Strategic Dynamic Sourcing from Competing Suppliers with Transferable Capacity Investment

Transcription

1 Strateg Dynam Sourng from Competng Supplers wth Transferable Capaty nvestment Cuhong L Laurens G. Debo Shool of Busness, Unversty of Connetut, Storrs, CT 0669 The Booth Shool of Busness, Unversty of Chago, Chago, L Cuhong.L@busness.uonn.edu ldebo@hagogsb.edu We study the suppler relatonshp hoe for a buyer that nvests n transferable apaty operated by a suppler. Wth a long-term relatonshp, the buyer ommts to soure from a suppler over a long perod of tme. Wth a short-term relatonshp, the buyer leaves open the opton of swthng to a new suppler n the future. The buyer has nomplete nformaton about a suppler s effeny, and thus uses autons to selet supplers and determne the ontrats. n addton, the buyer faes unertan demand for the produt. A long-term relatonshp may be benefal for the buyer beause t motvates more aggressve bddng at the begnnng, resultng a lower ntal pre. A short-term relatonshp may be advantageous beause t allows swthng, wth the apaty transferred at some osts, to a more effent suppler n the future. We fnd that there exsts a rtal level of swthng osts above whh a long-term relatonshp s better for the buyer than a short-term relatonshp. n addton, ths rtal swthng ost dereases wth demand unertanty, mplyng a long-term relatonshp more favorable for a buyer fang volatle demand. Fnally, we fnd that n a long-term relatonshp, apaty an be ether hgher or lower than n a short-term relatonshp. 1 ntroduton Fang nreasng ompetton, manufaturers soure from external supplers produts and serves wth nreasng omplexty and strateg mportane Gottfredson et al., 005; Maurer et al., 004. n a dynam envronment, apabltes of supplers may hange and new supplers may emerge over tme. Hene, suppler relatonshp management s rtal for a manufaturer buyer Lker and Cho, 004; Beth et al., 003. A buyer may hoose to develop a long-term or a short-term relatonshp wth a suppler. A long-term relatonshp features the ommtment of sourng from a suppler over a long-perod of tme, whle a short-term relatonshp usually only bnds for a short perod of tme wth the buyer frequently swthng to other supplers Pyke and Johnson, 003. A long-term ommtment wth a suppler hampers a buyer n tappng nto more effent alternatve soures n the future. Sako 199 reported that Japanese ar manufaturers lamented the dffultes they had n breakng up exstng relatonshps wth supplers and swthng to new supplers. Yet, the reent years have wtnessed a growng trend of ompanes onsoldatng ther supply base and formng long-term relatonshps wth ther key supplers n whh the manufaturer has lmted or no busness wth ompetng supplers Maurer et al., 004; Pyke and Johnson,

2 For example, Chrysler s average ontrat length nearly doubled over the perod from 1989 to 1994 Helper, 1991; Dyer, n ths paper, we study the optmal relatonshp hoe when a buyer nvests n transferable and spef apaty operated by a suppler. nvestment of spef apaty may be needed for a suppler to produe parts or systems that are ustomzed to the buyng frm s needs. The seleton of the suppler relatonshp nfluenes the level of upfront spef apaty nvestment. The spef apaty an take the form of faltes that are loated n lose proxmty to the buyer s plants, physal assets suh as ustomzed mahnery, tools, or equpment, or employees that have relatonshp-spef nformaton or experene that allow effetve oordnaton between the buyer and suppler Dyer, 000. These assets are dedated to the buyer and therefore typally owned by the buyer although operated by a suppler. For example, Ford owns the buldngs n ts supply park that st one-half mle from the Chago assembly plant, and leases these buldngs to eleven supplers Peter, 004. n the automotve ndustry, the manufaturer usually provdes the spef tools or remburses toolng osts to supplers Vsteon, 003. t s also ommon for a manufaturer to assgn dedated employees to work wth a suppler, even on a suppler s ste Maurer et al., 004; Dyer, 000. n ase of the buyer swthng to a new suppler, the spef apaty s typally transferred, at some osts, from the numbent to the new suppler. Ths transfer may not only refer to the physal reloaton of mahnes or tools, but may also mean to adapt the new suppler to the dedated falty, or tranng spealzed workers for the new suppler. n the automotve ndustry, a suppler that loses the busness to a new suppler an even be asked to shp the tools to the new suppler and help the new suppler to get up and runnng Dyer, When the buyer faes unertan market demand for the fnal produt, how muh spef apaty to nvest s a non-trval queston. The return of the nvestment depends not only on the realzaton of the demand, but also on the length of the relatonshp wth a suppler and the suppler effeny. Thus the nvestment of spef apaty should take nto onsderaton not only the unertanty of demand but also the governane struture of suppler relatons Dyer, No matter whh relatonshp to use, a buyer wants to ontrat wth the most effent suppler that an provde the same produton at the least ost. The nformaton about the effeny of a suppler s typally not fully aessble to a buyer. Beause supplers tend to understand the tehnal proesses better than the purhasng ompany, they are better postoned to dentfy areas of savngs: for example, redung the number of omponents by ombnng separate parts, applyng advaned fabraton tehnques to redue subsequent steps, hangng part geometres and nreasng mahnng toleranes, alternatng materals that an redue ost of nonrtal omponents,

