Strategic Dynamic Sourcing from Competing Suppliers: The Value of Commitment

Transcription

1 Strategi Dynami Souring from Competing Suppliers: The Value of Commitment Cuihong Li Laurens G. Debo Shool of Business, University of Connetiut, Storrs, CT0669 Tepper Shool of Business, Carnegie Mellon University, Pittsburgh, PA1513 Building a long-term relationship by ommitting to soure from a single supplier over time may plae a buyer at a disadvantage. With ommitment, the buyer foregoes the option of swithing to a new supplier, whih is benefiial if the effiieny improvement is greater than the assoiated osts of swithing. On the other hand, ompetition among suppliers may inrease if the buyer ommits to soure from the winning supplier over a long term, whih is advantageous for the buyer. We onsider the value of ommitment in an environment where the supplier operates apaity that is owned by the buyer, the buyer faes unertainty about the downstream market demand, and a supplier s prodution ost is private information. The buyer thus uses buffer apaity to hedge against market unertainty and a ompetitive bidding proess to eliit a supplier s ost. We analyze when the buyer should ommit to soure from a single supplier over a long term, and show that there exists a ritial level of swithing osts above whih the buyer should ommit to a single supplier. Furthermore, we find that with ommitment, apaity an be either higher or lower than without ommitment. Finally, we find that when market unertainty inreases, ommitment is optimal over a wider range of swithing osts. 1

2 1. ntrodution Should a buyer ommit to soure from a single supplier over a long period of time? n fast hanging business environments, keeping the option open to swith in the future to a more effiient supplier, if the expeted effiieny improvement is greater than the osts assoiated with swithing, seems to be of great value. However, ommitment to alloate business to a single supplier over a long term may be benefiial to the buyer. This is beause ommitment inreases the expeted business volumes for the winning supplier and therefore may also inrease the ompetition between suppliers to seure the long-term ontrat. n this paper, we study the value, to the buyer, of ommitment to a supplier. We fous on the ase in whih a supplier operates prodution apaity that is owned by the buyer and transferrable between suppliers. Examples are omplex ast and mahined aluminum omponents used in many industrial systems. The speial purpose mahines or speifi tools neessary to produe the omponents are typially owned by the buyer of aluminium omponents Walker, 005. f the buyer swithes to a new supplier, these speifi apaities are also transferred from the old to the new supplier. Similar arrangements in whih the buyer owns speial equipment, fixtures, dies or tools that are used by the supplier are ommon in the automotive industry Hayes et al., 005. Due to the omplexity of the operations of the potential suppliers, the ost struture of suppliers may exhibit signifiant variane. For example, potential suppliers of ast and mahined aluminum omponents to ASEA Brown Boveri ABB have their own multi-tiered supply hains that may span the globe: Some of the asting, mahining and tool building ativities are done by subontrators in different ountries and ontinents. Logistis ost, differenes in labor rates, intermediaries markups and differenes in quality and delivery performane all ontribute to a high ost variane among potential suppliers of the same input Walker, 005. Furthermore, due to its omplexity, the ost struture may not be fully transparent to the buyer Çakanyildirim et al., 006. n the ase that new souring opportunities arise, the buyer may want to swith to a new supplier. For example, emerging tool manufaturers in Taiwan, that an potentially produe at half the ost and twie the speed, ause ABB to onsider the option of swithing from their inumbent European suppliers Walker, 005. However, if the buyer has ommitted to soure from the inumbent supplier over a long horizon, he annot tap the new souring opportunity. For example, Japanese ompanies in the automobile industry, organized as

3 keiretsu whih features ommitment to inumbent suppliers through mutual shareholdership, oasionally lamented not being able to make a lean, though drasti, break with unwanted sub-ontrators Sako, 199. We refer to a strategy involving ommitment of a buyer to a single supplier over a long term as a long-term relationship. The resulting supply hain that delivers the final produt to the market remains stable over time. A strategy that does not involve ommitment to a single supplier, is referred to as a short-term relationship. The resulting supply hain is flexible and may hange its omposition over time. A buyer thus needs to determine whether to ommit or not to a supplier, when to possibly swith to another supplier, and how muh to invest in apaity, taking unertainty about the market demand and about the supplier s ost struture into aount. Li and Debo 006 analyze the deision of a buyer whether to ommit to a single supplier or leave the option open to soure from a new supplier in the future. n their paper, the apaity invested by a supplier annot be transferred to another supplier. One the buyer deides to swith to an entrant supplier, new apaity has to be invested by the entrant in order to satisfy any demand from the buyer, and the sunk investment by the inumbent supplier has no use any more. n this paper, we onsider speifi apaity that is owned by the buyer and transferrable between suppliers. When supplier swithing ours, the speifi apaity is transferred from the inumbent to the new supplier without investing in new apaity. This is appropriate, for example, in the automotive industry, where buyers have ontrol over the apaity e.g. molds or speifi mahines and an fore, at a ertain ost, an inumbent supplier to transfer the apaity to a new, entrant supplier Dyer, We develop a model that allows us to study the value of ommitment when a buyer soures from ompeting suppliers, onsidering transferrable apaity investment in the presene of demand unertainty. Competitive bidding proesses are used to eliit the supplier s nontransparent ost struture and selet the most effiient supplier. Buffer apaity is installed to hedge against market unertainty. We study the key operational deisions that the buyer needs to make: How muh apaity to ontrat for, with whih supplier and for how long. The questions that we address in this paper are: What is an optimal strategy of a buyer under eah supplier relationship? What is the influene of the supplier relationship on the apaity investment deision? How do harateristis of the environment, in partiular the swithing ost, supplier ost unertainty, and demand unertainty, impat the supplier relationship seletion? 3

