Canne Deision-Making Eya Biyaogorsky Graduate Soo of Management University of Caornia Davis, Davis, CA 9566 eyaog@udavis.edu Oded Koenigsberg Coumbia Business Soo Coumbia University, New York, NY 007 ok08@oumbia.edu 008
Canne Deision-Making Abstrat In many industries firms ave to make quantity deisions before knowing te exat state of demand. In su ases, te anne members ave to deide wo wi own te units unti demand unertainty is resoved. Te deision about wo soud retain ownersip depends on te baane of benefit and risk to ea member. Ownersip, after a, is osty. Wiever member owns te units aepts te risk of oss more units are produed tan an be sod. But ownersip aso grants firms te fexibiity to respond to demand, one it beomes known, by adjusting prie. In tis study, we anayze ownersip deisions in distribution annes and ow tose deisions are affeted by demand unertainty. We mode demand based on miro-modeing of onsumer utiity funtions and apture demand unertainty reated to market size and prie sensitivity. Te study demonstrates tree important onusions. First, as ong as te degree of unertainty about market size is intermediate, te retaier and te manufaturer bot benefit wen te manufaturer maintains ownersip of te units. Seond, wen tere is substantia unertainty about market size, te retaier and te anne are better off te retaier retains ownersip but te manufaturer wi sti prefer to maintain ownersip. Tus, tere is potentia for anne onfit under tese onditions. Finay, te pass-troug rate varies wit te degree of unertainty regarding prie sensitivity. Te optima pass-troug rate is ess tan 00% wen tere is itte unertainty regarding prie sensitivity. Te rate inreases wit an inrease in unertainty regarding prie sensitivity and an exeed 00% te unertainty is great enoug. Key words: Cannes of distribution; Demand unertainty; Lead time; Priing; Pass-troug.
. Introdution One of te important tasks faing firms in setting up distribution annes is organizing dferent fows troug te anne to ensure te best possibe performane. Cougan et a. (006 identied eigt generi ativities tat must be onsidered: pysia possession, ownersip, promotion, negotiation, finaning, risk, ordering, and payment. In tis paper we investigate ow te ownersip fow in a anne soud be organized. Ownersip is te power to exerise ontro over an asset (Grossman and Hart 986. In a distribution anne, one of te ownersip deisions is wi member soud own (ontro te inventory arried by te anne te manufaturer or te retaier and under wat onditions. Ownersip matters in a anne wen demand is unertain. Te firm tat owns te units in te anne an adjust its ations in response to new information regarding atua demand by onsumers. For exampe, a manufaturer retains ownersip of te units in te anne and finds tat demand for te produt is iger tan expeted, it an inrease te woesae prie in response. Conversey, a anne member tat does not own te units as imited abiity to respond to new information. If te manufaturer transfers ownersip of te units to te retaier before earning tat demand is iger tan expeted, te manufaturer oses te abiity to inrease its woesae prie in response. Tus, ownersip onveys te abiity to respond to anges in te market (Grossman and Hart 986. Ownersip, owever, is risky, and ene osty. Te owner is iabe for any unsod units, wi an be osty demand turns out to be ow. Tis risk an prompt ea anne member to prefer not to own te units (Caon 00; Netessine and Rudi 00. Tus, it is not ear a priori Anoter aspet of ownersip in a anne is vertia integration weter anne members soud be independent entities. Tis issue as reeived extensive attention in te iterature (see, for exampe, MGuire and Staein (983 and is not deat wit in tis paper. 3
wat sort of ownersip arrangement is in te best interest of te retaier, te manufaturer, and te anne under a partiuar set of onditions. Te iterature on annes as argey ignored te issue of ownersip of te units in a anne. In many ases, anges in ownersip foow anges in te pysia oation of te units, so tere appears to be an impiit assumption tat modes of inventory oation aso expain te ownersip deisions in te anne. Modes of inventory oation address were to pysiay oate te units to generate ogistia and ost effiienies. Te basi idea beind tese modes is tat a ost is inurred in anding inventory (tere are wareousing, sipping, and anding osts and tat te ost varies aording to te eve in te anne tat arries te inventory. Terefore, optimay oating te inventory an redue overa osts in te anne. In a singe-manufaturer mutipe-retaier setting, for exampe, it may be more effiient to poo and oate inventory entray wit te manufaturer (Anupindi and Bassok 999. Ownersip, owever, is oneptuay distint from te pysia oation of te units (Cougan et a. 006. Many internet retaiers use drop-sipping arrangements in wi tey take ownersip of units tat remain pysiay in manufaturer or distributor wareouses and are sipped direty from tose wareouses to te fina onsumers (Wa Street Journa 003; Netessine and Rudi 006. In onsignment arrangements, units tat are stored on te retaier s premises are sti owned by te suppier (Dong, Dresner, and Sankar 005; Rubinstein and Woinsky 987; Vaentini and Zavanea 003; Wang, Jiang, and Sen 00. Tus, inventoryoation modes are not suffiient to understand te optima ownersip arrangements in a anne of distribution. In tis paper we examine a anne faing demand unertainty and determine wi member in te anne te manufaturer or te retaier soud retain ownersip of te units.