3 et. Ulrh and ppnger, 004. Ths knowledge allows a suppler to hold prvate nformaton of produton osts. For tehnologally omplex produts, there s generally substantal prvate nformaton about produtvty or tehnologes of a suppler Lyon, 006. Wthout knowng the atual ost of a suppler, the buyer usually selets a suppler and negotates the ontrat by a Request-for-Proposal, or a ompettve bddng proess. n ths stuaton the proft of the buyer depends on how muh proft a suppler an retan due to nformaton asymmetry. We study the tradeoff between long-term and short-term relatonshps when a buyer soures from ompetng supplers and nvests n transferable apaty that s operated by a suppler. We take both nformaton asymmetry onernng a suppler s ost struture and unertanty onernng the market demand nto aount. n order to understand the fundamental eonom determnants of the suppler relatonshp deson, we analyze a model wth a two-perod horzon. Wth a longterm relatonshp the buyer ommts to soure from a sngle suppler over the entre horzon. Wth a short-term relatonshp the buyer does not make suh ommtment but nstead keeps the opton of swthng to a new suppler open n the seond perod. Compettve bddng proesses are used n eah perod to selet a suppler and determne the ontrat. We study the key operatonal desons that the buyer needs to make: How muh apaty to ontrat for, wth whh suppler and for how long. The questons that we address n ths paper are: What s an optmal strategy of a buyer under eah suppler relatonshp? What s the nfluene of the suppler relatonshp on the apaty nvestment deson? How do haratersts of the envronment, n partular the swthng ost and demand unertanty, mpat the suppler relatonshp seleton? Lterature Revew A body of researh n eonoms and operatons management has been developed that provdes us wth nsghts n dynam sourng strateges see lmaghraby 000 for an overvew of the lterature. n the followng we provde a revew of the papers that onsder smlar ssues as n our paper: suppler swthng, suppler ommtment, and apaty nvestment n a ontext of sourng from ompetng supplers wth prvate nformaton. Dynam sourng strateges wth suppler swthng: n a mult-perod settng where suppler apabltes are prvate nformaton and hange over tme, the buyer must make swthng desons onsderng the trade-off between ompettve advantage realzed by swthng, and the beneft of workng wth the same suppler. Laffont and Trole 1988, Stole 1994 and Rob 1986 study how a buyer should ontrat wth a suppler and make the swthng deson when the frst suppler strategally makes nvestments to redue the future ost. Anton and Yao 1987, Klotz 3

4 and Chatterjee 1995, and Lews and Yldrm 00 model the dynam swthng deson for a buyer when the numbent generally has an effeny advantage over an entrant due to learnng-bydong. The mpat of the swthng ost on dynam seleton of supplers s spefally analyzed by Ba 000 and Cabral and Greensten Generally these papers argue that although swthng may ntrodue system neffeny, t nfuses ompetton between supplers and therefore redues the buyer s nformaton rent. The tradeoff between the neffeny and nformaton rent determnes the optmal swthng deson of a buyer. All these papers assume that the buyer never ommts to a sngle suppler, n other words, they only onsder short-term relatonshps. Long-term versus short-term relatonshps: The onluson that the buyer should swth under some ondtons wth a short-term relatonshp does not deny the beneft of establshng a long-term relatonshp. Motvated by prourement n the defense ndustry wth ertan demand, Rordan and Sappngton 1989 ompare sole sourng and seond sourng, whh are analogous to long-term and short-term relatonshps, onsderng a suppler s nvestment to mprove the projet s value n the future. By assumng dental future osts for all supplers, they fnd that a short-term relatonshp s of lmted value and dsourages nvestments. n ther paper, nvestment n produt enhanement nreases the probablty of swthng beause t mproves the value of the produt, and thus redues the relatve sgnfane of the swthng ost. Our nsght s dfferent n that the apaty of the numbent dereases the swthng probablty, and as a result, a short-term relatonshp may ndue more apaty nvestment than a long-term relatonshp. Ths suggests that to hoose a suppler relatonshp, a buyer has to arefully dentfy the mpat of nvestment on the swthng deson and the motvaton of swthng. Consderng the effet of learnng-by-dong, lmaghraby and Oh 004 ompare an eroson rate poly aganst two base ases n whh the buyer holds an ndependent, short-term auton n eah perod, and the buyer proures all her demand n a sngle bundle auton. Grmm 004 and Menezes and Montero 003 ompare sequental autons and a bundled auton for two tems when synerges of tem values exst. All these papers fous on the nformaton struture, assumng determnst demand or supply as n Menezes and Montero 003 n a forward auton settng. When both demand unertanty and suppler ost unertanty exst, as s the ase n our researh, the suppler relatonshp and prourement ontratng must take nto onsderaton apaty nvestment along wth suppler seleton under asymmetr nformaton. Swnney and Netessne 007 study the hoe of a buyer between offerng long-term and shortterm ontrats to a suppler onsderng the suppler default rsk. Assumng publ nformaton, they show that the possblty of suppler default offers a reason for a buyer to prefer long-term 4

5 ontrats to short-term ontrats. We onsder prvate nformaton about the ost of a suppler. The prvate nformaton provdes a dfferent motvaton for the buyer to selet a long-term relatonshp. n ths paper, we onsder a stuaton where the suppler s spef apaty s owned by the buyer and transferable between supplers. Ths s dfferent from L and Debo 008 among some other modellng dfferenes, who assume non-transferable apaty. Thus the ompetton models between the numbent and entrant supplers are dfferent n these two papers: Wth non-transferable apaty, the frton of sourng from an entrant suppler s attrbutable to the nstalled apaty advantage of the numbent and the new apaty nvestment ost of the entrant. Wth transferable apaty, the frton s due to the swthng ost for transferrng the nstalled apaty from the numbent to entrant suppler. As a result, although the drver of a long-term ommtment s the same n both papers, how the demand unertanty nfluenes the buyer s deson s dfferent. Partularly, when demand unertanty nreases, wth non-transferable apaty, L and Debo 008 show that leavng the opton of alternatve sourng open s more favorable, whle wth transferable apaty, we show that ommttng to a sngle suppler s a more lkely hoe. We thus omplement the results of L and Debo 008 wth nsghts based on dfferent features of suppler apaty. Capaty nvestment n ompettve sourng: Cahon and Zhang 006 onsder smultaneously sourng and apaty nvestment strateges n the presene of demand unertanty. They study sngle sourng mehansms of a buyer wth nformaton asymmetry about a suppler s ost. The buyer and supplers nterat only one to award the ontrat. The supply apaty and ontrat are drven by the ompetton only between smultaneously exstng supplers. However, n a dynam envronment where suppler osts and pools are subjet to hange, a suppler not only ompetes wth other supplers n the same perod but also wth supplers that emerge wth dfferent osts n the future. n summary, whle the exstng lterature provdes useful nsghts n dynam suppler ompetton and ompettve apaty nvestment, to the best of our knowledge, there has been no researh provdng nsghts that onsder both. We develop and analyze a model that allows an understandng of optmal relatonshp seleton onernng apaty nvestment n the presene of both demand and suppler ost unertanty. The remander of the paper s strutured as follows: The dynam sourng model wth long-term and short-term relatonshps s desrbed n Seton 3. The optmal mehansms wth long-term and short-term relatonshps are presented n Seton 4. Seton 5 ompares the profts and apaty n the two relatonshps. We dsuss the system effeny of the optmal mehansms n Seton 5

