Strategic Sourcing in the Presence of Uncertain Supply and Retail Competition

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1 Vol. 2, No. 10, October 2014, pp ISSN EISSN DOI /poms Production nd Opertions Mngement Society Strtegic Sourcing in the Presence of Uncertin Supply nd Retil Competition Jinqing Chen Jindl School of Mngement, The University of Texs t Dlls, 00 West Cmpbell Rod, Richrdson, Texs 7500, USA, chenjq@utdlls.edu Zhiling Guo School of Informtion Systems, Singpore Mngement University, 0 Stmford Rod, Singpore 17902, Singpore, zhilingguo@smu.edu.sg T his study develops n nlyticl model to evlute competing retil firms sourcing strtegies in the presence of supply uncertinty. We consider common supplier tht sells its uncertin supply to two downstrem retil firms engging in price competition in horizontlly differentited product mrket. The focl firm hs dul-sourcing option, while the rivl firm cn only source from the common supplier. We ssess the system-wide effects of supply uncertinty on the focl firm s incentive to pursue the dul-sourcing strtegy. We find tht the focl firm s dul-sourcing strtegy cn crete win win sitution tht leds to incresed retil prices nd expected profits for both firms. Furthermore, under certin conditions, we show tht it is beneficil for the focl firm to strtegiclly source from the common supplier, even if its lterntive supplier offers lower wholesle price. Overll, we identify two types of incentives for dopting the dulsourcing strtegy the incentive of mitigting supply risk through supplier diversifiction nd the incentive of strtegic sourcing for more effective retil competition. Key words dul sourcing; supply uncertinty; uniform lloction; price competition; supply chin History Received April 2012; Accepted Mrch 201 by Anil Ary, fter revisions. 1. Introduction With the growing trend of outsourcing, offshoring, nd globliztion, supply uncertinty hs become n incresing concern nd mjor source of supply chin inefficiency. Mny externl cuses (e.g., wether issues nd nturl dissters) nd internl cuses (e.g., mchine brekdown nd defective products) could result in supply fluctutions. For exmple, recent explosion t the production plnt of Evonik, big supplier of specilty resin for uto prts in Germny, led to significnt inventory shortflls (Bennett nd Hromdko 2012). As result, Ford hd to dely the rollout of its new Rnger pickup truck to the Asin mrket (Rmsey 2012). Similrly, the flooding in Thilnd hurt the supply of disk drives nd relted components from Intel (Clrk 2012b), nd the erthquke nd tsunmi in Jpn cused supply shortge of electronic gdgets (Fletcher 2012). Apple s ipd2 shipment ws not severely ffected by the supply disruption becuse the firm hd plnned production round multiple component suppliers (Clrk 2012). Sourcing from multiple suppliers clerly cn minimize the supply disruption risk nd enhnce the firm s flexibility in the presence of supply chin uncertinty. 174 Dul sourcing, form of supply diversifiction, hs become common procurement strtegy in prctice (Anupindi nd Akell 199). For exmple, the min supplier for HP s DeskJet printers is in Singpore. At the sme time, HP hs locl source of supply in Vncouver to respond fster to demnd increses or supply disruptions in the North Americn mrket. Similrly, the Spnish toy mnufcturer Fmos receives pproximtely 0% of its products from Chin, nd the rest comes from Europen sources only when the Chinese production is insufficient. Although the dul-sourcing benefit of mitigting supply risks is well recognized, firms might prefer single sourcing, for instnce, to stremline their supplier bse or for more effective qulity control nd coordintion (Lrson nd Kulchitsky 199). As n exmple, over 9% of Ford s outsourced prts re supplied by single-source suppliers. Evidently, whether to choose single sourcing or dul sourcing is firm s strtegic decision, nd supply uncertinty is key fctor, mong others, in crfting the firm s sourcing strtegy. In ddition, in tody s networked mrkets, risks resulting from supply uncertinty re often interdependent, leding to the chin effect of demnd-side shortges mong competing retilers. Consequently,

2 Production nd Opertions Mngement 2(10), pp , 201 Production nd Opertions Mngement Society 1749 the effect of supply uncertinty on firm profitbility should be evluted in the context of both the supplyside uncertinty nd the demnd-side competition. So fr, previous reserch hs shed little light on how different sourcing strtegies would ffect both the verticl buyer supplier reltionship nd the horizontl mrket competition. We im to fill this gp in the literture. In this study, we build n nlyticl model to study firms incentives to choose dul-sourcing strtegy from both risk mitigtion nd strtegic sourcing perspectives. We exmine how different sourcing strtegies would ffect firm performnce in the presence of both supply uncertinty nd retil competition. Specificlly, we consider supply chin in which one supplier, who is subject to yield uncertinty, supplies n essentil input to two downstrem retil producers. The two downstrem firms one of which dopts single sourcing nd the other dul-sourcing strtegy trnsform the essentil input into differentited products nd compete in the consumer mrket. While the dul-sourcing firm cn respond effectively to supply shortge, the single-sourcing firm might suffer from the exclusive supplier s lock-in. This representtive supply chin structure cptures clss of relworld scenrios in which competing firms dopt distinct sourcing strtegies. For exmple, Philips Electronics ws mjor microchip supplier for both Noki nd Ericsson cell phones. In erly 2000, fire broke out in one of Philips s chip mnufcturing plnts in Mexico, which cused significnt supply shortge. Noki survived the mishp by sourcing from lterntive suppliers, while Ericsson experienced substntil operting loss s result of the component shortge. Our model delivers severl insights. First, we demonstrte the incentive of mitigting supply risk through supplier diversifiction, s is typiclly discussed in the literture. In ddition, we show tht the dul-sourcing firm s lterntive sourcing strtegy benefits not only itself but lso its singlesourcing rivl, creting win win outcome. The dul-sourcing firm directly benefits from hving its lterntive supplier becuse, in the event of supply shortge, the firm cn fulfill the residul demnd tht is not covered by the common supplier. Compred with its single-sourcing competitor, the dul-sourcing firm hs monopoly power over the residul demnd, which induces the dulsourcing firm to rise its retil price. Consequently, the increse in the retil price by the dul-sourcing firm softens the price competition with its singlesourcing rivl. The single-sourcing rivl, in turn, rises its retil price nd indirectly benefits from the softened competition, leding to higher retil prices nd profits for both firms. Under certin conditions, the totl consumer utility nd socil welfre lso increse. Second, we find tht the dul-sourcing focl firm hs incentive to