays his reservation profit of

zero.

F.J. Sting, A. Huchzermeier / European Journal of Operational Research 207 (2010) 725–735 731

Theorem 2 appears to be a special case of Theorem 3 with contract terms wo = cB and we = mB. It is not, however, because the manufac-turer’s offshore investment quantity is not part of the contract in Theorem 2, even though the manufacturer credibly selects Qcen

M . In con-trast to Theorems 2, 3 is based on bilateral forced compliance. Both parties are obligated to obey the capacity investments specified in thecontract. Furthermore, the options contract under bilateral forced compliance distributes pay-off variability continuously between the twosupply chain agents. If q = 0, then the options contract is written as (wo,we) = (cB,mB); that is, the supplier receives just the exact reimburse-ment for his capacity and production expenses, and all variability is borne by the manufacturer. For q – 0, pay-off variability is shifted from

the manufacturer to the supplier. As q ? �mB, we have ðwo;weÞ ! ðcB þ mBQcenB

VðQ cenB ;Qcen

M Þ; 0Þ; that is, the supplier receives a flat-rate fee for his

backup service in the limit. Assuming that cBQcen

BVðQcen

B ;QcenM Þ

< r þ g, and with q! cBQcen

BVðQcen

B ;Q cenM Þ

, the supplier’s expenses for backup capacity are

fully amortized in expectation through an upvalued exercise price because ðwo;weÞ ! ð0; mB þ cBQcenB

VðQcenB ;Qcen

M ÞÞ. For any q, however, the pay-

off variability is irrelevant for both risk-neutral agents and the supplier is left just with his reservation profit of zero.

4.2. Voluntary compliance regime

Under voluntary compliance, both the manufacturer and the supplier cannot be forced to adhere to contractual obligations for theirrespective capacity investments. This situation can arise because capacity investments may be hard to observe or verify. Thus, in the lattercase, they may not be enforceable by a court. After the fact, the parties may observe how much capacity the respective contractual partnerinstalled. Demonstrating misconduct in court, however, may not be economically viable. From the backup supplier’s point of view, it maybe unreasonably hard and costly to prove that the manufacturer installed more capacity at an offshore site than she was obligated to justbecause of the geographical distance. Conversely, from the manufacturer’s point of view, it could be disproportionately hard and costly toprove that the backup supplier installed less responsive capacity than he was obligated to in the contract. In court, the manufacturer wouldhave to provide evidence demonstrating that the backup supplier is to blame for a willful default. All payments from the manufacturer tothe backup supplier, which are not linked to actual deliveries by the latter, do not stimulate responsive capacity investments but onlytransfer wealth from the manufacturer to the backup supplier. Thus, in analogy to Cachon and Lariviere (2001), the manufacturer’s onlyreasonable contract consisting of firm commitments and supply options is to offer a special case of an options contract (o > 0,l = 0) thatfeatures an execution fee only, that is, wo = 0,we > 0. This, in fact, is a price-only or wholesale price compensation for delivered units;any additional contractual statement about quantities is irrelevant because the parties make their own capacity choices.2

We now formulate the manufacturer’s and supplier’s first-stage capacity investment problems and the second-stage order call-off(manufacturer) and production (supplier) decisions under voluntary compliance with price-only contracts. We begin with the backup pro-duction subgame in the second stage in which the manufacturer and the supplier maximize their operating profits pdec

M and pdecB , respec-

tively. To simplify the notation, we let w = we, and we let qt P 0 denote the quantity of backup production that is transferred from thesupplier to the manufacturer. The manufacturer requests supply qM

t ; the supplier decides on how to fill this call by offering a productionquantity qB

t :

2 In tto the s

pdecM ðQ ; qt ;D;KÞ ¼ max

qMt 2Rþ

rðqM þ qtÞ � gðD� qM � qtÞ þ vðqM � DÞþ �mMS�wqt ð12aÞ

subject to qMt 6 ðD� SÞþ; qt ¼min qM

t ; qBt

� ; ð12bÞ

and

pdecB ðQ ; qt ;D;KÞ ¼ max

qBt 2Rþ

qtðw�mBÞ ð13aÞ

subject to qBt 6 Q B; qB

t 6 qMt ; qt ¼ min qM

t ; qBt

� : ð13bÞ

The supplier will fill the manufacturer’s request to the best of his abilities, that is, he will offer qBt ¼min qM

t ;QB

� if w > mB. Otherwise, if

w 6mB, no responsive production will take place. The manufacturer, in turn, will request responsive production qMt ¼ ðD� SÞþ if w < r + g

and qMt ¼ 0 otherwise,. If w is chosen such that w 2 R n ½mB; r þ g�, then no responsive production and consequently no transfer occurs for

any ðD;KÞ 2 R2þ. For such w, this mechanism for initiating responsive production is therefore Pareto inefficient. We now restrict our atten-

tion to the case of w 2 [mB,r + g] in which trade occurs. We observe that qt ¼ min qMt ; q