4 . Literature Review A body of researh in eonomis and operations management has been developed that provides us with insights in dynami souring strategies see Elmaghraby 003 for an overview of the literature. n the following we provide a review of the papers that onsider similar issues as in our paper: supplier swithing, supplier ommitment, and apaity investment in a ontext of souring from ompeting suppliers with private information. Among other papers in operations that onsider souring strategies, Taylor and Plambek 005 and Debo and Sun 004 study the impat of repeated interation with a single supplier on apaity investment and supply hain oordination over infinite horizons, Tuna and Zenios 006 examine the ompetition between short-term prourement autions and long-term relational ontrats for produts with non-verifiable quality, Cahon and Zhang 004 and Baiman and Netessine 004 analyze inentives for multi-souring, Bernstein and de Veriourt 004 examine the equilibrium of supplier ompetition for prourement ontrats with servie guarantees, and Çakanyildirim et al. 006 studies the optimal ontrat design for a buyer who faes a newsvendor problem and soures from a supplier with private information on the prodution ost. Dynami souring strategies with supplier swithing: n a multi-period setting where supplier apabilities are private information and hange over time, the buyer must make swithing deisions onsidering the trade-off between ompetitive advantage realized by swithing, and the benefit of working with the same supplier. Laffont and Tirole 1988, Stole 1994 and Rob 1986 study how a buyer should ontrat with a supplier and make the swithing deision when the first supplier strategially makes investments to redue the future ost. Anton and Yao 1987, Klotz and Chatterjee 1995, and Lewis and Yildirim 00 model the dynami swithing deision for a buyer when the inumbent generally has an effiieny advantage against an entrant due to learning-by-doing. The impat of the swithing ost on dynami seletion of suppliers is speifially analyzed by Ba 000 and Cabral and Greenstein Generally these papers argue that although swithing may introdue system ineffiieny, it infuses ompetition between suppliers and therefore redues the buyer s information rent. The tradeoff between the ineffiieny and information rent determines the optimal swithing deision of a buyer. All these papers assume that the buyer never ommits to a single supplier, in other words, they only onsider short-term relationships. 4

5 Long-term versus short-term relationships: The onlusion that the buyer should swith under some onditions with a short-term relationship does not deny the benefit of establishing a long-term relationship. Motivated by the defense prourement industry with ertain demand, Riordan and Sappington 1989 ompare sole souring and seond souring, whih are analogous to long-term and short-term relationships, onsidering a supplier s investment to improve the projet s value in the future. By assuming idential future osts for all suppliers, they find that a short-term relationship is of limited value and disourages investments. Considering the effet of learning-by-doing, Elmaghraby and Oh 004 ompare an erosion rate poliy against two base ases in whih the buyer holds an independent, short-term aution in eah period, and the buyer proures all her demand in a single bundle aution. Grimm 004 and Menezes and Monteiro 003 ompare sequential autions and a bundled aution for two items when synergies of item values exist. All these papers fous on the information struture, assuming deterministi demand or supply as in Menezes and Monteiro 003 in a forward aution setting. When both demand unertainty and supplier ost unertainty exist, as is the ase in our researh, the supplier relationship and prourement ontrating must take into onsideration apaity investment along with supplier seletion under asymmetri information. Capaity investment in ompetitive souring: Cahon and Zhang 006 onsider simultaneously souring and apaity investment strategies in the presene of demand unertainty. They study single souring mehanisms of a buyer with information asymmetry about a supplier s ost. The buyer and suppliers interat only one to award the ontrat. The supply apaity and ontrat are driven by the ompetition only between simultaneously existing suppliers. However, in a dynami environment where supplier osts and pools are subjet to hange, a supplier not only ompetes with other suppliers in the same period but also with suppliers that appear with different osts in the future. n summary, while the existing literature provides useful insights in dynami supplier ompetition and ompetitive apaity investment, to the best of our knowledge, there has been no researh providing insights that onsider both. We develop and analyze a model that allows an understanding of optimal relationship seletion onerning apaity investment in the presene of both market and supplier ost unertainty. The remainder of the paper is strutured as follows: The dynami souring model with eah relationship is desribed in Setion 3. We present the optimal souring mehanism with eah relationship in Setion 4. Built on the analysis in Setion 4, Setions 5 and 6 5