6 6. Some extended analyss s provded n Seton 7. We summarze the man nsghts and dsuss future researh n Seton 8. 3 The model 3.1 Model desrpton n order to analyze the tradeoff n the buyer s suppler relatonshp seleton, we buld a model wth two perods τ = 1, and one monopoly buyer that soures the produton of a rtal omponent from external supplers. Capaty: We fous on spef apaty that s owned by the buyer but operated by a suppler. The apaty lmts the produton quantty of a suppler n eah perod. We denote by k the unt ost of the apaty. f the buyer swthes supplers, the apaty s transferred from the numbent to the new suppler at unt ost s. Wthout loss of generalty we assume the buyer nurs the swthng ost; otherwse the suppler who nurs ths ost an be equvalently ompensated wth the buyer s ontratual payments. Sne the apaty has features that are ustomzed to the buyer s needs, t has no salvage value outsde the buyer s busness. We assume that the lead-tme of apaty nvestment s so long that the apaty an only be nvested at the begnnng of the frst perod but not n the mddle of the horzon. Thus the apaty annot be expanded n the seond perod. Sne the apaty has zero salvage value, a suppler wll never redue exstng apaty dedated to the buyer. We also assume that the buyer s revenue s large enough so that n ase of swthng to a new suppler, all apaty of the numbent wll be transferred to the new suppler. Therefore, the apaty wll not be shrunk ether n the seond perod. n Seton 7, we relax the assumpton of fxed apaty n the seond perod, and extend the analyss to the stuaton when the apaty an be expanded or shrunk n the seond perod. The suppler pool: n a dynam envronment, both the suppler pool and the osts of a suppler may hange. Denote by n 1 the number of avalable supplers n perod 1, and n the number of entrant supplers, not nludng the numbent, n perod. We assume that the supplers who lose the frst perod ompetton wll stay and partpate n the seond-perod auton n a short-term relatonshp. Thus the n entrant supplers n the seond perod nlude the n 1 supplers exept the numbent n the frst perod. n eah perod a suppler s unt produton ost s determned by ndependent, prvately observed shoks. A suppler does not know hs ost untl he enters that perod. All other players the buyer and other supplers only know that the unt produton ost of a suppler n eah perod s drawn from an dental dstrbuton F densty f on the 6

7 support [, ], wth mean µ and standard devaton σ. Ths assumpton of ndependent osts aross perods s reasonable when the duraton of a perod s long, or the ost shoks are ted to hanges n, e.g., labor and subontrator management, srap rates, materals management, nbound and outbound logsts, et., that an happen qukly and frequently. Smlar assumptons are also arred n Menezes and Montero 003. n lne wth auton models Krshna, 00; Laffont and Trole, 1993 we assume that F s log-onave,.e., F /f s an nreasng funton of. Ths ondton s satsfed by a wde varety of ommonly used dstrbutons, suh as the normal and Beta dstrbutons Roslng, 00; Bagnol and Bergstrom, 005. We denote by F n = 1 1 F n f n = nf 1 F n 1 the umulatve probablty probablty densty of the lowest value realzed amongst n varables that are dentally and ndependently dstrbuted aordng to F. The omplementary dstrbuton s F n = 1 F n. Market demand: The buyer sells the fnal produt at unt pre r. The demand D for ths produt n eah perod s unertan and ndependently drawn from a umulatve probablty dstrbuton Gd densty gd and Gd = 1 Gd on the support [ d, d ]. Let X be a random varable wth a symmetr densty funton, mean 0 and standard devaton 1. We onsder D of the form µ d +σ d X, whh has µ d as expeted demand and σ d as standard devaton. Gd s known by the buyer and all the supplers. When the suppler apaty s Q, the demand to be satsfed by the suppler n one perod s mn{q, D}, and ts expetaton s SQ = [mn{q, D}]. t s easly proven that for Q µ d, σ d SQ 0 nreases wth Q,.e., when the demand unertanty nreases, the expeted satsfed demand dereases, but at a lower rate when the apaty s hgher. The ontrats: Both the buyer and suppler follow a make-to-order poly,.e., the buyer plaes an order to the suppler after the demand s known, and gven the order the suppler produes subjet to the apaty onstrant. The ontrat n the frst perod s spefed by Q, w, where Q s the sze of the apaty to be nstalled, and w s the unt pre to be pad for eah unt delvered. n the seond perod, the supply ontrat only spefes the unt pre, wth the apaty gven n the frst perod. Long-term and short-term relatonshps: At the begnnng of the frst perod, the buyer dedes whether to establsh a long-term or a short-term relatonshp wth a suppler. Wth the former seleton, the buyer ommts to soure from the frst-perod wnner n both perods. Wth the latter seleton, the buyer s allowed to swth supplers n the seond perod. We ndate long-term and short-term relatonshps by subsrpts l and s, respetvely. Due to the transaton ost of sourng from multple supplers, for example, the osts of montorng supplers performanes, ommunatng and oordnatng wth supplers, ahevng qualty onssteny aross supplers, et. Rhardson 7

8 and Roumasset, 1995, we assume that the buyer soures from only one suppler at a tme,.e., even wth multple supplers avalable n the seond perod of a short-term relatonshp, the buyer wll soure exlusvely from the numbent or an entrant nstead of splttng the produton over multple supplers. The auton protool: As supplers produton ost s prvate nformaton, n eah perod, the buyer selets one suppler from the avalable pool and dedes the supply ontrat va an auton. n the seond perod of a long-term relatonshp, sne the buyer an only soure from the numbent, the auton has only one bdder the numbent and an be regarded as a renegotaton between the buyer and the numbent. To elmnate the dependene of results on the spef auton forms used, we analyze the optmal auton mehansm for the buyer. Based on the revelaton prnple Myerson, 1981, the onsderaton of an optmal auton mehansm an be restrted, wthout loss of generalty, to dret mehansms that are nentve ompatble and ndvdually ratonal. n a dret mehansm, the buyer offers eah suppler a menu of ontrats, wth eah ontrat orrespondng to a profle of supplers osts. ah suppler then bds ther osts, whh may dffer from the true osts. bds are awarded to supplers. Gven the bds, the ontrats that orrespond to the profle of A dret mehansm s nentve ompatble C f bddng the true ost onsttutes a Bayes-Nash equlbrum. A mehansm s ndvdually ratonal R f the expeted proft s non-negatve for any suppler wth any ost. Other papers bult on dret auton mehansms nlude Cahon and Zhang 006, Dasgupta and Spulber 1989/90 and Laffont and Trole Sequene of events: llustrated n Fgure Formulaton The sequenes of events n long-term and short-term relatonshps are We shall frst formulate the seond perod deson problems of the buyer n long-term and shortterm relatonshps, and then the frst perod deson problem wth eah relatonshp. Seond perod, long-term relatonshp: Assume the apaty nvested n the frst perod s Q. n the seond perod of a long-term relatonshp, the buyer offers the numbent suppler a menu {wl,, p l, }, where p l, ĉ s the probablty that the numbent stays as the suppler and ws, ĉ ĉ s the unt pre f hs reported ost s ĉ. The suppler s proft s u l,,, Q = wl, ĉ S Q p l, ĉ f he reports ost ĉ whle hs true ost s. Reall that the buyer s unt revenue s r. relatonshp s Therefore, the buyer s deson problem n the seond perod of a long-term 8