Our mode adds to te iterature by exporing te inentives for manufaturers and retaiers to own te units in a anne wen ownersip is not tied to te pysia oation of te units. We deveop a mode in wi a manufaturer ses its produt to a retaier tat ten ses te units to onsumers. Canne members initiay are unertain regarding two dimensions of demand for te produt market size and prie sensitivity and must produe te units before subsequenty reeiving information tat resoves te unertainty. By taking ownersip of te units, a anne member ontros wat is done wit tem wen te demand unertainty is resoved. We mode demand based on miro-modeing of onsumer utiity funtions and inorporate unertainty regarding bot market size and prie sensitivity. Te ost of pysiay anding te units is set at te same amount in ea struture so tat te pysia oation of te units is immateria to te ownersip deisions in te mode. Tis setting enabes us to determine weter and wen te benefit of ownersip, in te form of te abiity to respond to new information regarding demand, outweigs te risk. We find tat te benefit of owning te units outweigs te ost wen te amount of unertainty regarding market size is suffiienty arge. In addition, te benefit of ownersip tends to be greater for te manufaturer tan for te retaier. As a resut, one an distinguis between tree dferent regions based on te amount of demand unertainty: Wen te amount of demand unertainty regarding market size is arge, bot te manufaturer and te retaier prefer to own te units, eading to potentia onfit in te anne. In ontrast, wen te degree of unertainty is ow, bot te manufaturer and te retaier prefer to se a of te units regardess of te reaization of demand unertainty. Consequenty, te benefit from ownersip is sma and it does not make mu dferene wo owns te units in te anne. If te amount of demand unertainty is intermediate, owever, bot te manufaturer and te retaier prefer to ave te 5
manufaturer retain ownersip. Te retaier is wiing to forego ownersip beause te sma benefit it woud obtain does not offset te effet tat te manufaturer inabiity to respond to te new information as on its deisions, and terefore on te retaier s profits. By expiity modeing demand unertainty regarding bot market size and prie sensitivity, we aso sed some igt on ow anne pass-troug is affeted by demand unertainty. We find tat te pass-troug of prie redutions inreases wit te retaier s initia unertainty about ustomers prie sensitivity. If te retaier is ertain about prie sensitivity, te pass-troug is ess tan 00% (regardess of unertainty about market size. Te pass-troug rate inreases as unertainty about prie sensitivity inreases. If tat unertainty is suffiienty arge, te pass-troug rate an surpass 00%. Te remainder of tis paper is organized as foows. In te next setion we desribe te previous iterature and in setion 3 we ay out te mode and our assumptions and present our basi anaysis. We introdue and disuss our resuts in Setion and onude in Setion 5. 6
. Reated Literature Te deision regarding ownersip fow in a anne omes down to te benefit and ost assoiated wit postponing te transfer of ownersip from te manufaturer to te retaier unti after demand unertainty is resoved. Intuitivey, te abiity to wait and make deisions after demand is known soud be vauabe, ene te interest in designing proesses tat aow deision postponement (Van Meigem and Dada 999. Most of te postponement iterature onentrated on produt-design strategies (see, for exampe, Lee and Tang (996 but tere as been some work on te effet of dferent ordering arrangements between retaiers and manufaturers. Ferguson (003 ooked at ow a retaier postponing te ordering deision (witout anging te retai prie, wi was exogenous affets te manufaturer s prodution deision. Caon (00 sowed tat offering advane-purase disounts and aowing te retaier to pae some orders before and some orders after demand is known an ep to oordinate te anne wen demand is unertain. Netessine and Rudi (00, 006 investigated ow demand unertainty affets te use of drop sipping, in wi te manufaturer/woesaer owns and stoks te inventory and sips units direty to ustomers at te retaier s diretion. A ommon teme in tese papers is tat pries are exogenous and ony te prodution deision is onsidered. In ontrast, our fous is on te effet tat te abiity to respond to new information by anging pries ex post (wie prodution deisions must be taken ex ante as on anne members. Wie te iterature generay points to te benefits of te abiity to deay deisions unti demand is known, oter papers point out tat te anges in firms initia deisions in response to te added fexibiity from postponement may not aways be benefiia. Iyer and Padmanaban (000 asked wen a manufaturer soud offer fexibe terms of trade to a retaier tat faes 7