6 ompare these two relationships without and with demand unertainty. We summarize the main insights and our ontribution in Setion The model n this setion, we introdue our model by desribing the aspets of the supplier pool, apaity, market demand, ontrat form, supplier relationships, aution protool, and the summary of sequenes of events. n order to analyze the tradeoff in the supplier relationship seletion, we build a model with two periods τ = 1, and a monopoly buyer that soures the prodution of a ritial omponent from outside suppliers. Capaity: We fous on the situation where apaity is owned by the buyer but operated by the supplier. This is ommon when the apaity an only be used to produe omponents with features that are speifi to the buyer, for example, dies, tools, speialized equipment, et., and annot be used to produe omponents for other buyers. Suh situations are ommon in the automotive industry Hayes et al., 005; Dyer, 000. Aordingly, the apaity has no salvage value and is observable and verifiable. We denote by k the unit ost of the apaity. The apaity limits the prodution quantity in both periods 1 and. f the buyer swithes to another supplier in a short-term relationship, the apaity has to be transferred from the inumbent to the new supplier. This transfer an be interpreted as the physial reloation of mahines or tools, and does not happen without a ost. The ost of swithing is t for eah unit of the apaity. This swithing ost orresponds to the ost of shipping and reinstalling prodution equipment, the expense on hiring key personnel from the inumbent or for training workers of the new supplier, et. n the automotive industry, a supplier that loses the business to a new supplier an be asked to ship the tools to the new supplier and help the new supplier to get up and running Dyer, Without loss of generality we assume the buyer inurs the swithing ost, otherwise the supplier who inurs this ost an be equivalently ompensated from the buyer s ontratual payments. The supplier pool: n a dynami environment, both the supplier pool and supplier effiieny may hange. The supplier pool in the seond period may be different from the supplier pool in the first period. Denote by n 1 the number of available suppliers in period 1, and n the number of entrant suppliers, not inluding the inumbent, in period. We model effiieny of a supplier by means of the unit ost. This ost may not only inlude the labor ost, but also the quality- and delivery-related osts, material ost, et. The effiieny of a 6

7 supplier an hange aross periods for reasons suh as hanges in his own supply hain or finanial situation. A supplier s ost is determined by independent, privately observed shoks in the two periods. A supplier does not know his prodution ost until he enters that period. All other players the buyer and other suppliers only know that the unit prodution ost of eah supplier in eah period follows a umulative probability distribution F density f, with finite support [, ]. The mean of a supplier s ost is µ, and the standard deviation is σ. The assumption of independeny of a supplier s ost aross periods is reasonable when the duration of a period is long or the environment of a supplier quikly hanges due to reasons suh as varying finanial situations, labor osts, material pries, situations of subontrators, et. Elmaghraby and Oh, 004. Similar assumptions are also arried in Menezes and Monteiro 003 and Grimm 004. n line with aution models Krishna, 00; Laffont and Tirole, 1993 we assume that F is log-onave, i.e., F /f is an inreasing funtion of. This ondition is satisfied by a wide variety of ommonly used distributions, suh as the normal and Beta distributions Rosling, 00; Bagnoli and Bergstrom, We denote by F n = 1 1 F n f n = nf 1 F n 1 the umulative probability probability density of the lowest value realized amongst n variables that are identially and independently distributed aording to F. The omplementary distribution is F n = 1 F n. Market demand: The buyer sells the final produt at unit prie r. The demand Ξ for this produt in eah period is unertain and independently drawn from a umulative probability distribution Gξ density gξ and Gξ = 1 Gξ. Let X be a random variable with a symmetri density funtion, mean 0 and standard deviation 1. We onsider Ξ of the form µ d +σ d X, whih has µ d as expeted demand and σ d as standard deviation. Gξ is known by the buyer and all the suppliers. When the supply apaity is Q, the satisfied demand out of the realized demand Ξ in one period is min{q, Ξ}, and the expetation is SQ = E [min{q, Ξ}]. t is easily proven that for Q µ d, σ d SQ 0 inreases with Q, i.e., when the demand unertainty inreases, the expeted satisfied demand dereases, but at a lower rate when the apaity is higher. The ontrats: The ontrat in the first period is speified by Q, w, where Q is the size of the apaity to be installed by the supplier, and w is the unit prie to be paid by the buyer for eah unit that is ordered and delivered after the demand is observed. n the seond period, the supply ontrat only speifies the unit prie, with the apaity given in the first period. 7

8 Long-term and short-term relationships: At the beginning of the first period and before the supplier seletion, the buyer hooses whether to ommit or not to the same supplier for both periods. f the buyer makes the ommitment, it results in a long-term relationship, otherwise a short-term relationship is seleted. We indiate long-term and short-term relationships by l and s, respetively. n a short-term relationship, the buyer may swith to a new supplier in the seond period by holding an aution among the inumbent and all other suppliers in the seond period supplier pool. With a long-term relationship, the winning supplier of the first period will provide the prodution for both periods. n other words, the aution in the seond period has only one bidder the inumbent and an be regarded as a renegotiation between the buyer and the inumbent. The aution protool: As suppliers prodution ost is private information, in eah period, the buyer selets one supplier from the available pool and deides the supply ontrat. Without loss of generality, we restrit the onsideration of an optimal aution mehanism to diret mehanisms that are inentive ompatible and individually rational, based on the revelation priniple Myerson, 198. n a diret mehanism, the buyer announes a menu of ontrats, with eah ontrat orresponding to one possible prodution ost of a supplier. The suppliers bid by reporting a ost, whih may differ from their true ost. The winner is seleted based on the reported ost by a pre-speified winner determination rule, and the ontrat that orresponds to the winner s reported ost is awarded. A diret mehanism is inentive ompatible if bidding the true ost onstitutes a Bayes-Nash equilibrium. A mehanism is individually rational if the expeted profit is non-negative for any supplier with any ost. Sequene of events: The sequenes of events in long-term and short-term relationships are illustrated in Figure 1, followed by desriptions. Long-term Relationship: see Figure 1i The interation between the buyer and suppliers in souring with a long-term relationship is governed by a sequene of events organized as follows: i At the beginning of the first period the buyer announes a menu of ontrats {Q l 1, w l,1 1, 1 [, ]} and a seletion rule for the first period. The suppliers observe and report their osts. The supplier is awarded the ontrat Q l 1, w l,1 1 for the first period, where 1 is the winner s prodution ost. ii The winning supplier builds the apaity Q = Q l 1. 8