9 Fgure 1: Sequene of events n long-term vs. short-term relatonshps. The two relatonshps are dfferent n the seond perod events. Whle wth a long-term relatonshp the buyer ommts to work wth the same suppler n the seond perod, wth a short-term relatonshp the buyer s allowed to swth. The apaty s transferred from the numbent to the new suppler f swthng happens. The suppler and ontrat n eah perod are determned va an auton wth the numbent as the only bdder n the seond perod of a long-term relatonshp. π l, Q = max {w l,,p l, } [ r w l, p l, ] S Q { ul, s.t., [, ] :, Q ĉ = max u l,, ĉ [,], Q u l,,, Q 0 C R The frst onstrant ensures that the mehansm s nentve ompatble C,.e., the suppler wll report hs ost truthfully. The seond onstrant guarantees ndvdual ratonalty R,.e., the suppler wll aheve non-negatve proft from partpaton. Defne u l, Q. = [ ul,,, Q] as the ex ante proft of the wnner n the seond perod of a long-term relatonshp. Seond perod, short-term relatonshp: Let =,1,...,n be the ost profle of all entrant supplers n the seond perod. Defne, j. =,1,...,,j 1,,j+1...,n as the profle of all supplers exept suppler j. The numbent s ost n the seond perod s. Dependng on the apaty Q, the buyer offers a menu { { ws,, p s, } to the numbent and w,j s,, p,j s, }, j = 1,..., n, to eah entrant. Gven the numbent s bd ĉ and entrants bds ĉ = ĉ,1,...ĉ,n, the probablty of the numbent seleted as the wnner s p s, ĉ, ĉ wth unt pre w s, ĉ, ĉ, and the probablty of the entrant j seleted as the wnner s p,j s, ĉ, ĉ wth unt pre w,j s, ĉ, ĉ. Let u s, ĉ,, Q. = [ w s, ĉ, p s, ĉ, ] S Q 9

10 be the expeted seond perod proft of the numbent wth ost f he bds ĉ and all entrants bd truthfully. Smlarly, let u,j s, [ ] ĉ,j,,j.=, Q w,j,, j s,, ĉ,j,, j,j p,j s,, ĉ,j,, j S Q be the expeted seond perod proft of entrant j wth ost,j f he bds ĉ,j and all other supplers bd truthfully. Reall that the unt apaty transferrng ost s s. The buyer s deson problem n the seond perod s π s, Q = { max w { s,, p s, } } w,j s,, p,j s, s.t. j = 1,..., n,,,j [, ] : [, r w s,, S Q p s,, + n j=1 r w,j s,, S Q sq p,j s,, ] u s,,, Q = max u ĉ ĉ [,] s,,, Q u,j s,,j,,j, Q = max u,j ĉ,j s, ĉ,j,,j, Q [,],, Q 0, u,j s,,j,,j, Q 0 u s, Let u s, Q =. [ u s,,, Q] and u s, Q =. [ ],j u,j s,,j,,j, Q be the ex ante profts of the numbent and an entrant suppler n the seond perod of a short-term relatonshp for gven apaty nvestment all entrants have the same expeted seond-perod profts beause they are ex ante dental. Seond perod summary: For both the short- and long-term relatonshps we have obtaned expressons for the numbent and entrant suppler s seond-perod expeted profts u l, Q, u s, Q and u s, Q, and expressons for the buyer s seond perod profts, π l, Q and π s, Q. We wll use these expressons when formulatng the frst perod problem. Frst perod: The buyer s frst perod desons n long-term and short-term relatonshps are smlar: They both maxmze the buyer s profts over the entre horzon, takng the seond perod optmzaton as an embedded problem. Therefore, n the formulaton we do not spefy the relatonshp but replae the relatonshp ndaton by subsrpt. Let 1 = 1 1,...n 1 1 be the ost profle of all supplers n the frst perod. Defne. 1 = 1 1,..., 1 1, n 1 1 as the profle of all supplers exludng suppler. n the frst perod, the buyer offers a menu { Q, w,1, p,1 }, = 1,..., n 1, where p,1 ĉ 1 s the probablty that suppler s seleted as the wnner, w,1 ĉ 1 s the unt pre of suppler, and Q ĉ 1 s the apaty to be nvested for suppler, f supplers C R 10

11 bds are ĉ 1 = ĉ 1 1,...ĉn 1 1. Defne and u l ĉ 1, 1. = 1 u s ĉ 1, 1. = 1 +u s, [[ w l,1 ĉ 1, 1 1 +u l, Q l ĉ 1, 1 [[ w s,1 ĉ 1, 1 1 S Q l ĉ 1, 1 ] p l,1 ĉ 1, 1 ] S Q s ĉ 1, ĉ Q s 1, ] 1 p s,1 ĉ 1, 1 + u s, j 1 kq l ĉ 1, 1 kq s ĉ 1, 1 ĉ Q j s 1, 1 p j s,1 ĉ 1, 1 as the total expeted proft of suppler over two perods n long-term and short-term relatonshps, f he bds ĉ 1 wth true ost 1 deson n the frst perod s: max {Q,w,1,p,1 } 1 and all other supplers bd truthfully. Then the buyer s optmal [ n1 r w,1 1 S Q 1 + π, Q 1 ] p,1 1 =1 { u s.t. = 1,..., n 1, 1, 1 = max u ĉ 1, 1 [, ] : ĉ 1 [,] 1 C u 1, 1 0 R. 4 The Optmal Mehansms of Long-term and Short-term Relatonshps We frst analyze the optmal mehansms n the seond perod Seton 4.1 for eah relatonshp, and then haraterze the optmal soluton n the frst perod Seton The seond perod Before presentng the outome of the optmal mehansms, we defne J = + F /f as the vrtual ost of a suppler wth the real produton ost Myerson, Beause F s log-onave, the vrtual ost J s an nreasng funton of the atual ost. We also assume the revenue s large enough so that r J + k + s. Under ths ondton, t s always proftable for the buyer to ontrat wth a suppler n eah perod even f takng the vrtual ost as the suppler s ost. Ths assumpton also mples that the the optmal apaty nvestment n ether relatonshp wll be at least µ, f the demand dstrbuton s symmetr. Ths s beause the margnal return of apaty nvestment over two perods s at least r J s, whh s greater than twe of the margnal ost k gven ths assumpton. Defne vrtual proft as the proft of the supply han f the vrtual ost were onsdered as the unt ost of the suppler. Then for a gven apaty Q, 11