demand unertainty and sowed tat tere are times wen a manufaturer wi offer rigid rater tan fexibe terms. Simiary, Iyer and Bergen (997 found tat manufaturers may not be better off under quik-response anne arrangements and tat rigid rater tan fexibe arrangements may improve quik-response arrangements. In a setting of a singe manufaturer and mutipe ompeting retaiers, Iyer, Narasiman, and Niraj (007 investigated ow improved information affets te manufaturer s preferene regarding were to keep te inventory. Tey found tat, wit more reiabe information, te manufaturer prefers to od te inventory ony te retai market is very ompetitive. Our resuts bear some simiarity to tese works. In our mode, te retaier as ownersip, te manufaturer strategiay anges its priing in su a way tat under some onditions te retaier prefers tat te manufaturer wi retain ownersip. Sting ownersip of units in te anne from te retaier to te manufaturer and vie versa aso sts te risk. Tis is somewat simiar to oter meanisms, inuding return poiies (Mantraa and Raman 999; Marve and Pek 995; Padmanaban and Png 997 and guaranteed profit margins (Mantraa, Basuroy, and Gajanan 005, wi provide for risksaring between retaiers and manufaturers. Su meanisms, owever, provide for risksaring witout sting a partiipant s ontro over te units in te anne. In ontrast, anging ownersip sts bot risk and ontro, and it is te question of wo soud ontro and ave te deision rigts over te units tat is entra to tis study. Te work most osey reated to te urrent study is a paper by Tayor (006. Tayor, studied a setting tat is simiar to our mode. Among te questions e posed was wen a manufaturer soud se to a retaier weter eary or ate in te seing season. He sowed tat te manufaturer aways (weaky prefers to se ate rater tan eary. One an interpret te sae- Tis may be party due to an inrease in manufaturer power as te retai market beomes more ompetitive. Iyer and Vias-Boas (003 sowed in a anne-bargaining mode tat ony a powerfu manufaturer wi vountariy 8
timing deision in Tayor as a deision about wen to transfer ownersip of te units in te anne from te manufaturer to te retaier. Tus, Tayor s resut is equivaent to our part B of proposition in Setion, wi desribes manufaturer preferenes regarding ownersip of units in te anne. Unike Tayor s work, our mode aptures demand unertainty regarding bot market size and prie sensitivity. We ater sow tat te nature of te demand unertainty affets te resuts in important ways. We aso dfer from Tayor in viewing te ownersip deision as a strategi oie for te anne rater tan ony for te manufaturer. Tus, we onsider issues affeting inentives for te retaier wie Tayor s mode inuded a onstraint tat te retaier ad to be no worse off under manufaturer ownersip tan under retaier ownersip. Our mode enabed us to determine weter tere are situations in wi anne members agree tat te retaier soud retain ownersip even inentives to te manufaturer (onsidered in isoation are su tat te manufaturer strity prefers to retain ownersip. Tis expains wen and wy we see ownersip rigts given to retaiers. In addition, we expore ow priing and promotion deisions are affeted by te nature of te demand unertainty and te presene of ead time in te anne. 3. Mode and Anaysis We onsider a biatera anne in wi a risk-neutra manufaturer ses its produt to a risk-neutra retaier tat ten ses it to onsumers. In te beginning, te manufaturer and te retaier ea ave some symmetria and exogenous unertainty about demand. Ten, at a ater point, tey earn true demand for te produt in te market. Prodution deisions must be made before te firms earn te true demand state but priing deisions an be made after. offer a return poiy. 9
Tis setting is typia of industries, su as fasion and toys tat must ommit to a prodution quantity very eary in te panning ye. In te fasion industry, for exampe, ead time between te start of prodution and avaiabiity of tose units for sae an be as ong as tweve monts (Fiser and Raman 996. In tese industries, prodution deisions are typiay made under onditions of more severe unertainty tan are priing deisions, and anging te initia prodution pan at a ater point in time is very osty wen possibe at a (see, for exampe, Caruana and Einav (005, Fiser and Raman (996, Jonson (00, and Seer (993. Given tese onditions, it is natura to ask wi member of te anne, te manufaturer or te retaier, soud ave ownersip of te units produed unti te priing deision must be made. If te manufaturer retains ownersip, it an adjust te woesae prie in response to te owered demand unertainty but aso risks being stuk wit units tat annot be sod or an be sod ony at a deepy disounted prie. Te retaier an aways adjust te retai prie as it earns more about