Bt

� ¼minfðD� SÞþ;QBg, which is precisely the opti-

mal contingent responsive production quantity of the centralized system in (2). Hence, price-only contracts may coordinate production.We now proceed to study the capacity investment game, in which the manufacturer decides on her offshore capacity investment and

the supplier decides on his responsive capacity investment, both being aware of how the outcome of the capacity investment game willimpact the responsive production subgame. The manufacturer’s best response (installment of offshore capacity QM) corresponding tothe backup supplier’s installment of responsive capacity QB can be characterized by

BrMðQBÞ � arg maxQM

PdecM ðQ M;QBÞ ¼ arg max

QM

E½pdecM ðQ ; qt ;D;KÞ� � cMQ M; 8Q B 2 Rþ: ð14Þ

Likewise, the supplier seeks to determine his best backup capacity investment response to any of the manufacturer’s possible offshore capac-ity strategies:

BrBðQ MÞ � arg maxQB

PdecB ðQ M;QBÞ ¼ arg max

QB

E½pdecB ðQ ; qt ;D;KÞ� � cBQ B; 8QM 2 Rþ: ð15Þ

In analogy to the centralized case, we define the shadow matrix as

his case, because wo = 0, options are free, and the manufacturer would purchase an infinite number of options. Thus, her options purchasing decision becomes meaninglessupplier.

MQcenMQ

cenSQ

BQ

MQBr ( )M

Br ( )B

BQ

Br ( )BM Q

Br ( )MB Q

( , ) 0cenM B

M

Q QQ

( , ) 0cen

M BB

Q QQ

( ,0) 'decMQQ

MQcenMQ

cenBQ

BQ

MQBr ( )M

Br ( )B

BQ

Br ( )BM Q

Br ( )MB Q

( , ) 0cenM B

M

Q QQ

( , ) 0cen

M BB

Q QQ

decMQ

decBQ

Fig. 3. Best response function (solid curves) in case (i) (left) and case (ii) (right) of Theorem 4 compared to optimality curves of the central decision maker (dashed curves).

732 F.J. Sting, A. Huchzermeier / European Journal of Operational Research 207 (2010) 725–735

Kdec �Kdec

M

KdecB

!�

kdecM ðQ ;XjðQ ÞÞ

kdecB ðQ ;XjðQ ÞÞ

!j¼1;...;6

¼0 0 0 v �mM w�mM r þ g �mM

w�mB 0 0 0 0 w�mB

� �;

where kdecMj

and kdecBj

represent the manufacturer’s and the supplier’s shadow prices for offshore capacity and responsive capacity in the eventsXj,j = 1, . . . ,6, respectively. The manufacturer’s best response BrM(QS) for any QS 2 Rþ can be obtained by solving the following system, withl 2 R2

þ

KdecPðQ Þ ¼

cM

cB

� �� l; l0Q ¼ 0 ð16Þ

for QM. Likewise, solving this system for QB, given any QM 2 Rþ, yields the supplier’s best response. Either best response correspondence can-not be derived explicitly. However, the best response correspondences have certain properties, summarized in the following lemma, that willenable us to establish the existence of a unique and globally stable Nash equilibrium.

Lemma 2. The best response correspondences BrM;BrB : Rþ ! Rþ are singlevalued and thus constitute the best response functions, which exhibitthe following properties:

(i) The best response functions are nonincreasing with �1 6 ddQM

BrB 6 0 and �1 6 ddQB

BrM 6 0.

(ii) The best responses to zero investments are BrMð0Þ ¼ QM > 0 and BrBð0Þ 6 QB, respectively.

(iii) The manufacturer’s best response to the central optimal responsive capacity investment is positive, that is, BrMðQBÞ > 0.