12 v Q,. = r J SQ s the vrtual proft of sourng from the numbent n the seond perod f the numbent s atual produton ost s. Proposton 1 n the seond perod of a long-term relatonshp, gven apaty Q, the expeted seond-perod proft of the buyer s π l, Q = [ r J ] S Q, 1 and the expeted seond-perod proft of the numbent s u l, Q = [ J ] SQ. Based on Proposton 1, the buyer s proft s equal to the expetaton of the vrtual proft generated by the suppler. The vrtual proft s lower than the atual proft of the supply han. Ther dfferene s u l, Q, representng the nformaton rent extrated by the suppler. Next we analyze the optmal results for the seond perod of a short-term relatonshp. Let be the lowest ost of the entrants. Proposton n the seond perod of a short-term relatonshp, the buyer stays wth the numbent f, Q, otherwse swthes to the lowest-ost entrant, where, Q [, ] s the soluton to J J S Q = sq 3 f suh soluton exsts, otherwse, Q = ; the expeted seond-perod proft of the buyer s π s, Q =, [ r J S Q sq, Q ] Pr, Q 4 + [ r J S Q F n, Q ], and the expeted seond-perod proft of the numbent s u s, Q = [ J S Q F n, Q ]. 5 The buyer selets a wnnng suppler by omparng the vrtual profts reated by the supplers. The vrtual proft generated an entrant wth ost s v Q,. = r J S Q sq, where sq s the total swthng ost. The log-onavty of F guarantees that the buyer favors the lowest-ost entrant over the other entrants. The buyer wll favor the lowest-ost entrant 1

13 over the numbent f and only f v n quaton 3 of Proposton. Q, v Q,,.e., s below, Q. Ths s stated quaton 4 states that the seond-perod expeted proft of the buyer s the expetaton of the vrtual proft from the numbent or from the lowest ost entrant, whhever s greater. From 5, the numbent aheves ex ante a gan equal to the expeted dfferene between hs total vrtual ost and atual ost. 4. The frst perod: the buy-n effet Takng the optmal seond perod mehansm and the expeted outome as gven, the frst perod mehansm s desgned to maxmze the buyer s total expeted proft over tme. Let 1 be the lowest ost of supplers n the frst perod. The optmal mehansm n the frst perod s haraterzed n Proposton 3: Proposton 3 n both long-term and short-term relatonshps, the buyer selets n the frst perod the suppler wth the lowest ost. The expeted frst-perod proft of the buyer s 1 [π,1 1, Q 1 ], where for gven apaty Q and frst-perod suppler ost 1, π,1 1, Q = r J 1 S Q kq + u, Q, 6 and Q 1 = arg max Q π,1 1, Q + π, Q s the optmal apaty nvested for a suppler wth ost 1. Note from quaton 6 that the numbent s expeted proft n the seond perod u, Q s nluded n the buyer s frst perod proft. n other words, n the frst perod the buyer an apture ex ante the seond perod nformaton rent of the numbent by lowerng the frst perod pre. Ths happens beause a suppler wll aept any pre n the frst perod that generates hm non-negatve expeted profts over two perods the R onstrant. Therefore, antpatng the numbent suppler s seond-perod proft, the buyer an aordngly lower by the same amount the payment offered to a suppler n the frst perod. The more the numbent s expeted seondperod proft, the lower the payment and the hgher the buyer s proft n the frst perod. Suh lowerng of the frst perod payment due to the future proft flow s referred to as the buy-n effet Dhebar and Oren, 1985; Padmanabhan and Bass, 1993; Anton and Yao, 1987; Beker, 196. The numbent s expeted seond perod proft rent, whh s aptured by the buyer va the buy-n effet, s alled the buyer s buy-n proft. 13

14 The buy-n effet an be nterpreted as more aggressve bddng by a suppler n the frst perod, motvated by the future beneft that a wnnng suppler wll obtan. Wth a long-term relatonshp, a suppler seures the seond perod proft f he wns n the frst perod. Wth a short-term relatonshp, wnnng n the frst perod allows the suppler to be favorably dsrmnated aganst entrants n the seond perod beause of the swthng ost. Gven the optmal mehansms, we are now ready to ompare the performane of long-term and short-term relatonshps and dentfy the key fores that drve the dfferene. 5 Relatonshp omparson n order to gan an understandng of the drvng fores, we frst examne the proft dfferene between long-term and short-term relatonshps assumng equal apaty nvestment. Defne π 1, Q. = π,1 1, Q+π, Q as the total proft assoated wth a frst-perod suppler type 1 gven apaty nvestment Q. Then the optmal total proft s π = 1 [max Q π 1, Q]. Lemma 1 haraterzes the dfferene between π s and π l. Lemma 1 π s 1, Q π l 1, Q =, [ J J S Q }{{} Gan from effeny mprovement J S Q }{{} Loss of buy-n profts sq }{{} Swthng ost, Q ] Pr, Q. From Lemma 1, the advantage of a short-term relatonshp over a long-term relatonshp s nfluened by three terms. Frst, a short-term relatonshp benefts the buyer by allowng hm to swth to a new suppler that has a lower ost than the numbent. f the buyer were not to swth n the seond perod, the vrtual ost would be J nstead of J, J > J f >. Ths s the gan from effeny mprovement term. Seond, a short-term relatonshp osts the buyer the swthng ost term. Thrd, by not ommttng to a suppler, the buyer lowers the numbent s expeted profts n the seond perod, whh results n less profts aptured va the buy-n effet term. These three effets jontly determne when a long-term or a short-term relatonshp s more proftable for the buyer. Whle the two relatonshps may result n dfferent apaty nvestments, Lemma 1 reveals the drvng fores that have the frst-order effet on the relatonshp hoe, wthout onsderng the 14