9 Figure 1: Sequene of events in long-term vs. short-term relationships. The two relationships are different in the seond period events. While with a long-term relationship the buyer ommits to work with the same supplier in the seond period, with a short-term relationship the buyer is allowed to swith. The apaity is transferred from the inumbent to the new supplier if swithing happens. The supplier and ontrat in eah period is determined via an aution with the inumbent as the only bidder in the seond period of a long-term relationship. 9

10 iii The buyer observes the realized demand, ξ 1, and plaes an order. The supplier produes and delivers q 1 = min{ξ 1, Q}. iv At the beginning of the seond period, the buyer offers a unit prie wl, given the installed apaity Q.The inumbent may aept it or rejet it. f the inumbent rejets it, the game is over and eah party obtains zero profits in the seond period. v f the inumbent aepts the prie, the buyer observes the realized demand, ξ, and plaes an order. The supplier produes and delivers q = min{ξ, Q}. Short-Term Relationship: see Figure 1ii The interations in a short-term relationship souring are different from those with a long-term relationship in that the inumbent has to ompete with all other suppliers entrants in the supplier pool in the seond period. The buyer has to speify a swithing rule in the seond period that deides the winner given the bids of the inumbent and ompeting entrants. Along with the swithing rule the buyer offers menus of unit pries to the inumbent and entrant suppliers in the seond period. A short-term relationship is similar to a long-term relationship in the first period. The timing of events in a short-term relationship is as follows: i At the beginning of the first period the buyer announes the menu of ontrats {Q s 1, w s,1 1, 1 [, ]} and the supplier seletion rule for the first period. Suppliers observe and report their types. The supplier seleted is awarded the ontrat Q s 1, w s,1 1 for the first period, where 1 is the winner s ost. ii The supplier builds the apaity Q = Q s 1. iii The buyer observes the realized demand, ξ 1, and plaes an order. The supplier produes and delivers q 1 = min{ξ 1, Q}. iv At the beginning of the seond period, given the installed apaity Q the buyer announes the menus of unit pries {ws, } provided to the inumbent, and {ws, E E } provided to the entrants, for the seond period. The buyer also provides an entrant seletion rule for seleting the most favorable entrant, as well as a swithing rule x E,, Q {0, 1}. This swithing rule says that between the inumbent with a prodution ost and an entrant with a prodution ost E, the buyer will swith to the entrant if x = 1, otherwise keep the inumbent, when the apaity from the first period is Q. 10

11 The inumbent and entrants observe their osts in that period. The winner is seleted between the inumbent and the most favorable entrant based on the entrant seletion rule and the swithing rule. f the buyer deides to swith, the apaity is transferred from the inumbent to the entrant at the buyer s ost t Q. v The buyer observes the realized demand, ξ, and plaes an order. The supplier produes q = min{ξ, Q} to satisfy the order. 4. Analysis n this setion we first present the first-best solution for the buyer, i.e., the optimal mehanism with eah relationship if the buyer ould observe the prodution ost of a supplier Setion 4.1. With the first-best solution as a benhmark, we then analyze the optimal mehanisms, starting with the seond period, when the prodution ost is private information of a supplier Setion 4., and then give the optimal solution in the first period Setion The first-best solution With omplete information the buyer an ask a supplier to invest in the desired level of apaities and pays the exat ost spent by the supplier. Therefore the buyer will optimize and extrat the profit of the supply hain, leaving no positive gains to suppliers. Denote by the ost of the inumbent, and by E the lowest ost of the entrants, in the seond period. The apaity established in the first period is Q. With a short-term relationship the buyer an always hoose between the inumbent and the most effiient entrant by omparing the profits that an be reated by them. Proposition 1 n the first-best solution of the seond period in short-term souring, the buyer stays with the inumbent if E ĉ, Q, where ĉ, Q. = t Q SQ, otherwise swithes to the entrant E. The threshold of the entrant type, ĉ, Q, is the unit prodution ost of an entrant with whih the buyer supply hain is indifferent to hoosing between this entrant and the inumbent, when the inumbent has a unit prodution ost, and the apaity is Q. Note that in the absene of market demand unertainty, Q = µ d and ĉ, µ d. = t, i.e., the 11

12 buyer swithes to an entrant only if the saving in the prodution ost is higher than the ost of swithing. Proposition The short-term relationship always brings the buyer a higher expeted profit than the long-term relationship, when there is no information asymmetry. The intuition for Proposition is that with omplete information, the buyer an repliate a long-term relationship by hoosing not to swith in the seond period of a short-term relationship. n Setions 5 and 6, we determine whether a long-term relationship may be preferred in the ase of information asymmetry. 4. The optimal mehanisms - seond period Before presenting the optimal mehanisms, we define J = + F /f as the virtual ost of a supplier with the real prodution ost. The virtual profit is defined as the profit of the supply hain with the virtual ost onsidered as the unit ost of the supplier. Then for a given apaity Q, r J SQ is the virtual profit from the inumbent in the seond period if the inumbent s atual prodution ost is. The virtual profit is lower than the atual profit to the supply hain, the differene representing the information rent extrated by the supplier. Beause F is log-onave, the virtual ost J is an inreasing funtion of the atual ost. We also assume the revenue large enough so that r J + k + t. Under this ondition, it is always profitable for the buyer to ontrat with a supplier in eah period, taking the virtual ost as the supplier s ost. Proposition 3 n the seond period of an optimal mehanism with a long-term relationship, given the installed apaity Q the buyer offers the unit prie wl, Q =. The expeted seond period profit of the buyer is π l, Q = E [ r J ] S Q. 1 and the expeted seond period profit for the inumbent is equal to u l, Q = E [ J ] SQ. Based on Proposition 3, the buyer s profit is equal to the expetation of the virtual profit reated by the supplier. Sine there is no supplier ompetition, the buyer needs to offer a prie that is at least as high as the most ineffiient supplier type,. 1