strtegiclly source from the common supplier even if its lterntive supplier offers lower wholesle price. By ordering from the common supplier, the dul-sourcing firm shres the scrce supply provided by the common supplier with the rivl firm in the event of supply shortge nd thus limits its rivl s supply to the mrket. Such strtegic sourcing comes with higher procurement cost, but the benefit resulting from the end consumer mrket competition cn outweigh the extr procurement cost pid to the common supplier. In the bttle for competitive dvntge, our results suggest tht strtegic sourcing should be considered s n integrl component of firm s overll business strtegy. The rest of the rticle is orgnized s follows. Section 2 briefly reviews relted literture. Section describes our bsic model setup. In section 4 we derive the equilibrium mrket outcomes nd demonstrte both the tcticl benefits (i.e., risk mitigtion) nd strtegic vlue (i.e., competitive dvntge) of the dul-sourcing strtegy. In section 5 we consider severl extensions of the bse setting. Section 6 concludes. 2. Relted Literture Uncertin yield is common problem in mny production systems, such s electronic fbriction nd ssembly, chemicl processes, nd procurement of rw mterils from suppliers (Yno nd Lee 1995). Yield uncertinty trditionlly hs been modeled using two generl pproches the rndom yield model, which ssumes the output level is rndom function of the input vribles (Henig nd Gerchk 1990, Kouvelis nd Li 201), nd the totl supply disruption model, which is of the ll-or-nothing form (Hu et l. 201, Tomlin 2006). We dopt simplified form of the rndom yield model in which the output cn only prtilly fulfill the order quntity with some probbility. With n incresing wreness of the high risks ssocited with single sourcing, considerble ttention hs been pid to multiple-sourcing opertions in the presence of yield uncertinty (Agrwl nd Nhmis 1997, Anupindi nd Akell 199) nd supply disruption (Prlr nd Perry 1996, Tomlin 2006). The benefits of multiple sourcing over single sourcing hve been well documented in the literture (Federgruen nd Yng 200, Tomlin nd Wng 2005). Much of the literture either focuses on single firm s upstrem supply diversifiction or ssumes independent downstrem demnd to isolte the effect of supply chin competition. In the presence of both yield uncertinty nd

3 1750 Production nd Opertions Mngement 2(10), pp , 201 Production nd Opertions Mngement Society buyer competition, Tng nd Kouvelis (2011) exmine the benefits of supplier diversifiction in the context of dul-sourcing duopolies. However, they focus on the effect of supplier correltion rther thn on strtegic sourcing, which we consider in this study. Moreover, we ssume tht the yield uncertinty hs n interdependent effect on competing firms order fulfillment, which is different from their work. When selling to multiple downstrem firms, suppliers fce the opertionl issue of quntity lloction in the presence of supply shortge. Suppliers usully mp firms orders to finl order delivery bsed on publicly known lloction mechnism. Cchon nd Lriviere (1999) show tht retilers generlly hve incentives to order more thn they need, hoping to gin more fvorble lloction. However, number of lloction rules cn induce truth-telling, including lexicogrphic lloction (i.e., retilers re rnked in some mnner independent of their order sizes, such s lphbeticlly) nd uniform lloction (i.e., ll orders either re completely fulfilled or receive the sme lloction s ll other prtilly fulfilled orders). It is well estblished in the economics literture tht the uniform lloction rule stisfies number of desirble properties, including strtegy-proofness, firness, efficiency, nd nonymity (Sprumont 1991). In the supply chin mngement context, Cchon nd Lriviere (1999) further demonstrte tht uniform lloction cn result in higher supply chin profits thn lexicogrphic lloction. For these resons, we dopt the uniform lloction rule in this study. As outsourcing production becomes n industrywide prctice, substntil work in the supply chin mngement literture studies the optiml sourcing strtegies under different supply chin competition structures. Bsed on the Hotelling product differentition model, Shy nd Stenbck (200) study strtegic decisions of Bertrnd competitors in differentited industries to outsource production of key component. They show tht symmetric firms outsource production to low-cost, common subcontrctor, which fully uses economies of scle. Our model differs from theirs in tht we introduce n symmetric outsourcing structure in which one firm dopts single sourcing nd the other firm chooses dul sourcing. In the presence of supply risk, our enriched model offers dditionl insights regrding competing firms different outsourcing nd pricing decisions. In ddition, we dd to the growing literture discussing strtegic incentives in outsourcing prctices. Building on price competition model, we demonstrte the existence of strtegic sourcing, which is similr to the cost-incresing strtegy discussed in Slop nd Scheffmn (19). Under the clssicl frmework of Cournot quntity competition, Slop nd Scheffmn (197) show tht firm my overpurchse inputs in n outside mrket even when it is more efficient to produce the input internlly in order to rise the input cost of competitors. More recently, Ary et l. (200) demonstrte the strtegic benefit of purchsing from common externl supplier. They show tht firm might hve incentives to outsource production even when the cost of outsourcing exceeds the firm s cost of in-house production. Although their results of strtegic sourcing re similr to ours, the underlying driving forces re fundmentlly different. Ary et l. (200) find tht the strtegic considertion is to limit the supplier s incentive to provide the rivl with fvorble terms. We show tht supply shortge cn be nother reson for the focl firm to strtegiclly source from common supplier.. The Bse Model We consider simple supply chin model consisting of common supplier selling n essentil input t unit wholesle price w to two retil producers, s shown in Figure 1. The two retil producers, lbeled s firm A nd firm B, trnsform the essentil input into differentited retil products nd sell t unit retil price p i, for i 2 {A, B}, in the end consumer mrket. The two firms differ in their sourcing options. While firm A relies solely on the common supplier for the essentil input, firm B hs n lterntive supplier tht cn provide unlimited supply t unit price s. In other words, firm A dopts single-sourcing strtegy nd firm B uses dul-sourcing strtegy. The sequence of events is illustrted in Figure 2. First, given the price pir (w, s), both firms decide their retil prices ðp A ; p B Þ simultneously. Anticipting the mrket demnd bsed on the price competition, the two firms plce orders ðq A ; q B Þ to the common supplier. Next, the common supplier fulfills the orders. The common supplier hs uncertin yield. With probbility, 2 (0,1), the common supplier hs high yield nd fulfills both firms orders in Figure 1 Supply Chin Model