15 dfferene of the apaty nvestment. n the followng, we frst examne the proft dfferene between long-term and short-term relatonshps, fousng on the mpat of the swthng ost and demand unertanty. Then we ompare the apaty nvestment n the two relatonshps. 5.1 Comparson of the proft mpat of swthng ost From Lemma 1, we an see that the profts from the two relatonshps dffer due to the events, Q, n whh ase the buyer swthes to an entrant n the short-term relatonshp. Based on the defnton of, Q n Proposton, t an be easly proved that, Q dereases wth the unt swthng ost s. Proposton 4 haraterzes the mpat of swthng ost on the relatonshp hoe. Proposton 4 When s s small, π s π l and π s π l dereases wth s. There exsts s > 0 suh that π s = π l for s > s and π s π l nreases wth s when s s less than but lose to s. f a suppler s ost follows a unform dstrbuton U, + and there s no demand unertanty, then there exsts ŝ [0, suh that π s π l > 0 for s < ŝ, π s π l < 0 for s ŝ,, and π s π l = 0 for s. When swthng s nexpensve s small, a short-term relatonshp s better than a long-term relatonshp. Ths s beause wth neglgble swthng ost, the hane of swthng s hgh s low. Thus the gan from effeny mprovement term s sgnfant and even hgher than the loss of buy-n profts term. Ths advantage of a short-term relatonshp dereases wth a hgher swthng ost. When swthng s expensve s lose to s, the relatonshp hoe s reversed a long-term relatonshp generates more profts than a short-term relatonshp. Ths s beause the gan from effeny mprovement, after beng offset by the swthng ost, s domnated by the loss of buy-n profts;.e., the net gan from swthng s domnated by the advantage of a long-term relatonshp resultng from supplers more aggressve bddng. When s further nreases, ths advantage of a long-term relatonshp beomes lower beomes the swthng probablty n a short-term relatonshp s smaller. n fat, when the swthng ost s very hgh s > s, a short-term relatonshp redues to a long-term relatonshp beause the buyer wll never swth even wth the opton of swthng open. 15

16 Table 1: Parameter values for numeral experments. onom parameters Demand parameters normal dst. gamma dst. [ ] r 3 d, d [0., 0.8], [0, 1] [0, 5] k 0.5 µ d n 1, n 1, 1, 1, 3, 1, 6, 3, 3, 3, 5 σ d 0.01, 0.1, 0., 1 0.5, 0.7, 0.9, 1.1 [, ] [0.35, 0.65], [0, 1] µ 0.5 σ 0.1, 0.3, 0.5, 0.7, 1 Assumng a unform dstrbuton of a suppler s ost and determnst demand, Proposton 4 further shows that the above ases of relatonshp hoe ompose the entre pattern of desons wth the full range of swthng ost: There exst two rtal values of swthng ost suh that the buyer strtly prefers a short-term to a long-term relatonshp when the swthng ost s less than the lower rtal value, the opposte when the swthng ost s between the two values, and s ndfferent on the relatonshp hoe for swthng osts above the hgher value. Therefore, we onlude that a long-term relatonshp s benefal for the buyer f the swthng ost s beyond a threshold, and the beneft s most sgnfant for moderately hgh swthng osts. We verfy the above nsghts n more general ondtons wth numeral experments. The proft dfferene between the two relatonshps s ompared numerally wth trunated normal ost dstrbutons and trunated normal or gamma demand dstrbutons. The parameter values used n the numeral experments throughout the paper are summarzed n Table 1 1. We fnd that the results of Proposton 4 stll hold n the numeral experments. A representatve numeral result s llustrated n Fgure. Dyer 000 has ponted out that a frm should use arm s length short-term relatonshps for non-strateg nputs. nputs are non-strateg when the outsoured tems are 1 ommodtes or standardzed produts, stand-alone, or modular wth no or few nteraton effets wth other nputs, and 3 haraterzed by a low degree of suppler-buyer nterdependene. We have shown 1 Sne Proposton 4 and the later results are drven by the swthng ost, ost varane and demand varane, we vary these parameters n the experments but keep r, k, µ and µ d fxed. The ost unertanty has to be sgnfant n order for supplers to gan nformaton rent and the omparson of relatonshps not to be trval. Therefore, the value of σ s hosen so that the relatve varablty of osts ranges from very low but stll sgnfant 0. to relatvely hgh. For a normal dstrbuton of the demand, the value of σ d s hosen to over a range of the relatve varablty from beng very low lose to zero to hgh. n order to ensure postve values of ost and demand, the normal dstrbutons for the ost and demand are trunated, and for eah dstrbuton we test two value supports for robustness. For the gamma dstrbuton of demand, σ d s set to realze dfferent shapes of the dstrbuton the shape parameter vares from about 0.8 to 4. For onvenene of omputaton, the gamma dstrbuton s trunated on the upper end but stll overs a great majorty of the mass. 16

17 π s π n = 1 n = 3 n = Swthng ost Fgure : xpeted proft dfferene between short-term and long-term relatonshps π s π l as a funton of swthng ost s. r = 3, k = 0.5, n 1 = 1, n {1, 3, 6}, the demand follows a trunated normal dstrbuton N 0.5, σ d on the support [0., 0.8], and suppler produton osts are drawn from trunated normal dstrbuton N 0.5, 1 on the support [0.35, 0.65]. that a short-term relatonshp s preferable when the swthng ost s small. These two nsghts an be onneted by the fat that the swthng ost tends to be low when the suppler s nput to the buyer s not strateg: t s easer to shft to a new suppler f the produton has a standardzed proess or low nterdependene on other nputs or systems of the buyer mpat of demand unertanty We ompare the senstvty dervatve of the proft dfferene, π s π l, wth respet to the standard devaton of demand σ d. n order not to make the notaton too umbersome, we drop the dependene on σ d n the formulas. We frst analyze how relatonshp hoe hanges when demand unertanty s ntrodued to a ertan market. n ths ase, the two relatonshps result n the same apaty nvestment equal to µ d. Then we numerally examne the mpat of demand unertanty n general stuatons when the apates n the two relatonshps may be dfferent. Lemma haraterzes the dervatve of π s π l wth respet to σ d when σ d s very small. 17