13 Proposition 4 n the seond period of an optimal mehanism with a short-term relationship, i The buyer stays with the inumbent if E, Q, otherwise swithes to the entrant E, where E is the lowest ost of the entrants, and, Q is the solution to J J S Q = tq. ii The expeted seond period profit of the buyer is π s, Q = E, E [ r J E S Q tq E, Q ] 3 +E [ r J S Q F n, Q ]. The expeted seond period profit of the inumbent is u s, Q = E [ J S Q F n, Q ]. 4 iii The unit pries w s,, Q and w E s, E, Q offered to the inumbent and entrants satisfy F ws,, Q = + n ρ, Q dρ, 5 F n, Q [ ] e E,Q ws, E E, Q = E F E n 1 ρ dρ + F n 1 E 1 F 1 E, Q, 6 where 1 E, Q is the solution to, Q = E when solved for, should a solution on [, ] exist. Otherwise the buyer will never swith to an entrant with ost E and w E s, E, Q = 0. With a short-term relationship the buyer selets the supplier by omparing the virtual profits reated by the suppliers. The virtual profit that the buyer an obtain from the inumbent with a ost is r J S Q, and from an entrant with a ost E is r J E S Q tq, with the swithing ost tq onsidered. The log-onavity of F guarantees that the buyer favors the lowest ost entrant E against the other entrants. Comparison of virtual profits allows determining the threshold entrant s ost, Q below whih the buyer will swith from the inumbent. This is stated in Equation of Proposition 4. We an easily show that, Q ĉ, Q, where, from Proposition 1, ĉ, Q is the threshold entrant s ost in the first-best solution. This means that the buyer s swithing deision is not system effiient. Suh ineffiient swithing benefits the buyer in the seond period beause it lowers the information rent. 13

14 Equation 3 states that the seond period expeted profit of the buyer is the expetation of the virtual profit from the inumbent or from the lowest ost entrant, whihever is greater. From 4, the inumbent ahieves ex ante a gain equal to the expeted differene between the virtual profit and the atual system profit reated by himself. n Equation 5 and 6, the numerators an be interpreted as the expeted information rent, on eah unit prodution, gained by the inumbent with ost and an entrant with ost E respetively. Note that the denominators are the probabilities of the inumbent and an entrant winning in the seond period, depending on their osts. Therefore the unit pries to the inumbent and entrant, w s, and w E s,, are determined so that their expeted marginal profits are equal to the information rent on eah unit prodution. 4.3 Optimal mehanism - first period: the buy-in effet Taking the optimal seond period mehanism and the expeted outome as given, the first period mehanism is designed to maximize the buyer s total expeted profit over time. Denote by ν, Q. = π, Q + u, Q the sum of the buyer and the inumbent s expeted profits in the seond period with either relationship the subsript represents either relationship, for a given apaity Q. The optimal mehanism in the first period is haraterized as follows: Proposition 5 n an optimal mehanism with either relationship, the buyer selets in the first period the supplier with the lowest ost. The apaity Q 1 is designed so that for a given 1, the buyer s profits, π 1, Q. = r J 1 S Q kq + ν, Q is maximized at Q = Q 1. The unit prie w,1 1 offered to a supplier with a prodution ost 1 satisfies [ ] w,1 1 = 1 F n1 1 ρ SQ ρdρ u, 1 Q 1 F n1 1 1 SQ n the first period, the aution is designed to maximize the total expeted profit of the buyer over two periods, with onsiderations of the impat of the apaity deision on the seond period profit. From Equation 7, we an see that design of the first period prie is determined by a similar inentive ompatibility onstraint, as explained for Equations 5 and 6. The Buy-in Effet. Note from Equation 7 that the inumbent s expeted profit in the seond period u, Q 1 is exluded from its payoff in the first period. n other words, 14