4 Production nd Opertions Mngement 2(10), pp , 201 Production nd Opertions Mngement Society 1751 Figure 2 Sequence of Events given (w, s), firms decide their retil prices (p A, p B ) firms plce orders (q A, q B ) to the common supplier the common supplier fulfills orders nd firm B decides its order from lterntive source mrket clers bsed on the relized delivery of products full; with probbility 1, the common supplier s relized yield is Q, Q 2 [0,1). In the ltter, the common supplier experiences supply shortge nd it rtions the orders from the two firms ccording to pre-nnounced lloction rule, nd firm B cn cquire dditionl supply from its lterntive source. Finlly, the mrket clers, bsed on the relized delivery of products from the two firms. Note tht here we ssume price commitment, implying tht firms determine the retil prices before the supply uncertinty is relized nd re committed to the chosen prices fterwords. For exmple, Apple commits to the retil price for its ipd before the strt of the selling seson, nd supply shortge does not ffect the product price. We further ssume tht firms re risk neutrl nd tht the supply chin structure is common knowledge. Ech firm optimlly chooses its retil price nd order quntity, nticipting its rivl s ction. In the following prgrphs, we describe the two retil firms competition nd the common supplier s lloction rule in detil. To simplify our exposition, we ssume tht one unit of the input from the supplier is required to produce ech unit of the retil product. The mrginl production costs for both retil producers re normlized to be zero. We further ssume tht products produced by the two firms re horizontlly differentited in tht consumers hve heterogeneous preferences towrd consuming the two firms products. Following Hotelling s horizontl product differentition model to cpture consumer preference (Hotelling 1929), we ssume tht products A nd B re locted t positions 0 nd 1, respectively, of line of length 1 (i.e., t the two ends of the line). A continuum of consumers of mesure 1 is uniformly distributed long the line, nd ech consumer hs unit demnd. Therefore, the totl mrket demnd is 1. Consumer utility for product is the reservtion vlue of the product v, net the disutility from the mismtch between the product nd the consumer s need, mesured by the distnce between the product s nd the consumer s loctions on the line. We denote t s the mrginl disutility. A consumer who is locted t x 2 [0,1] incurs disutility tx if purchsing from firm A nd t(1 x) if purchsing from firm B. Therefore, the net surplus purchsing from firm A is v tx p A nd from firm B is v tð1 xþ p B. To focus on mrket competition, we ssume tht v is lrge enough for ech consumer to derive positive utility from both products nd for the mrket to be fully covered. A consumer purchses the product tht gives her higher net surplus. We cn esily derive the loction of the indifferent consumer s ^x ¼ 1=2 þðp B p A Þ=2t. Thus, consumers locted between 0 nd ^x on the Hotelling line buy from firm A, nd the remining consumers buy from firm B. Accordingly, the demnd for the two firms cn be expressed s D A ¼ 1 2 þ p B p A 2t D B ¼ 1 2 þ p A p ð1þ B 2t Following Sprumont (1991) nd Cchon nd Lriviere (1999), we ssume tht the common supplier dopts uniform lloction rule becuse of its desirble properties, which include its being both fir nd strtegy-proof. Under the uniform lloction, both firms re eqully likely to receive ech unit produced by the supplier until one firm s order is completely fulfilled or ll produced units re llocted. Denote q i, i 2 {A, B}, s firm i s order quntity to the common supplier. Mthemticlly, the uniform lloction rule lloctes g i ðq i ; q i Þ to firm i, where fi; ig¼fa; Bg, s follows q i if q i \ Q 2 or q i þ q i \Q g i ðq i ;q i Þ¼ Q q i if q i \ Q 2 q i nd q i þ q i Q ð2þ Q 2 if minfq i ;q i g Q 2 More specificlly, if the sum of the two firms order quntities is smller thn the supplier s relized cpcity Q, or if firm s order quntity is smller thn Q 2, the ltter firm s order cn be completely fulfilled without being ffected by the supply uncertinty. If both firms order quntities re higher thn Q 2, then the two firms shre the limited cpcity nd ech firm gets Q 2. If one firm s order mount is greter thn Q 2, but the other firm s order mount is smller thn Q 2, then the smller size order gets fulfilled in full, nd the remining units re llocted to the lrger size order. To ese exposition without cusing ny confusion, we suppress the rguments nd use g A nd g B to denote firm A s lloction nd firm B s lloction, respectively. To deliver key mngeril insights, we focus on the most interesting cses, where the common supplier s relibility is not too low (e.g., 1 2 ; otherwise, firm A needs to consider n lterntive supplier or the common supplier should expnd its cpcity), nd

5 1752 Production nd Opertions Mngement 2(10), pp , 201 Production nd Opertions Mngement Society where the wholesle price from the common supplier is not significntly different from firm B s lterntive supply price (otherwise firm B might simply choose the low-cost source, nd the dul-sourcing strtegy degenertes to single sourcing). Anlysis of other scenrios is vilble from the uthors upon request. 4. Equilibrium Mrket Outcomes In this section, we first formulte firms optimiztion problems nd derive their ordering strtegies. Bsed on benchmrk cse tht no lterntive sourcing is vilble, we consider the benefit of dul sourcing s tcticl hedge ginst supply shortge in section 4.1. We further identify conditions under which dul sourcing becomes strtegic considertion in section 4.2. Becuse of the competition for scrce resources, both firms might strtegiclly mnipulte their orders from the common supplier, hoping to gin fvorble shre of lloction in the event of supply shortge. In the context of single sourcing nd independent demnd from retilers, Cchon nd Lriviere (1999) show tht uniform lloction cn induce truth-telling. In our setting with dul sourcing nd retil competition, Lemm 1 shows tht firms equilibrium order strtegies must stisfy the following properties. LEMMA 1. In equilibrium, q A ¼ D A nd q B mx fd B ; Q 2 g. PROOF. Notice tht g i is wekly incresing in q i. For firm A, ordering less thn D A is not optiml becuse the only effect of ordering less thn D A is to curtil its own demnd. Next, we show tht firm A hs no incentive to order more thn D A. According to Eqution (2), if D A Q 2 or if D A [ Q 2 nd D A þ q B \ Q, ordering D A leds to g A ¼ D A. So the demnd cn be fully stisfied even in the event of supply shortge. Ordering more thn D A might entil the risk of overstock if the order cn be completely fulfilled. Therefore, firm A hs no incentive to order more thn D A in this cse. If D A [ Q 2 nd D A þ q B Q, ordering more thn D A gets the sme lloction s ordering D A in the event of shortge, but it leds to overstock if the supply is sufficient. Therefore, firm A hs no incentive to order more thn D A in this cse s well. For firm B, when D B [ Q 2, ordering more thn D B leds to