Having characterized the best response functions, we are now in a position to write out the capacity strategies implemented by themanufacturer and the backup supplier in equilibrium:

Theorem 4. Suppose the manufacturer offers a price-only contract with w 2 [mB,r + g]. A unique Nash equilibrium for the capacity investmentgame Q dec 2 R2

þ exists and has, depending on the backup supplier’s marginal capacity cost cB, one of the following two distinct forms:

(i) The backup supplier does not install responsive capacity; only the manufacturer makes an (offshore) capacity investment if and only if

cB P �cdecB , where �cdec

B < �cB is given by �cdecB ¼ Kdec

B P Q decM ;0

� �, and Qdec

M is the single offshore sourcing capacity solving for

cM ¼ KdecM P Q dec

M ;0� �

. Then the equilibrium investment quantities are QdecM ¼ Q dec

M ¼ Q M and QdecB ¼ 0.

(ii) Both the manufacturer and the supplier install respective capacities if and only if cB < �cdecB . The equilibrium capacity vector Qdec then is a

unique solution to KdecPðQ decÞ ¼ cM

cB

� �. In both cases, the supply chain’s capacity investments are not aligned efficiently, because

QdecM > Qcen

M and QdecB < Qcen

B , which results in lower overall supply chain profits, that is, PdecM ðQ

decÞ þPdecB ðQ

decÞ < PcenðQ cenÞ.

Although the responsive production decision in the second-stage interaction of the manufacturer and the supplier may be coordinatedthrough price-only contracts, this is not true for the capacity strategies that result from the investment game. For case (i) of Theorem 4, it isapparent that the supply chain profit is not maximized. Although a central decision maker would make responsive capacity investments forall cB 2 ð0;�cBÞ, the decentralized system will omit this option for all cB 2 ½�cdec

B ;�cBÞ. Thus, the supply chain profit is not maximized in this case.For case (ii), we can assert that, for any w, Kdec – Kcen. Consequently, the optimality conditions of the decentralized system under a price-only contract (4) and in the centralized system (4) differ, implying that the respective portfolios of offshore and backup supply differ ingeneral as well. Compared to a centralized optimal capacity portfolio, the manufacturer overinvests in offshore capacity, whereas the back-up supplier underinvests in responsive capacity. Fig. 3 illustrates cases (i) and (ii) of Theorem 4 on the left and right panels, respectively. Inboth cases, the manufacturer’s best response function is located above the optimality curve that defines the optimal centralized solution;

F.J. Sting, A. Huchzermeier / European Journal of Operational Research 207 (2010) 725–735 733

that is, above the curve @@QM

PcenðQ M;Q BÞ ¼ 0. Conversely, the supplier’s best response functions are located below the optimality curve thatdefines the optimal centralized solution, that is, below the curve @

@QBPcenðQ M;Q BÞ ¼ 0. In case (i), the best response function intersects the

manufacturer’s best response function at BrB = 0; no responsive capacity investment is made. The manufacturer would pay little in scenar-ios in which she depends on the backup supplier’s capacity. Her trouble is just that the supplier would not have installed any responsivecapacity at all, because it is not viable for him economically. Decreasing the price-only compensation may backfire on the manufacturer asthere may not be any responsive capacity to resort to. Moreover, the decentralized system’s service level is directly linked to w, as the fol-lowing corollary establishes.

Corollary 2. The decentralized system’s service level resulting from equilibrium Qdec is given by PS5

i¼2XiðQ decÞ� �

. Let 1decB � w�mB�cB

w�mBdenote the

critical fractile of the backup supplier in the decentralized price-only situation.

(i) If the equilibrium responsive capacity investment is zero, that is, if cB > �cdecB , then

P[5i¼2

XiðQ cenÞ !

¼ P[4i¼3

Xi Q cen� � !P 1dec

B : ð17Þ

(ii) Otherwise, if the equilibrium responsive capacity investment is positive, that is, cB < �cdecB , then

P[5i¼2

XiðQ decÞ !

¼ 1decB : ð18Þ

(iii) The service level of the optimized centralized system is weakly (strictly if w < r + g) greater than that of the decentralized system in equi-librium, that is,

P[5i¼2

XiðQ cenÞ !

P P[5i¼2

XiðQ decÞ !

: ð19Þ

We have asserted that price-only contracting mechanisms will not lead the decentralized system to acquire the Pareto optimal expectedprofit and service level. In particular, this holds even if the manufacturer can determine the optimal value of w. So far, we have not madeany statement about the manufacturer’s optimal contract offer; that is, we have not calculated an optimal w. In fact, the manufacturer’scontract design problem, which can be formulated as

maxw2Rþ

PdecM Qdec

M ;Q decB ; w

� �¼max

wE pdec

M QdecM ;Qdec

B ;D;K; w� �h i

� cMQ decM ð20aÞ

subject to mB 6 w 6 r þ g; Q decB ¼ BrB Q dec

M ; w� �

; QdecM ¼ BrM Q dec

M ; w� �

; ð20bÞ

turns out to be intractable analytically. Because we have not imposed any restrictions on the probability measure P, apart from continuity,the existence and uniqueness of an optimizer w* that solves program (20) cannot be claimed in general. However, the next proposition shedslight on how local variations in w can impact the optimal capacity investments, the optimal expected profits, and the service level of theoptimized system.