15 in the first period the buyer an apture ex ante the seond period information rent of the inumbent by lowering the first period prie. This is beause a supplier will aept any prie in the first period that generates him non-negative expeted profits over two periods the individual rationality onstraint. We refer to this lowering of the first period payment due to the future profit flow as the buy-in effet or low-balling Dhebar and Oren, 1985; Padmanabhan and Bass, 1993; Anton and Yao, 1987; Beker, 196. The inumbent s expeted seond period profit rent, whih is aptured by the buyer via the buy-in effet, is alled the buyer s buy-in profits. The buy-in effet an be interpreted as that a supplier bids more aggressively by asking for a lower prie in the first period, seeing the improvement on the future profit resulting from the supplier s winning the first period aution. With a long-term relationship, a supplier seures the seond period profit if he wins in the first period. With a short-term relationship, winning in the first period allows the supplier to be favorably disriminated against entrants in the seond period beause of the swithing ost. Given the optimal mehanism for eah relationship, we now are ready to ompare the performane of a long-term and a short-term relationship in dynami souring, identify the key fores that drive the differene, and haraterize the impat of some environment parameters on the hoie of the relationship. n order to study the tradeoffs in relationship seletion in the presene of both demand unertainty and supplier ost unertainty, we shall first explore the situation with supplier ost unertainty only Setion 5, and then examine the impat of demand unertainty in the presene of supplier ost unertainty Setion Relationship omparison with deterministi demand: the role of supplier ost unertainty n this setion we ompare the buyer s profits in the long-term and short-term relationships when there is no demand unertainty: σ d = 0. Let the demand in eah period be µ d. The apaity deision with ertain demand is trivial: The supplier will install µ d units of apaity in the first period; i.e., Q l 1 = Q s 1 = µ d for any prodution ost 1 [, ] in eah relationship. Then the swithing deision in the seond period of a short-term relationship only depends on the inumbent s and entrants osts: The buyer will swith from the inumbent with a ost to an entrant with a ost lower than, µ d. Let πs and π l be the buyer s optimal expeted profits from a short-term and a long-term relationship. 15

16 Proposition 6 The expeted profit advantage of the short-term relationship for the buyer is independent of n 1 and given by: π s π l = µ d E, E [ J J E }{{} i Gain from effiieny improvement. t }{{} ii Swithing ost J }{{} iii Loss of buy-in profits E, µ d ]. From Proposition 6, the advantage of a short-term relationship over a long-term relationship is determined by three terms. First, a short-term relationship may bring the buyer a higher profit beause it allows the buyer to swith to a new supplier that has a lower ost than the inumbent. f the buyer were not to swith in the seond period, the virtual ost would be J instead of J E, J > J E if > E. This is the gain from effiieny improvement term i. Seond, a short-term relationship osts the buyer the swithing ost term ii. Third, by not ommitting to a supplier, the buyer lowers the inumbent s expeted profits in the seond period, whih results in less profits aptured via the buy-in effet term iii. This an also be interpreted as that a supplier bids more aggressively and thus lowers the buyer s ost in the first period if the buyer ommits not to swith. These three effets jointly determine when a long-term or a short-term relationship is more profitable to the buyer. Note that π s π l does not depend on n 1 beause in the first period of these two relationships the same supplier will be seleted from the same supplier pool, and generate the same virtual profit. n order to be able to ompare analytially the buyer s expeted profits π s and π l in these two relationships, we base our analysis on uniform distributions of a supplier s ost. Profit omparison: Proposition 7 haraterizes the impat of the swithing ost and supplier ost unertainty on the relationship seletion for uniform distributions of supplier osts. We assume that a supplier s prodution ost is uniformly distributed on [, ] with the mean µ = + / and standard deviation σ = / 3. Proposition 7 When the supplier s ost follow a uniform distribution over [, ], then i There exists t [ 0, 4 3σ suh that πs π l > 0 for t < t and π s π l 0 for t t. iithere exists > t 4 suh that π 3 s π l > 0 for σ > and π s π l 0 for σ. iii A short-term relationship redues to a long-term relationship if t 4 3σ. 16

17 The results of Proposition 7 are illustrated in Figure. We plot the differene π s π l as a funtion of the swithing ost t the left plot and as a funtion of the supplier ost unertainty σ the right plot with the horizontal axis with different values of n. Reall from Proposition 6 that π s π l does not depend on n Profit differene Short term Long term n =1 n =3 n =6 Profit differene Short term Long term n =6 n =3 n = Swithing ost Supplier ost unertainty Figure : Profit differene between long-term and short-term souring with ertain demand. n is the number of entrant suppliers in the seond period. The vertial axis is π s π l. µ d = 0.5, r = 3 and k = 0.5. For the left plot, = 0.4 and = 0.6. For the right plot, t = 0.. Proposition 7 and Figure both show that the relative performane of the long-term and short-term relationships depends on both the supplier ost unertainty σ and the swithing t. We shall explain the impat of the swithing ost first. When swithing is inexpensive, a short-term relationship is better than a long-term relationship. This is beause with negligible swithing ost fritions, the gain from effiieny improvement term i is signifiant and higher than the loss of buy-in profits term iii when n > 1. This an be onsidered as the option value of swithing in a short-term relationship. But when swithing beomes more expensive, the gain from effiieny improvement in a short-term relationship, after being offset by the swithing ost, is less and may be dominated by the loss of buy-in profits; i.e., the net gain from swithing is dominated by the advantage of a long-term relationship resulting from suppliers more aggressive bidding. Therefore, there exists a ritial swithing ost level at whih the buyer is indifferent between a short term and long term relationship. When the swithing ost is high, a short-term relationship redues to a long-term relationship beause then the buyer is unlikely to swith in the seond period even with the option of swithing open. Hene we onlude that it is for moderately high swithing osts that ommitting to a supplier is stritly benefiial for the buyer. 17