tht g A ¼ g B ¼ Q 2 if D A [ Q 2 nd g A = D A nd g B = Q D A if D A Q 2. So firm B does not hve incentive to order more thn D B from the common supplier becuse doing so gets the sme lloction s ordering exctly D B, but with the risk of overstocking. When D B Q 2, ordering more thn D B my ffect firm A s fulfillment g A = Q q B nd thus firm B s sles in the event of supply shortge. However, firm B does not hve incentive to order more thn Q 2, s doing so does not ffect firm A s lloction but increses its own overstocking cost. Menwhile, becuse it hs the lterntive supplier, firm B might hve incentive to order from the lterntive supplier in some cses. Therefore, q B mxfd B ; Q 2 g. h An importnt property of the uniform lloction rule is its robustness ginst strtegic mnipultions (Sprumont 1991). In the context of dul sourcing, Lemm 1 confirms tht firm A will order truthfully ccording to the nticipted mrket demnd; tht is, q A ¼ D A where D A is defined in Eqution (1). However, firm B does not lwys hve incentive to order exctly D B from the common supplier. In prticulr, in the specil cse when D B \ Q 2, becuse of the competition in the end consumer mrket, firm B might consider ordering more thn D B from the common supplier. On the one hnd, this strtegic considertion cn limit firm A s supply to the mrket, thus incresing firm B s sles in the event of supply shortge. On the other hnd, it incurs cost of overstocking if the supply from the common supplier is sufficient. Firm B hs to trde off the potentil benefit ginst the inherent cost. For ese of exposition, we simply ssume tht the overstocking cost is reltively high such tht firm B hs no incentive to inflte its order more thn it needs, nd thus q B D B (As we shll show lter, in the equilibri we study, D B is no less thn Q/2, so relxing the bove ssumption does not ffect our results.) Notice tht, by Lemm 1 nd D A derived in Eqution (1), firm A s order decision is completely determined by the two firms retil prices. When the supply is sufficient, firm A s entire order cn be fulfilled. When the supply is short, firm A s order is rtioned ccording to the lloction rule specified in Eqution (2). Therefore, the expected sles for firm A is q A þð1 Þg A, nd firm A s optimiztion problem is to choose the optiml price to mximize expected profit mx Ep A ¼ ½q A þð1 Þg A Šðp A wþ ðþ p A When the two suppliers prices re comprble (i.e., w nd s re not significntly different from ech other), firm B orders q B, q B 2½0; D B Š, from the common supplier nd uses the lterntive supplier to fulfill the remining demnd, if necessry. In this cse, firm B needs to decide the optiml order quntity from the common supplier, long with its pricing. Subject to the condition q B D B, firm B s optimiztion problem cn be formulted s mxep B ¼ ½q B þð1 Þg B Šðp B wþ p B ;q B þ½ðd B q B Þþð1 Þð1 g A g B ÞŠðp B sþ ð4þ

6 Production nd Opertions Mngement 2(10), pp , 201 Production nd Opertions Mngement Society 175 The first nd second prts in this objective function re the expected profit from the common supplier nd the expected profit from the lterntive supplier, respectively. When no supply shortge occurs, firm B gets q B from the common supplier nd orders the remining mount D B q B from the lterntive supplier. When supply shortge occurs, firm B gets lloction g B nd secures the remining mrket demnd 1 g A g B from the lterntive supplier. To exmine the effects of the dul-sourcing strtegy on firms pricing strtegies nd expected profits, we use single sourcing s benchmrk. In the singlesourcing environment, the two firms re symmetric. Firm B s decision problem is the sme s tht of firm A. Solving the two firms decision problems simultneously, we hve the following equilibrium retil prices nd expected profits. PROPOSITION 1. If both firms use single-sourcing strtegy, the equilibrium retil prices nd the expected profits re p s A ¼ ps B ¼ w þ t ½ þð1 ÞQŠ ð5þ Ep s A ¼ Eps B ¼ t 2 ½ þð1 ÞQŠ2 ð6þ PROOF. All proofs re in the Supporting Informtion ppendix unless otherwise indicted. h We see tht both firms chrge the sme equilibrium retil price. As result, the expected demnd for ech firm is D i ¼ 1 2 by Eqution (1). Tht is, ech firm serves hlf of the end consumer mrket, nd both firms ern the sme expected profit. Next, we exmine the equilibrium outcome when firm B hs the dul-sourcing option. We first consider the cse in which the wholesle price of the common supplier is no higher thn tht of the lterntive supplier (i.e., w s), nd then we consider the reverse cse (i.e., w > s). In ech cse, we compre the equilibrium outcome with the single-sourcing benchmrk The Wholesle Price Is Lower thn the Alterntive Supply Price (w s) When the wholesle price of the common supplier is not higher thn tht of the lterntive supplier, firm B orders ll the supply it needs from the common supplier; tht is, q B ¼ D B. When no supply shortge occurs, ordering ny lesser mount from the common supplier would only increse firm B s procurement cost from w to s for the rest of its supply needs when w < s (or doing so hs no effect when w = s). In the event of supply shortge, by the uniform lloction rule, ordering ny mount less thn its demnd (wekly) decreses firm B s own order fulfillment from the common supplier nd (wekly) increses the order fulfillment of firm A. Therefore, ordering less thn D B is never optiml for firm B. Thus, by Lemm 1, we hve q B ¼ D B, nd by Eqution (1), q A þ q B ¼ D A þ D B ¼ 1, which is greter thn Q. Hence, the uniform lloction rule in Eqution (2) cn be simplified to q A if q A \ Q 2 g A ¼ Q q B if q B \ Q 2 Q 2 if minfq A ; q B g Q 2, ð7þ nd g B ¼ Q g A. Bsed on this lloction, solving the two firms constrined optimiztion problems in Equtions () nd (4) simultneously, we hve the following equilibrium outcome. h PROPOSITION 2. When ðs wþ 2 0; equilibrium prices re p t 2 þ þð1 ÞQ A ¼ w þ ½ Š p t 4 ð1 ÞQ B ¼ w þ ½ Š ; t½5 þ þð1 ÞQŠ 6 i, the ðþ nd equilibrium orders re q i ¼ D i [ Q 2, where D i is defined in Eqution (1) with the bove equilibrium p i, i 2 {A, B}. The expected profits re Ep A Ep B t 2 þ þð1 ÞQ ¼ ½ Š2 1 t 4 ð1 ÞQ ¼ ½ Š2 1ð1 Þðs wþð1 QÞ 1 ð9þ The upper bound in the condition (s w) implies tht, to mke the dul-sourcing strtegy vible choice for firm B, the lterntive supply price cnnot be prohibitively higher thn the common supplier s price. Intuitively, if the lterntive source of supply is too expensive, firm B will forgo the opportunity of ordering from the lterntive supplier. Note tht the supply uncertinty is wht mkes the lterntive sourcing ply role in the price competition. If no supply uncertinty exists (i.e., if = 1), firm B does not order from the lterntive supplier, nd the equilibrium pricing strtegies re the sme for the two firms, regrdless of the lterntive sourcing opportunity. Intuitively, given the dditionl sourcing option, firm B enjoys competitive dvntge over firm A in the retil mrket. The following proposition compres the two firms equilibrium prices nd profits under the single-sourcing nd dul-sourcing scenrios.