18 Lemma The dervatve of π s π l wth respet to σ d when σ d = 0, an be haraterzed by: d π s π l dσ d [ =, J J J ], µ d Pr, µ d S µ d σ }{{ d } dfferene n seond perod proft f an entrant wns ] [J S µ d F n σ, µ d }{{ d } hange of the buy-n profts due to the hange of the swthng probablty 7 n order to understand n whh dreton demand unertanty drves the relatonshp hoe, we fous on the sgn of d dσ d π s π l when the two relatonshps aheve same profts but wth a postve swthng probablty n the short-term relatonshp. The dervatve beng postve negatve means that an nrease of market unertanty favors the short-term long-term relatonshp. The term of quaton 7 haraterzes the dret mpat of demand unertanty through ts nfluene on the expeted sales, σ d Sµ d. t s the multplaton of two fators. The seond fator σ d Sµ d s negatve;.e., as the market unertanty nreases, the expeted sales derease. The frst fator s the dfferene between the expeted gan from effeny mprovement and the loss of buy-n profts generated by sourng a unt from the wnnng entrant, whh an be nterpreted as the margnal proft advantage of a short-term relatonshp. When the two relatonshps aheve same profts, ths fator s postve beause t exatly overs the swthng ost. Ths means that ompared to a long-term relatonshp, the short-term relatonshp has a hgher margnal proft, and hene has the total proft more senstve to the sales. Gven that the expeted sales derease wth demand unertanty, the term s negatve. The term haraterzes the ndret mpat of demand unertanty through ts nfluene on the swthng probablty n a short-term relatonshp. Wth hgher demand unertanty, the expeted sales are lower. Hene the buyer requres the entrant to be more effent for swthng to happen so that the total gan from swthng overs the swthng ost: σ d < 0. Therefore, wth demand unertanty nreasng, the swthng probablty F n, Q s dereases, generatng more buy-n profts. As a result, term s postve, whh reverses the effet of term. Based on a unform ost dstrbuton, Proposton 5 shows that the effet of term domnates that of term. A long-term relatonshp s thus preferred n a more volatle market. Reall from Proposton 4 that ŝ s the threshold swthng ost at whh π s = π l and the relatonshp hoe s reversed. 18

19 Proposton 5 Wth a suppler s ost followng a unform dstrbuton on [, ], for σ d = 0 and s = ŝ. d dσ d π s π l < 0 Next, we examne numerally the mpat of demand unertanty on relatonshp hoe n more general settngs based on the parameter values n Table 1. n the experments we alulate π s π l over a range of dfferent σ d values whle keepng the expeted demand µ d onstant. As an example, Fgure 3 draws π s π l wth dfferent values of σ d and a varyng swthng ost s. Consstent wth the π s π σ d= Swthng ost Fgure 3: xpeted proft dfferene between short-term and long-term relatonshps π s π l for dfferent levels of demand unertanty σ d. r = 3, k = 0.5, n 1 = 1, n = 3, the demand follows a trunated normal dstrbuton N 0.5, σ d on the support [0, 1], and suppler produton osts are drawn from trunated normal dstrbuton N 0.5, 1 on the support [0.35, 0.65]. nsghts revealed n Proposton 5, the numeral results show that nreasng demand unertanty only shfts the threshold swthng ost at whh the relatonshp hoe s reversed towards the left. Ths ndates that a long-term relatonshp beomes more favorable for the buyer when he faes a more volatle market. 5. Comparson of the apaty: the lok-n effet Comparng π s and π l at σ d = 0 allows us to understand the frst-order effet of the envronment parameters wthout onsderng the dfferene of apaty nvestment n the two relatonshps. When σ d > 0, the two relatonshps generally result n dfferent apaty nvestments n the frst perod. n order to ompare the optmal apaty nvestment, we frst ompare the margnal return of apaty nvestment n these two relatonshps. 19

20 Lemma 3 For any 1, the dervatve of π s Q, 1 π l Q, 1 wth respet to Q s: Q π s Q, 1 π l Q, 1 [ =, J J, Q ] Pr, Q G Q }{{} Gan from effeny mprovement + [ J F n, Q ] G Q }{{} Loss of buy-n profts - [ J S Q Q F n, Q } {{ } v Lok-n + [ Fn, Q ] s }{{} ], Swthng ost - where the sgn of eah term s ndated n the braket followng the name. From Proposton 3, we know that wth a short-term relatonshp, the buyer gans from the effeny mprovement term, but aptures less buy-n profts term and pays the swthng ost term. Lemma 3 shows that the apaty dretly nfluenes the magntudes of these three terms by affetng the volumes: Both the gan from effeny mprovement and the loss of buy-n profts depend on the expeted volume S Q provded by the suppler n the seond perod wth S Q = G Q, and the total swthng ost s proportonal to Q. The apaty also ndretly nfluenes the buyer s proft by affetng the swthng deson n a short-term relatonshp term v: The swthng probablty F n dereases wth the apaty Q. Ths s beause a hgher apaty nreases the ost of swthng, and n turn requres the entrant suppler to be more effent beomes lower when swthng takes plae. We refer to ths lowerng of the swthng probablty resultng from a hgher apaty as the lok-n effet of the apaty n a short-term relatonshp. The lower the swthng probablty, the hgher the numbent s expeted seond-perod proft, and the more buy-n profts obtaned by the buyer. Therefore, the lok-n effet nreases the margnal value of apaty nvestment n a short-term relatonshp. Thus based on Lemma 3, ompared to a long-term relatonshp, a short-term relatonshp may nrease the apaty due to the gan from effeny mprovement term and the lok-n effet term v, whereas t may also derease the apaty due to the loss of buy-n profts term and the ost of swthng term. The overall effet s haraterzed n Proposton 6. Reall from Proposton 4 that s s the threshold swthng ost beyond whh a short-term relatonshp redues to a long-term relatonshp. Proposton 6 For any frst perod suppler ost 1, when s s small, Q S 1 > Q L 1 wth the dfferene dereasng wth s. 0