18 The impat of the supplier ost unertainty is based on similar effets. When the spread of supplier osts is small, there will be no big differene between the inumbent and entrant s osts, hene swithing is unlikely and a short-term redues to a long-term relationship. When the spread of supplier osts is wide, the gain from effiieny improvement is signifiant, dominating the swithing ost plus the loss of buy-in profits; a short-term relationship is better. When the spread of supplier osts is moderate, the opposite is true and a long-term relationship beomes better. When the supplier pool in the seond period is larger, the lowest ost entrant is stohastially more effiient, and the gain from effiieny improvement in a short-term relationship is higher. Therefore, a short-term relationship beomes more favorable with the inrease of n see from Figure that the area on the horizontal axis orresponding to positive π s π l expands with n. Dyer 000 has pointed out that a firm should use arm s length short-term relationships for non-strategi inputs. nputs are non-strategi when the outsoured items are 1 ommodities or standardized produts, stand-alone, or modular with no or few interation effets with other inputs, and 3 haraterized by a low degree of supplier-buyer interdependene. We have shown that a short-term relationship is preferable when the swithing ost is small. These two insights an be onneted by the fat that the swithing ost tends to be low when the supplier s input to the buyer is not strategi: t is easier to shift to a new supplier the prodution with a standardized proess or low interdependene on other inputs or systems. 6. Relationship omparison with unertain demand: the role of apaity investment We have ompared long-term and short-term relationships with deterministi demand. n this setion we study the impat of demand unertainty on the relative performane of these two relationships. With unertain demand, the deision of apaity investment plays a role in the relationship seletion. We first ompare the apaity investment levels in both relationships Setion 6.1, and then ompare the buyer s expeted profits and determine the impat of demand unertainty on the profits Setion

19 6.1 Comparing apaities: the lok-in effet The apaity affets not only how muh demand an be satisfied, but also the supplier s information rent and in a short-term relationship the swithing ost. n order to ompare the optimal apaity investment, we first examine the marginal profit of apaity investment in these two relationships. Reall from Proposition 5 that in eah relationship, the apaity Q 1 maximizes π Q, 1. = r J 1 SQ kq+ ν, Q, where r J 1 SQ kq is the first period virtual profit from a supplier type 1, and ν, Q is the sum of the buyer and inumbent s expeted seond period profits, when the apaity investment assoiated with 1 is Q. n order to ompare the optimal apaities in long-term and short-term relationships, we first examine the differene of Q π Q, 1 between the two relationships. We see that the derivative of the first period virtual profit r J 1 SQ kq with respet to Q is the same for both relationships. Therefore the differene of Q π Q, 1 is equal to the differene d of dq ν, Q, and does not depend on 1. Note that d S Q = G Q. dq Lemma 1 The derivative of π s Q, 1 π l Q, 1 with respet to Q is: Q π s Q, 1 π l Q, 1 [ = E, E J J E E, Q ] G Q }{{} i Gain from effiieny improvement + [ E J F n, Q ] G Q }{{} ii Loss of buy-in profits - [ E J S Q Q F n, Q } {{ } iv Lok-in + E [ Fn, Q ] t }{{} ], iii Swithing ost - where the sign of eah term is indiated in the braket following the name. From Proposition 1, we know that with a short-term relationship, the buyer gains from the effiieny improvement term i, but aptures less buy-in profits term ii and pays the swithing ost term iii. Lemma 1 shows that the apaity diretly influenes the magnitudes of these three terms by affeting the volumes: Both the gain from effiieny improvement and the loss of buy-in profits depend on the expeted volume S Q provided by the supplier in the seond period, whih is a funtion of Q, and the swithing ost is proportional to Q. 19

20 The Lok-in Effet. The apaity also indiretly influenes the buyer s profit by affeting the swithing deision in a short-term relationship term iv: The swithing probability F n dereases with the apaity Q. This is beause a higher apaity inreases the ost of swithing, and in turn requires the entrant supplier to be more effiient the threshold ost de of the entrant is lower: < 0 when swithing takes plae. We refer to this lowering of the dq swithing probability resulting from a higher apaity as the lok-in effet of the apaity in a short-term relationship. The lower the swithing probability, the higher the inumbent s expeted seond period profit, the more buy-in profits obtained by the buyer. Therefore the lok-in effet inreases the marginal value of apaity investment to the buyer in a short term relationship. Based on Lemma 1, ompared to a long-term relationship, a short-term relationship may inrease the apaity due to the gain from effiieny improvement term i and the lok-in effet term iv, whereas it may also derease the apaity due to the loss of buy-in profits term ii and the ost of swithing term iii. Capaity omparison: We now ompare the optimal apaities in a long-term and a short-term relationship, with a varying swithing ost. Proposition 8 With a supplier s ost following a uniform distribution on [, ], when the demand unertainty, σ d, is very small: i There exist t L and t H, 0 < t L < t H < 4 3σ, suh that E 1 [Q s 1] inreases with t for t [t L, t H ], and dereases with t for t [0, t L ] [ t H, 4 3σ ]. ii There exists t [ 0, 4 3σ ] suh that E 1 [Q s 1] > E 1 [Q l 1] for t t, 4 3σ. iii The optimal short-term relationship redues to a long-term relationship for t 4 3σ. Proposition 8 shows that when the demand unertainty is lose to zero, with the inrease of the swithing ost, the optimal apaity investment in a short-term relationship hanges in three phases: the apaity first dereases, then inreases, and finally dereases until the short-term relationship redues to a long-term relationship. The first phase is due to the inrease of the swithing ost, whih provides an inentive to redue the apaity investment in a short-term relationship. The seond phase is due to the lok-in effet, whih provides an inentive to inrease the investment; when swithing is not very expensive, inreasing the swithing ost magnifies the impat of the apaity on the swithing probability, and hene enhanes the lok-in effet, generating more buy-in profits. But with the swithing 0