7 1754 Production nd Opertions Mngement 2(10), pp , 201 Production nd Opertions Mngement Society PROPOSITION. Compred with h the single-sourcing i benchmrk, when ðs wþ 2 0;, nd in t½5 þ þð1 ÞQŠ 6 the presence of firm B s lterntive sourcing, () both firms increse their prices in equilibrium, with firm B incresing its price more thn firm A does; tht is, p B [ p A [ ps A ¼ ps B ; nd (b) both firms expected profits increse; tht is, Ep A [ Eps A nd Ep B [ Eps B. Compred with the single-sourcing benchmrk, Proposition () shows tht both firms chrge higher prices in the dul-sourcing environment. The intuition is s follows. The uncertin supply leds to n symmetric demnd structure for the two firms. In the event of supply shortge, there is residul demnd 1 Q tht is not covered by the common supplier but cn be fulfilled by firm B s lterntive supplier. With the option of dul sourcing, firm B thus hs monopoly power over the residul demnd, which induces it to rise its retil price. Consequently, this price increse by firm B reduces the pressure on firm A s pricing. Firm A thus rises its retil price s well, but not to the extent tht firm B does becuse of firm B s competitive dvntge over the residul demnd. Proposition (b) further shows tht one firm s pursuit of the dul-sourcing strtegy cn benefit both itself nd its rivl. Becuse firm A chrges reltively lower price thn firm B, it hs higher demnd nd thus higher expected sles, compred to the single-source benchmrk cse. The incresed price nd sles led to higher expected profit for firm A. Becuse firm B, in the event of supply shortge from the common supplier, cn secure n lterntive supply to stisfy the residul demnd, firm B s expected profit is lso higher thn it is in the single-source benchmrk cse. Contrry to conventionl wisdom, the seemingly vulnerble, single-sourcing firm s performnce is not necessrily hurt by its more flexible nd responsive dul-sourcing competitor. Insted, we find tht the presence of lterntive sourcing for one firm cretes positive externlity for the other. The positive externlity rises becuse of softened competition t the downstrem level, which comes from the residul demnd fulfilled by firm B s result of the lterntive supply tht otherwise would be lost becuse of the supply shortge. Note lso tht the expected overll consumer utility nd socil welfre cn increse in the presence of dul sourcing. The relized utility for ech consumer is ffected by two fctors whether the consumer is served by the mrket nd, if so, which product the consumer consumes. When consumer is not served by either firm, the consumer derives zero utility. When served, the consumer derives utility v tx, where x is the distnce between the consumer nd product consumed. In the benchmrk cse with single sourcing, p s A ¼ ps B. When no supply shortge occurs, consumers locted t ½0; 1 2Þ consume product A, nd consumers locted t ð 1 2 ; 1Š consume product B. When supply shortge occurs, 1 Q consumers re not served by the mrket. In contrst, in the presence of dul sourcing, ^x ¼ 1 2 þ p B p A 2t. On the one hnd, becuse p B [ p A, the consumers locted t ½ 1 2 ; ^xš consume product A insted of product B, lthough they derive higher utilities from product B. On the other hnd, given dul sourcing, when supply shortge occurs, ll consumer demnds re stisfied, mong which Q is served by the common supplier nd 1 Q by the lterntive supplier. As we cn show, s long s consumers reservtion vlue v is higher thn threshold (see the Supporting Informtion ppendix for the detiled condition nd proof), both the expected overll consumer utility (i.e., the totl vlue relized) nd the socil welfre (i.e., the totl vlue minus the totl procurement cost) increse in the dul-sourcing environment The Wholesle Price Is Higher thn the Alterntive Supply Price (w > s) In this section, we consider the cse where the wholesle price is higher thn the lterntive sourcing price; tht is, w > s. Becuse ordering from the common supplier is more expensive, firm B might choose to plce ll its orders with the lterntive supplier. For strtegic resons, however, firm B lso might still order prt of its expected mrket demnd from the common supplier, to compete with firm A for the scrce supply on which firm A completely depends. The following lemm chrcterizes firm B s incentive to order from the common supplier. LEMMA 2. When w > s, if q A Q 2, firm B hs no incentive to order from the common supplier; if q A [ Q 2, firm B orders t most Q 2 from the common supplier. The intuition for Lemm 2 is s follows. When q A is smll (i.e., q A Q 2 ), by the uniform lloction rule, firm A lwys receives wht it orders no mtter whether supply shortge occurs or how much firm B orders from the common supplier. In other words, in this cse, firm B s sourcing decision hs no effect on the lloction to firm A. As result, firm B strictly prefers to order from the lterntive supplier becuse its price is lower thn the wholesle price offered by the common supplier. When q A is lrge (i.e., q A [ Q 2 ), ny order greter thn Q 2 from firm B will result in the sme lloction to firm A (i.e., g A ¼ Q 2 ). Agin,

8 Production nd Opertions Mngement 2(10), pp , 201 Production nd Opertions Mngement Society 1755 becuse the lterntive supply price is lower, firm B hs no incentive to order more thn Q 2 from the common supplier. Lemm 2 implies tht firm B lwys orders no more thn Q 2 when w > s. Immeditely, we hve q B 2 0; minf Q 2 ; D Bg. As result, firm B s order to the common supplier q B is lwys fulfilled even in the event of supply shortge ccording to Eqution (2). Therefore, g B ¼ q B. By the uniform rtioning rule in Eqution (2), we cn specify g A in this cse s g A ¼ q A if q A \Q q B Q q B if q A Q q B. ð10þ Subject to the condition q B 2 0; minf Q 2 ; D Bg nd the bove lloction rule, we solve the constrined optimiztion problems in Equtions () nd (4) simultneously to derive the equilibrium prices nd order quntity s follows. PROPOSITION 4. ðw sþ 2 0;min When ½ð2þÞð1 QÞ QŠt ; ð1 Þ½4ð4 Þ 7ð1 ÞQŠt 4ð2þÞ firm B orders q B ¼ Q 2 from the common supplier, nd the equilibrium prices