Proposition 2. Consider a capacity investment equilibrium with Qdec > 0 in case (ii) of Theorem 4 (i.e., both the manufacturer and the suppliermake investments in offshore and responsive capacity, respectively) and define Pmn � P(Xm(Qdec) [Xn(Qdec)). Then the impact of marginalchanges in w

(i) on the equilibrium investment quantities is given by

@Q decM

@w¼ J21P16 � J22P5

detðJÞ and@Qdec

B

@w¼ �J11P16 þ J12P5

detðJÞ ; ð21Þ

where Jij < 0 is the ijth entry of the Jacobian J, of the optimality condition (4) w.r.t. QM and QB, where det (J) > 0;(ii) on the equilibrium service level is given by

@

@wP[5i¼2

XiðQ decÞ !

¼ @

@w1dec

B ¼ cB

ðw�mBÞ2; ð22Þ

(iii) on the equilibrium profits is given by

@PdecM Q dec

M ;Q decB

� �@w

¼ ðr þ g �wÞ P16@Q decB

@w� E½qt � and

@PdecB Q dec

M ;Q decB

� �@w

¼ �wP6@Q dec

M

@wþ E½qt�: ð23Þ

Decreasing the wholesale price will decrease the system’s service level. This result conforms to the responsive capacity’s function ofdetermining the service level in the centralized system. We cannot sign the impacts on the equilibrium quantities as well as the expectedprofits in general. However, provided that P16 is sufficiently larger than P5 (i.e., high-demand–high-supply or high-demand–low-supplyevents are sufficiently likely) a higher wholesale price may increase the investments in responsive capacity and improve the manufac-turer’s expected profit. Conversely this implies that decreasing the wholesale price may also backfire on the part of the manufacturer’s ex-pected profits.

Fig. 4. Utilization-dependent wholesale prices as e ? 0 and aligned capacity investments.

734 F.J. Sting, A. Huchzermeier / European Journal of Operational Research 207 (2010) 725–735

5. Utilization-dependent compensation for backup supply

In this section, we will show how a simple utilization-dependent price-only contract can lead to supply chain coordination under vol-untary compliance. A utilization-dependent wholesale price is a contract that maps responsive supply into a single price tariff payable perunit delivered; that is, the wholesale price w is a nonnegative function on the (state-dependent) transfer quantity qt. Moreover, we restrictour attention to the class of piecewise-linear (i.e., staircase function type) wholesale prices. To simplify notation, we defineEmn½ð�Þ� � E½ð�Þ jXm Q cen

M ;Q cenB

� �[Xn Qcen

M ;QcenB

� �and Pmn � PðXm Q cen

M ;QcenB

� �[Xn Qcen

M ;Q cenB

� �Þ. The following theorem introduces a utilization-

dependent contract that leads to coordination of responsive production as well as enables the contractual partners to achieve channel opti-mal offshore and responsive backup investments.

Theorem 5. Suppose the manufacturer offers a contract composed of a staircase function w : Rþ ! Rþ that maps responsive transfer quantitiesand states into single wholesale prices such that

wðqtÞ ¼0; if qt ¼ 0 and ðD;KÞ0 2 X3 [X4;

mB þ e; if 0 < qt < Q cenB and ðD;KÞ0 2 X2 [X5;

r þ g; if Q cenB 6 qt and ðD;KÞ0 2 X1 [X6:

8><>:

For any e 2 (0,r + g �mB], however small, responsive production is coordinated, that is, qt = min{(D � S)+,QB}. As e ? 0, the Nash equilibrium con-verges to the central optimal capacity portfolio, that is, Qdec

M ! QcenM and Qdec

B ! QcenB , if E25½qt � > ðr þ g �mBÞQdec

B � P5=P25. In the limit, the manu-facturer earns the total profit Pdec

M ! PcenðQ cenÞ, and the supplier covers his reservation profit of zero.Theorem 5 establishes a sufficient condition for the existence of a Nash equilibrium converging to the Pareto optimal solution under a

utilization-dependent contract, based on a continuity argument. Note that it is essential to fix the second step of w at the optimal respon-sive capacity investment of the centralized system, that is, at Q cen

B . This implies that the manufacturer has to determine the optimal cen-tralized system’s service profile in order to establish the right incentives for the supplier. In turn, the supplier will just install the systemoptimal offshore capacity because he knows that the manufacturer’s best response will be in line with that of a central decision maker. Thisculminates in the compensation. In states in which additional responsive capacity could not improve the centralized system’s overall profit,the backup supplier will be compensated only for his production expenses for any unit called off. In states in which additional responsivecapacity investments would enhance the centralized system’s profit, the supplier will receive compensation equal to the centralized sys-tem’s shadow price for responsive capacity, that is, market price plus saved goodwill loss per unit produced. In other words, in states of theworld in which the manufacturer needs at least the (Pareto optimal) responsive capacity installed, the manufacturer should pass on all theadditional profit from responsive production to the fully utilized backup supplier. Fig. 4 illustrates the utilization-dependent wholesaleprice as e ? 0 and its connection to the supply and demand state space under coordinated offshore and backup capacity investments.

6. Conclusion

The main question we addressed in this article is how a manufacturer can ensure responsive capacity by contracting with a backup sup-plier given that the manufacturer installs offshore capacity at the same time. Our findings highlight the importance of flexibility in con-tracts with backup suppliers. Under forced compliance, supply options are the most elegant way to achieve a channel optimal capacityportfolio of offshore and responsive capacity. With supply options, the manufacturer’s objective perfectly duplicates the central decisionmaker’s investment and production problem, and the backup supplier receives perfect reimbursement for his investment and productionexpenditures such that there is no need to incorporate the manufacturer’s offshore investment quantity in the contract. However, if themanufacturer commits to channel optimal capacity, this opens up a continuum of coordinating options type of contracts. Contracting basedon firm commitments, on the other hand, is wasteful.

F.J. Sting, A. Huchzermeier / European Journal of Operational Research 207 (2010) 725–735 735

Under voluntary compliance, from the class of options and firm commitment contracts, only the special case of a price-only contract isreasonable to induce backup investment. However, it does not lead to channel coordination. In addition, a price-focused strategy decreasesthe overall service level and may even reduce the manufacturer’s expected profit. In equilibrium, the manufacturer overinvests in offshorecapacity, whereas the supplier underinvests in responsive capacity, compared to the benchmark of a central decision maker. The manufac-turer can overcome this misalignment by offering a utilization-dependent price-only contract whose quantity steps are based on the cen-tral decision maker’s optimal capacity decision. Under such a contract, both agents’ best responses resemble the ‘‘partial” decisions of acentral decision maker. Thus, there is no incentive to deviate from the channel optimal capacities. The optimal utilization-dependentprice-only compensation agrees with economic theory (Hirshleifer, 1956): transfer prices (minus variable production costs) for the respon-sive production should be set equal to the entire system’s opportunity cost.

We believe that our model is sufficiently expandable to serve as a building block for further investigations along several research dimen-sions. One dimension could be to relax the dichotomy of forced and voluntary compliance and, instead, to consider compliance regimesthat are located within the range spanned by these extremes. The capacity decision may not be observable while investments are beingmade. However, actually delivered responsive or offshore supply provide evidence for shirking behavior. This may open up room for con-tractual penalty clauses. Another dimension that warrants further investigations is to relax the one-shot-game character of the model to arepeated interaction (cf. Taylor and Plambeck, 2007). The prospect of future interaction may create additional incentives to achieve Paretoefficient solutions under price-only contracts.

Appendix A. Supplementary material

Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.ejor.2010.05.044.

References

Babich, Volodymyr, 2006. Vulnerable options in supply chains: effects of supplier competition. Naval Research Logistics 53 (7), 656–673.Cachon, Gérard P., 2003. Supply chain coordination with contracts. In: Graves, Stephen C., de Kok, Ton (Eds.), Handbooks in operations research and management science:

supply chain management, Supply Chain Management: Design, Coordination and Operation, vol. 11. Elsevier Publishing Company, North-Holland, Amsterdam.Cachon, Gérard P., Lariviere, Martin A., 2001. Contracting to assure supply: how to share demand forecasts in a supply chain. Management Science 47 (5), 629–646.Chopra, Sunil, Reinhardt, Gilles, Mohan, Usha, 2007. The importance of decoupling recurrent and disruption risk in a supply chain. Naval Research Logistics 54 (5).Chopra, Sunil, Sodhi, ManMohan S., 2004. Managing risk to avoid supply-chain breakdown. MIT Sloan Management Review Fall 2004, 53–61.Christopher, Martin, Peck, Helen, 2004. Building the resilient supply chain. International Journal of Business Logistics 15 (2), 1–13.Ciarallo, Frank W., Akella, Ramakrishna, Morton, Thomas E., 1994. A periodic review, production planning model with uncertain capacity and uncertain demand – optimality

of extended myopic policies. Management Science 40 (3), 320–332.Dada, Maqbool, Petruzzi, Nicholas C., Schwarz, Leroy B., 2007. A newsvendor’s procurement problem when suppliers are unreliable. Manufacturing and Service Operations

Management 9 (1), 9–32.Donohue, Karen, 2000. Efficient supply contracts for fashion goods with forecast updating and two production modes. Management Science 46 (11), 1397–1411.Fraunhofer, 2008. Production offshoring in reverse. Fraunhofer Institut System- und Innovationsforschung Press Release, downloadable under: <http://www.isi.fhg.de/pr/

2008engl/epr02/epr02.htm>.Hayes, Robert, Pisano, Gary, Upton, David, Wheelwright, Steven, 2005. Operations, Strategy, and Technology – Pursuing the Competitive Edge. John Wiley and Sons, Danvers,

MA.Hirshleifer, Jack, 1956. On the economics of transfer pricing. Journal of Business 29 (3), 172–184.Huchzermeier, Arnd, Cohen, Morris A., 1996. Valuing operational flexibility under exchange rate risk. Operations Research 44 (1), 100–113.Kouvelis, Panos, Milner, Joseph M., 2002. Supply chain capacity and outsourcing decisions: the dynamic interplay of demand and supply uncertainty. IIE Transactions 34, 717–

728.Lippman, Steven A., McCardle, Kevin F., 1997. The competitive newsboy. Operations Research 45 (1), 54–65.Minner, Stefan, 2003. Multiple-supplier inventory models in supply chain management: a review. International Journal of Production Economics 81–82, 265–279.Parlar, Mahmut, 1988. Game theoretic analysis of the substitutable product inventory problem with random demands. Naval Research Logistics 35, 397–409.Pasternack, Barry Alan, 1985. Optimal pricing and return policies for perishable commodities. Marketing Science 4 (2), 166–176.Porteus, Evan L., 1990. Stochastic inventory theory. In: Heyman, Daniel P., Sobel, Matthew J. (Eds.), Handbooks in Operations Research and Management Science Stochastic

Models, vol. 2. North-Holland, Amsterdam, pp. 605–652.PRTM. 2008. Global Supply Chain Trends 2008-2010. PRTM Management Consultants.Sheffi, Yossi., 2005. The Resilient Enterprise: Overcoming Vulnerability for Competitive Advantage. The MIT Press, Cambridge, MA.Sting, Fabian J., Huchzermeier, Arnd. 2009. Dual sourcing – responsive hedging against (interrelated) supply and demand uncertainty. Working Paper, WHU – Otto Beisheim

School of Management.Swafford, Patricia M., Ghosh, Soumen, Murthy, Nagesh, 2006. The antecedents of supply chain agility of a firm: scale development and model testing. Journal of Operations

Management 24 (2), 170–188.Taylor, Terry A., Plambeck, Erica L., 2007. Supply chain relationships and contracts: the impact of repeated interaction on capacity investment and procurement. Management

Science 53 (10), 1577–1593.Tomlin, Brian, 2005. Selecting a disruption management strategy for short life-cycle products: diversification, contingent sourcing, and demand management. Working Paper,

University of North Carolina at Chapel Hill.Tomlin, Brian, 2006. On the value of mitigation and contingency strategies for managing supply chain disruption risks. Management Science 52 (5), 639–657.Tsay, Andy A., 1999. The quantity flexibility contract and supplier–customer incentives. Management Science 45 (10), 1339–1358.Van Mieghem, Jan A., 1998. Investment strategies for flexible resources. Management Science 44 (8), 1071–1078.Van Mieghem, Jan A., 1999. Coordinating investment, production, and subcontracting. Management Science 45 (7), 954–971.Williamson, Oliver E., 1985. The Economic Institutions of Capitalism. Free Press, New York.Yano, Candace Arai, Lee, Hau L., 1995. Lot sizing with random yields. Operations Research 43 (2), 311–334.