21 For any frst perod suppler ost 1, when s < s and s s suffently large, Q S 1 > Q L 1 wth the dfferene dereasng wth s. f a suppler s ost follows a unform dstrbuton U [, + ], and the demand unertanty, σ d, s very small, then there exst s L and s H, 0 < s L < s H <, suh that Q s 1 nreases wth s for s [s L, s H ], and dereases wth s for s [0, s L ] [s H, ], and there exsts s s L, suh that Q s 1 > Q l 1 for s s,. Proposton 6 shows that a short-term relatonshp results n more apaty nvestment than a long-term relatonshp not only when the swthng ost s very small but also when t s relatvely large but less than the level above whh a short-term relatonshp redues to a long-term relatonshp. The result for the frst range s ntutve beause that s when the gan from effeny mprovement s sgnfant whle the swthng ost s neglgble. The result for the seond range s somewhat ounter-ntutve beause one would thnk that hgher swthng ost redues the return of apaty nvestment n a short-term relatonshp. Ths result s due to the ndret lok-n effet, whh provdes an nentve to nrease the nvestment. When swthng ost s relatvely large, the apaty has a sgnfant mpat on the swthng probablty, and hene the lok-n effet s promnent. Based on unform ost dstrbutons and small demand unertanty, Proposton 6 further haraterzes the movement of apaty nvestment n a short-term relatonshp over the full range of swthng ost. The optmal apaty nvestment n a short-term relatonshp hanges n three phases: the apaty frst dereases, then nreases, and fnally dereases untl the short-term relatonshp redues to a long-term relatonshp. Note the apaty nvestment n a long-term relatonshp does not hange wth the swthng ost. Thus ths movement also means that the short-term relatonshp ndues a hgher apaty level than the long-term relatonshp for swthng osts relatvely hgh. Agan, numeral experments show that the above nsghts an be extended to more general stuatons. Fgure 4 shows a representatve example. n ths fgure, the apaty dfferene between short-term and long-term relatonshps s drawn as a funton of the swthng ost wth dfferent n left plot and σ d rght plot. The dfferene of apaty nvestment between the two relatonshps n the presene of demand unertanty adds a new element to the mpat of demand unertanty on the proft dfferene, besdes those revealed n Lemma. Hgher apaty mples that the expeted sales are more robust to the hange of demand unertanty. Ths s beause when the apaty s hgher, the expeted sales 1

22 s * * [ Q 1 Q 1 ] 10 x 10-3 s * * [ Q 1 Q 1 ] 10 x 10-3 n = 6 8 n = n = 1 4 σ d = Swthng ost Swthng ost Fgure 4: xpeted apaty dfferene [Q s 1 Q l 1 ] between the short-term and long-term relatonshps as a funton of swthng ost s. r = 3, n 1 = 1, k = 0.5, and suppler produton osts are drawn from trunated normal dstrbuton N 0.5, 1 on the support [0.35, 0.65]. For the left plot, n = {1, 3, 6}, and the demand follows a trunated normal dstrbuton N 0.5, 1 on the support [0., 0.8]. For the rght plot, n = 3 and the demand follows a trunated normal dstrbuton N 0.5, σ d, σ d {0.01, 0.1, 0., 1} on the support [0, 1]. derease slower wth the nrease of demand unertanty. Numeral evaluatons show that when the buyer s ndfferent between long-term and short-term relatonshps, the apaty n a longterm relatonshp s always hgher than n the other. Therefore, the expeted sales n a long-term relatonshp are more robust to demand volatlty than n a short-term relatonshp. Ths, besdes a lower proft margn, further leads the preferene shftng to a long-term relatonshp when demand unertanty s hgher. 6 System effeny We have analyzed the optmal mehansms of long-term and short-term relatonshps wth the objetve of maxmzng the buyer s profts. n ths seton we examne how the buyer s optmal deson nfluenes the proft of the supply han. Ths s done by omparng the buyer s optmal results to the frst-best soluton, whh maxmzes the total expeted proft of the supply han. n a frst-best soluton, the pre s not a onern beause t s a transfer wthn the system. Therefore, we fous on the suppler seleton deson n eah perod and apaty nvestment n the frst perod of both relatonshps. Suppler seleton n the seond perod of a long-term relatonshp s trval. Reall that n the seond perod of a short-term relatonshp, the buyer swthes to the lowestost entrant f and only f the lowest-ost of entrants,, s lower than, Q. s determned based on the vrtual proft see Proposton. n the frst-best soluton, the buyer wll swth to the lowest-ost entrant f and only f the system proft of the suppler han from ontnung wth

23 the numbent s less than that from swthng to the entrant, r S Q < r S Q sq. Ths results n a dfferent threshold level of the entrant s ost, ĉ, Q, as haraterzed n Proposton 7. t an also be shown that, Q ĉ, Q. Thus asymmetr nformaton makes an entrant, rather than the numbent, more favorable n the ompetton see also Laffont and Trole Suh neffent swthng deson benefts the buyer beause t lowers the overall nformaton rent. Proposton 7 n the frst-best soluton of short-term sourng, the buyer swthes to the lowestost entrant f < ĉ, Q where ĉ {, Q. = max s Q SQ },, otherwse stays wth the numbent., Q ĉ, Q. n the frst perod, note that the buyer always selets the lowest-ost suppler even wth nformaton asymmetry. Therefore, suppler seleton n the frst perod s system-effent n the buyer s optmal soluton. However, the stuaton of the apaty nvestment deson s more omplated. nformaton asymmetry leaves rent to the suppler that nreases the buyer s margnal ost of sourng. As a result, the apaty nvestment n a long-term relatonshp s lower ompared to the frst-best soluton. But nformaton asymmetry does not neessarly result n a lower apaty as well n a short-term relatonshp. Ths s beause the lok-n effet drves up the apaty nvestment level n the presene of nformaton asymmetry see Lemma 3. Next we ompare the relatonshp hoe deson. Note that f there s no nformaton asymmetry n the seond perod, then the numbent should expet zero seond-perod proft, and hene the buy-n effet does not exst any more n ether short-term or long-term relatonshps. Therefore, n the frst-best soluton, a long-term relatonshp does not have the advantage of generatng more buy-n profts as n the ase wth nformaton asymmetry see Lemma 1. As a result, a long-term relatonshp s always nferor to a short-term relatonshp. Proposton 8 n the frst-best soluton, a short-term relatonshp s always better than a long-term relatonshp. Proposton 8 an be understood further by notng that f there s no nformaton asymmetry n the seond perod, a long-term relatonshp an be regarded as a onstraned ase of a shortterm relatonshp n whh the swthng probablty s zero. We onlude that the seond perod nformaton asymmetry s a key drver for a long-term relatonshp. 3