re p A ¼ s þ 2w t 2 þ þð1 ÞQ þ ½ Š p B ¼ 2s þ w t 4 ð1 ÞQ þ ½ Š ð11þ The equilibrium profits re Ep A ¼ ½tð2þþð1 ÞQÞ ðw sþš2 1t Ep B ¼ ½tð4 ð1 ÞQÞþðw sþš2 9tQðw sþ 1t ð12þ This proposition shows the effect of strtegic sourcing. Tht is, if the wholesle price w is within the identified intervl, firm B hs incentive to order from the common supplier, even if the lterntive supplier offers lower wholesle price. By ordering from the common supplier, firm B shres the scrce supply provided by the common supplier with firm A nd thus limits its rivl s supply to the mrket in the event of supply shortge. This strtegic sourcing comes with higher procurement cost, but the benefit resulting from the end consumer mrket competition cn outweigh the extr cost pid to the common supplier. In other words, firm B pys premium (reltive to the lterntive supply price) to the common supplier to rise its rivl s opportunity cost. Menwhile, note tht the wholesle price w is bounded. If the wholesle price is higher thn the upper bound, firm B hs no incentive to pursue strtegic sourcing becuse ordering from the low-cost supplier is more cost effective. PROPOSITION 5. Compred with h the single-sourcing n 2tð 1 Þð1 QÞ benchmrk, when ðw sþ 2 0; min ; oi, nd in the ½ð2þÞð1 QÞ QŠt ; ð1 Þ ½ 4ð4 Þ 7ð1 ÞQ Št 4ð2 þ Þ presence of firm B s lterntive sourcing, () both firms increse their prices in equilibrium, with firm B incresing its price more thn firm A does; tht is, ¼ ps B ; nd (b) both firms expected profits increse; tht is, Ep A [ Eps A nd Ep B [ Eps B. p B [ p A [ ps A We see tht, even when the common supplier s wholesle price is higher thn the lterntive supplier s price, both firms chrge higher prices nd ern higher expected profits in the dul-sourcing environment thn in the single-sourcing benchmrk, nd firm B still chrges higher price thn firm A does. The insights follow similr lines of resoning s in Proposition. 5. Extensions nd Discussions In this section, we relx some of our ssumptions to discuss severl model vritions. Our objective is to demonstrte tht the mjor insights re robust when the common supplier s wholesle price is endogenous, when the common supplier cn price discriminte between the two firms, nd when one firm obtins priority lloction on scrce resources Endogenous Wholesle Price To show tht firm A cn still benefit from firm B s dul-sourcing strtegy nd tht firm B still hs incentive to pursue strtegic sourcing when we endogenize w, we need to demonstrte tht the cses discussed in sections 4.1 nd 4.2 cn rise in equilibrium for n endogenously determined wholesle price w. Denote the common supplier s mrginl production cost s c. Recll tht, if w s, then by Proposition 2, the totl order from the two firms is 1 (i.e., q A þ q B ¼ 1). If w > s, then by Proposition 4, q A ¼ 1 2 þ s w ð1 Þð1 QÞ þ 6t nd q B ¼ Q 2. The totl order q A þ q B \ 1. The common supplier compres its expected profit under ech cse nd chooses n optiml wholesle price w to mximize its expected profit ðw cþ½ðq A þ q B Þþ ð1 ÞQŠ.

9 1756 Production nd Opertions Mngement 2(10), pp , 201 Production nd Opertions Mngement Society If w s, the common supplier hs fixed expected demnd of + (1 )Q. Becuse its profit function linerly increses in the wholesle price, the common supplier would like to chrge price s high s possible. However, n extremely high wholesle price pushes up the firms retil prices nd leves some consumers unserved in the mrket. Hence, s in the bseline model, we impose full mrket coverge condition tht ensures ll consumer demnds get stisfied. By Proposition, we hve p B [ p A. Thus, full mrket coverge requires tht the consumer locted t point zero on the Hotelling line derives non-negtive utility from buying product B. Solving v t p B ¼ 0, we cn derive the upper-bound wholesle price s t½4 þ 2 ð1 ÞQŠ w 1 ¼ v Therefore, within the rnge of w s, the common supplier might optimlly set wholesle price w 1 if w 1 s, or, equivlently, if t½4 þ 2 ð1 ÞQŠ v v 1 s þ ; otherwise, the supplier optimlly sets wholesle price s. Similrly, if w > s, the full mrket coverge condition requires tht the wholesle price not be too high. By Proposition 5 we hve p B [ p A. Bsed on p B in Proposition 4, we cn derive the upper-bound wholesle price s t 4 þ 2 ð1 ÞQ w 2 ¼ v ½ Š 2s The condition w 2 [ s is equivlent to v [ v 1. Furthermore, by substituting q A nd q B from Proposition 4 into the common supplier s expected profit function, we cn solve the unconstrined optimiztion problem nd derive its optiml wholesle price w e ¼ c þ s 2 Note tht w e w 2 requires tht t½2 þ 4Q þ ð1 QÞŠ þ 2 v 5s þ c ð2 þ Þð5 þ QÞt þ v By simple lgebr, we cn verify tht when t½2 þ 4Q þ ð1 QÞŠ s c \, w e [ s nd v 1 \ v 2. So in this cse, by the concvity of its objective function, the common supplier cn optimlly set wholesle price w e if v [ v 2 nd wholesle price w 2 if v 2ðv 1 ; v 2 Š. Combining the bove two cses, the optiml wholesle price is w 1 if v v 1.Ifv 2ðv 1 ; v 2 Š, the supplier fces trde-off between chrging higher w 2 but with lower expected totl order quntity nd chrging lower wholesle price s but with higher expected totl order quntity. Therefore, the optiml wholesle price is w 2 if ðw 2 cþ 1 2 þ s w 2 þ 6t ðs cþ½ þð1 ÞQŠ; ð1 Þð1 QÞ þ Q 2 þð1 ÞQ ð1þ where the left-hnd side is the expected profit under wholesle price w 2 nd the right-hnd side is the expected profit under wholesle price s. (If v [ v 2, the optiml wholesle price cn lso be similrly chrcterized.) We cn verify tht the wholesle price ssumed in Proposition 2 nd the wholesle price ssumed in Proposition 4 cn rise in equilibrium s the common supplier s optiml wholesle price. For exmple, when v is less thn but close to v 1, the common supplier optimlly chooses w 1 (where w 1 \ s) s the wholesle price, nd ðs w 1 Þ cn be in the intervl specified in Proposition 2. When v 2ðv 1 ; v 2 Š nd (s c) is smll enough, the inequlity condition in Eqution (1) holds, nd the common supplier optimlly sets w 2 [ s. In ddition, when v is close to v 1, ðw 2 sþ cn be in the intervl specified in Proposition 4. Therefore, the scenrios in both