21 ost inreasing higher in the third phase, the swithing probability gets loser to zero. This is when the short-term relationship redues to a long-term relationship, and approahes the apaity level in the latter. Note that the apaity investment in a long-term relationship does not depend on the swithing ost. Given the movement of these three phases, the short-term relationship indues a higher apaity level than the long-term relationship for swithing osts in the third phase as a suffiient but not neessary ondition. We examine the situation with general demand unertainty levels by numerial evaluations. The result shows that the insights revealed in Proposition 8 also arry on to general situations. Figure 3 shows an example based on a uniform demand distribution on [0., 0.8]. n this figure, the apaity differene between short-term and long-term relationship is drawn as a funtion of the swithing ost with different n. 10 x 10 3 Expeted apaity differene Short term Long term 5 0 n =1 n =3 n = Swithing ost Figure 3: Capaity differene between long-term and short-term relationships. The vertial axis is E 1 [Q s 1 Q l 1 ]. n is the number of entrant suppliers in the seond period. r = 3, n 1 = 1, k = 0.5, = 0.35, = 0.65, or, σ = Figure 3 shows that a short-term relationship indues a higher apaity than a long-term relationship when the swithing ost is high. This is onsistent with our reasoning outlined above: With a high swithing ost, the probability of swithing is small, and the three diret effets, whih present when swithing happens, are dominated by the indiret lok-in effet. 1

22 6. Comparing profits Reall from Setion 5 that with ertain demand, the advantage of a short-term relationship is determined by the ombination of three fators: the gain from effiieny improvement, the loss of buy-in profits, and the swithing ost. Now with unertain demand, these fators are influened by the apaity see Lemma 1. The demand unertainty affets the parameter settings for whih a long-term or a short-term relationship is more profitable for the buyer. We ompare the sensitivity derivative of the profit differene, π s π l, with respet to the demand unertainty σ d. n order not to make the notation too umbersome, we drop the dependene on σ d in the formulas. At the ritial swithing ost level, t, when π s = π l with σ d = 0, this derivative allows us to understand the first order effet of an inrease in market demand unertainty: f the derivative is positive negative, it means that when a buyer is indifferent between the two relationships in absene of market unertainty, an inrease in market unertainty makes the buyer stritly prefer a short-term long-term relationship. n the following we first analyze these derivatives when unertainty is introdued in a ertain market, σ d very small. We then provide numerial examples of how the preferene between a short-term and long-term relationship hanges for greater values of σ d. Changing the demand unertainty in a period, σ d, at σ d = 0, results in the following hange in profits: Lemma The derivative of π s π l with respet to σ d when σ d = 0, an be haraterized by: d π s π l dσ d [ J J E J E ], µ d S µ d σ }{{ d } = E, E i differene in seond period profit if an entrant wins [ E J S µ d ] F n σ, µ d }{{ d } ii hange of the buy-in profits due to the hange of the swithing probability 8 Let us first onsider term i, whih haraterizes the diret impat of demand unertainty through its influene on the expeted satisfied demand. t is the multipliation of two fators. The seond fator is the influene of demand unertainty on the expeted satisfied demand.

23 Note the seond fator σ d Sµ d < 0; i.e., as the market unertainty inreases, the expeted satisfied demand dereases. The first fator is the differene between the expeted gain from effiieny improvement and the loss of buy-in profits generated by souring a unit from the winning entrant. Reall from Proposition 7 that without demand unertainty, the expeted unit profit advantage of the short-term relationship is equal to the first fator minus the swithing ost. When t = t, the short-term relationship ahieves the same expeted profit as the long-term relationship, and hene the first fator overs the swithing ost and is positive. The first fator an be interpreted as the marginal profit advantage exluding the swithing ost of the short-term relationship relative to the long-term relationship. Thus a positive sign of the first fator means that the profit margin assoiated with eah unit sale in a short-term relationship is higher than in a long-term relationship. t then follows that term i is negative; i.e., when the buyer is indifferent between the short-term and long-term relationships, the buyer s profit from a short-term relationship is more sensitive to the hange of demand unertainty than from a long-term relationship. Now we shall examine term ii, whih haraterizes the indiret impat of demand unertainty through its influene on the swithing probability in a short-term relationship. Reall from Proposition 4 that, Q s is the highest possible ost of the new supplier when the inumbent supplier with ost and apaity Q s is swithed away from in the seond period, and it satisfies Equation. With higher demand unertainty, the expeted satisfied demand is lower. As a result, the buyer requires the entrant to be more effiient when swithing happens so that the total gain from swithing overs the swithing ost see Equation : e σ d < 0. Therefore, with demand unertainty inreasing, the swithing probability F n, Q s is lower, generating more buy-in profits. Hene term ii is positive, whih mitigates the sensitivity of the buyer s profit in a short-term relationship to the hange of demand unertainty. Lemma leads to the following results in Proposition 9. Proposition 9 With a supplier s ost following a uniform distribution on [, ], d dσ d π s π l < 0 for σ d = 0 and t = t at whih π s = π l. Proposition 9 says that the buyer should shift from a short-term to a long-term relationship, when the demand unertainty inreases from zero. This result is due to the domination of term i in Lemma, whih an be further explained as follows. When the buyer is indifferent to the two relationships, the marginal profit in a short-term relationship has to over 3