sections 4.1 nd 4.2 cn rise in equilibrium, nd our mjor insights re not ffected when the wholesle price is endogenously determined Wholesle Price Discrimintion In our bse model we ssume tht the common supplier offers the sme wholesle price w to the two firms. Such n ssumption mkes sense for two resons. First, the previling Anti-Price Discrimintion Act (i.e., The Robinson Ptmn Act) prohibits nti-competitive wholesle price discrimintion for identicl products by producers. Second, price discrimintion cn induce rbitrge/resle behviors tht hurt fir competition. For instnce, the firm tht gets fvorble price my procure more nd resell the input to the other firm in the secondry mrket. In this extension, we look t the cse where the common supplier cn price discriminte between the two retil firms. We show tht our min insights continue to hold, even in the presence of wholesle price discrimintion. Denote w A nd w B s the wholesle prices offered by the common supplier to the two firms. For ese of exposition, we ssume the difference between the two wholesle prices is not too lrge. Following n

10 Production nd Opertions Mngement 2(10), pp , 201 Production nd Opertions Mngement Society 1757 pproch similr to tht in Proposition 1, we cn derive the equilibrium retil prices nd the expected profits for the single-sourcing benchmrk s p s A ¼ 2w A þ w B þ t þ p s B ¼ w A þ 2w B þ t þ ð1 Þ tq ð1 Þ tq nd Ep s A ¼ ½tð þ Q QÞ ðw A w B ÞŠ 2 1t Ep s B ¼ ½tð þ Q QÞþðw A w B ÞŠ 2 1t ð14þ ð15þ Note tht now the equilibrium retil prices re the functions of the wholesle prices chrged to both firms nd tht the equilibrium profits depend on the wholesle price difference. In the dul-sourcing environment, we first consider the cse in which the wholesle price offered to firm B is less thn the lterntive supply price (i.e., w B s). As in Proposition 2, the equilibrium retil prices nd the expected profits for the two firms re p A ¼ 2w A þ w B p B ¼ w A þ 2w B þ t ½2 þ þð1 ÞQŠ þ t ½4 ð1 ÞQŠ nd Ep A ¼ ½½2 þ þð1 ÞQŠt ðw A w B ÞŠ 2 1t Ep B ¼ ½½4 ð1 ÞQŠt þ ðw A w B ÞŠ 2 1t 1tð1 Þðs w BÞð1 QÞ 1t ð16þ ð17þ Similr to the proof of Proposition, we cn verify tht, compred with the single-sourcing benchmrk, both firms increse their prices nd both firms expected profits increse. Therefore, the presence of firm B s dul sourcing lso benefits firm A. The min insight from the bseline model continues to hold in the cse of wholesle price discrimintion. The mjor effect of wholesle price discrimintion is tht the equilibrium price difference, p B p A ¼ w B w A þ 2tð1 QÞð1 Þ ; now depends on the difference between the wholesle prices. In the bseline model, firm B lwys chrges higher retil price thn firm A. In contrst, given wholesle price discrimintion, firm B might chrge lower retil price thn firm A when it gets more fvorble wholesle price from the common 2tð1 QÞð1 Þ supplier (i.e., w B \ w A ). For the cse in which the wholesle price offered to firm B is higher thn the lterntive supply price (i.e., w B [ s), we cn similrly derive the equilibrium retil prices nd equilibrium profits for the two firms, s in Proposition 4. The sme driving force continues to exist, nd the min insight bout strtegic sourcing derived in the bseline model continues to hold. In generl, firm B hs n incentive to order from the common supplier becuse doing so would put its rivl t disdvntge in the event of supply shortge. With the common supplier s bility to price discriminte between the two firms, more fvorble price to firm A would discourge firm B from pursuing strtegic sourcing becuse of the decrese in firm B s benefit, while more fvorble price to firm B would strengthen its incentive. Therefore, the common supplier cn leverge price discrimintion to influence firm B s incentive to pursue strtegic sourcing. 5.. Priority Alloction Now we consider the scenrio in which the two firms bid for the common supplier s priority lloction. By ccepting n up-front fee (i.e., the priority fee) from one of the two firms, the common supplier grees to fulfill tht firm s order first in the event of supply shortge. A nturl method to use by the common supplier is stndrd seled-bid secondprice uctions, where the firm with the highest bid wins the uction nd pys the second highest bid. For illustrtion purposes, we consider simple cse where Q \ minfq A ; q B g; tht is, the supply shortge is significnt enough to wrrnt the bidding for priority lloction. We focus on strtegic sourcing by looking t the w > s cse. Other cses cn be similrly nlyzed. First, we consider the cse when the single-sourcing firm hs the priority lloction. In this cse, the single-sourcing firm receives Q in the event of supply shortge, by the ssumption Q \ q A. Becuse w > s, the dul-sourcing firm hs no incentive to order from the common supplier. Therefore, the two firms optimiztion problems cn be formulted s ( mx pa Ep 1A ¼ ðp A wþ 1 2 þ p B p A 2t þð1 ÞQ mx pb Ep 2B ¼ ðp B sþ 1 2 þ p A p B þð1 Þð1 QÞ Following n pproch similr to tht in the bseline model, we cn derive the firms optiml retil prices nd expected profits 2t

11 175 Production nd Opertions Mngement 2(10), pp , 201 Production nd Opertions Mngement Society nd p 1A ¼ s þ 2w p 2B ¼ 2s þ w þ Ep 1A Ep 2B t½2 þ þ 2ð1 ÞQŠ þ t½4 2ð1 ÞQŠ ½tð2 þ þ 2ð1 ÞQÞ ðw sþš2 ¼ 1t ½tð4 2ð1 ÞQÞþðw sþš2 ¼ 1t We next consider the cse when the dul-sourcing firm hs the priority. Note tht, by ordering Q from the common supplier, the dul-sourcing firm in the event of supply shortge cn deplete the supply from the common supplier so tht the single-sourcing firm hs no supply to the mrket. Menwhile, becuse w > s, the dul-sourcing firm ccrues no dditionl benefit by ordering more thn Q from the common supplier. Therefore, the dul-sourcing firm orders Q from the common supplier nd the rest from the lterntive supplier, bsed on our ssumption tht Q q B. We formulte the two firms optimiztion problems s mx pa Ep 2A ¼ ðp A wþ p B p A 2t þ 1 2 mx pb Ep 1B ¼ðp B wþq þðp B sþ ½ 1 2 þ p A p B 2t Q þð1 Þð1 QÞ Similrly, we cn derive the firms optiml retil prices nd expected profits nd p 2A ¼ s þ 2w tð2 þ Þ þ p 1B ¼ 2s þ w þ tð4 Þ Ep 2A ¼ ½tð2 þ Þ ðw sþ Š2 1t Ep 1B ¼ ½tð4 Þþðw sþ Š2 1tQðw sþ 1t It is well known tht bidding its true vlue is ech bidder s wekly dominnt strtegy in secondprice uctions. In our cse, the vlue of the priority lloction for ech firm is the difference between the expected profit from receiving the priority lloction nd the expected profit when not receiving it. Ech firm s equilibrium bid cn be derived s b A ¼ Ep 1A Ep 2A 2ð1 ÞQ½tð2 þ þð1 ÞQÞ ðw sþš ¼ 9 b B ¼ Ep 1B Ep 2B Q½2ð1 Þtð4 ð1 ÞQÞ ð2 þ 7Þðw sþš ¼ 9 Note tht s long s (w s) is not too lrge, both firms hve incentives to submit positive bids. By simple lgebr, we hve b A b B ¼ Q½ð4 þ 5Þðw sþ 4ð1 Þ2 ð1 QÞtŠ 9 Therefore, if ðw sþ [ ð4ð1 Þ 2 ð1 QÞtÞ=ðð4 þ5þþ, the single-sourcing firm wins the uction nd hs the priority in the common supplier s lloction; otherwise, the dul-sourcing firm wins the uction nd hs the priority. The intuition is s follows. When the price difference is smll, the single-sourcing firm in generl is in disdvntgeous position becuse its competitor hs n lterntive supplier, which limits the vlue of priority lloction to the single-sourcing firm. As result, the dul-sourcing firm wins the uction. However, when the wholesle price from the common supplier is sufficiently higher thn its lterntive supplier, the benefit to the dul-sourcing firm from ordering from the chep lterntive is lrge enough to compenste for the loss from not securing the priority lloction (i.e., from preventing the single-sourcing firm from serving the mrket in the event of supply shortge). Therefore, the singlesourcing firm wins the uction. In sum, when both firms cn bid for the common supplier s priority lloction, the dul-sourcing firm s incentive for strtegic sourcing continues to exist (i.e., it hs incentive to plce positive bid for the priority lloction). Moreover, when the price difference is not too lrge, the dul-sourcing firm even outbids the single-sourcing firm nd ctully pys premium for the more expensive source of supply to deplete the single-sourcing firm s supply to the mrket in the event of supply shortge. 6. Conclusion In this study, we develop n nlyticl model to study the joint effects of both uncertin supply nd retil competition on firms sourcing strtegies, price equilibrium, nd expected profits. We find number of insights concerning both the tcticl benefits nd strtegic vlue of dul sourcing. Compred with the single-sourcing benchmrk, we find tht one firm s dul-sourcing strtegy cn crete win win sitution tht leds to incresed retil prices nd expected profits

12 Production nd Opertions Mngement 2(10), pp , 201 Production nd Opertions Mngement Society 1759 for both firms. We lso show tht, under certin conditions, the dul-sourcing firm might strtegiclly source from the more expensive common supplier even if n lterntive, cheper source of supply exists. In fct, the dul-sourcing procurement strtegy bers certin similrities to the concept of tper integrtion discussed in the strtegic outsourcing literture. Following the originl notion of Hrrign (194) nd recent work by Rothermel et l. (2006), tper integrtion is defined s the sitution in which firm sources inputs externlly from independent suppliers, s well s internlly within the boundries of the firm. The simultneous pursuit of in-sourcing (i.e., verticl integrtion) nd outsourcing of the tper integrtion strtegy fits well with our dul-sourcing frmework. For exmple, we cn interpret firm A s firm tht does not hve inhouse production cpbility nd therefore outsources its input production to the common supplier. Firm B, in contrst, hs n in-house production cpbility with per unit production cost s, but it might prefer to outsource prt or ll of its production to the common supplier. In this context, we sy firm A pursues outsourcing nd firm B the tper integrtion strtegy. Rothermel et l. (2006) empiriclly demonstrte tht the tper integrtion strtegy cn enhnce firm s product portfolio, new product success, nd firm performnce. Under the risk mngement frmework, our model sheds new light on the competitive dvntge nd potentil synergy creted by this unique orgniztionl form. We cn identify number of opportunities for building on our work. Clerly, firms rections to supply uncertinty criticlly depend on the lloction rule tht the common supplier uses to rtion orders. In our current frmework, we consider the uniform rtioning rule. Other lloction rules, such s proportionl lloction nd liner lloction, lthough prone to order mnipultion, re lso used in prctice. A comprehensive comprison of different lloction rules is n re for future reserch. In ddition, in this study, we consider price competition for horizontlly differentited products. In prticulr, we consider model with price commitment by the retil firms. Another interesting direction to explore is to consider quntity competition, which cn be modeled, for exmple, s Cournot gme. The extent to which our min insights cn be crried over to the Cournot gme setting is uncler. The comprison between price competition nd quntity competition deserves future study. References Agrwl, N., S. Nhmis Rtionliztion of the supplier bse in the presence of yield uncertinty. Prod. Oper. Mng. 6() Anupindi, R., R. Akell Diversifiction under supply uncertinty. Mnge. Sci. 9() Ary, A., B. Mittendorf, D. E. M. 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13 1760 Production nd Opertions Mngement 2(10), pp , 201 Production nd Opertions Mngement Society Tng, S. Y., P. Kouvelis Supplier diversifiction strtegies in the presence of yield uncertinty nd buyer competition. Mnuf. Serv. Oper. Mng. Advnce online publiction. doi /msom Tomlin, B On the vlue of mitigtion nd contingency strtegies for mnging supply chin disruption risks. Mnge. Sci. 52(5) Tomlin, B., Y. Wng On the vlue of mix flexibility nd dul sourcing in unrelible newsvendor networks. Mnuf. Serv. Oper. Mng. 7(1) Yno, C. A., H. L. Lee Lot sizing with rndom yield A review. Oper. Res. 4(2) Supporting Informtion Additionl Supporting Informtion my be found in the online version of this rticle Appendix S1. Proofs.