demand. If te retaier takes ownersip of te units, te woesae prie arged by te manufaturer is fixed and te retaier reaps most of te windfa demand turns out be ig, at te ost of getting stuk wit unwanted units demand turns out to be ow. Te sequene of events in te mode is as foows: Under te retaier ownersip senario, te retaier assumes ownersip of te units before te unertainty is resoved (Figure a. Te manufaturer sets a inear per-unit woesae prie wie unertainty remains regarding demand 3 and te retaier deides ow many units to order. Te units are produed and deivered to te 3 We onsider in tis anaysis ony inear per-unit woesae arrangements. Tis is a reasonabe starting point in view of te wide use of su arrangements in pratie (Lariviere and Porteus 00 and beause it is te optima outome expeted of bargaining in annes under unertainty (Iyer and Vias-Boas 003. In addition, understanding firms inentives under inear ontrats is a neessary first step in determining weter more ompex arrangements su as side payments and noninear pries are aed for. 0
retaier. After te firms earn te true demand onditions, te retaier sets te retai prie. Any unsod units are srapped. Under tis senario, te retaier bears te ost of unsod inventory. Under te manufaturer ownersip senario, te manufaturer retains ownersip of te units unti te unertainty is resoved (see Figure b and te retaier paes its order wit te manufaturer ony after earning wat te true demand in te market is. Te manufaturer deides ow many units to produe based on its estimate of ow many units te retaier wi order and wie unertainty about demand remains. After te firms earn te true demand ondition, te manufaturer sets te woesae prie and te retaier paes orders wit te manufaturer and sets te retai prie. Te manufaturer sips te requested units to te retaier and sraps any eftover units. Under tis senario, te manufaturer bears te ost of unsod inventory. As a referene, we aso depit in Figure (see Figure te sequene of events wen tere is no ead time in te anne. In tat ase, prodution takes pae after te demand unertainty as been resoved and bot woesae and retai pries are set after demand is known. Note tat ownersip in tis ase does not matter beause a deisions are made after te unertainty is resoved. Insert Figure Demand Unertainty We mode demand and unertainty in te foowing manner: Let φ be onsumers vauation of te servie provided by te produt. We assume tat φ is distributed unormy in te interva 0, ; tat tere are onsumers in te market, ea independenty drawn from te
distribution of φ; and tat ea onsumer uses at most one produt. From tese assumptions, te quantity demanded as a funtion of prie, p, is p q = Pr φ p = Pr φ p = ( = ( p. / Tus, te market demand funtion q is given by q = ( p, ( were represents market size and represents onsumer prie sensitivity. Tere are two possibe soures of unertainty: ( te firm may be unertain about te exat number of onsumers in te market, ; and/or ( te firm may be unertain about onsumers vauation of te produt, wi in tis ase means unertainty regarding te upper bound of te vauation distribution. Unertainty regarding onsumer vauation is refeted as unertainty regarding te prie sensitivity in te market,. Note tat, in ontrast to te usua inear demand funtion formuation, in equation we keep as a mutipiative term outside te parenteses. Tis is done to avoid onfounding te effets of potentia market size (number of onsumers and prie sensitivity. It is ommon to write te preeding demand funtion in redued form as q = ' p wit ' = and to mode unertainty as an additive inear error term on wie keeping ' fixed. Su an approa onfounds unertainty regarding te number of onsumers and teir vauation of te produt beause keeping ' fixed requires tat must ange in negative orreation to. Tis onfounding auses probems in interpretation of te matematia resuts. To avoid tis, we use te demand formuation in equation. Tese assumptions ead to a inear demand-funtion formuation. We aso onduted an anaysis using an exponentia demand formuation. A of te resuts of te inear ase od for te exponentia ase as we. Detais are avaiabe from te autors upon request.
We assume tat te manufaturer and te retaier are unertain about bot market size and prie sensitivity and apture unertainty for bot as a disrete two-state distribution. We denote parameters reated to te ig-demand state wit a subsript and parameters reated to te owdemand state wit a subsript. Tus, anne members are unertain about te number of potentia onsumers in te market. Market size an be arge ( wit probabiity or sma ( wit probabiity ( were >. Canne members are aso unertain about onsumer prie sensitivity; prie sensitivity an be strong ( wit probabiity or weak ( wit probabiity ( were >. 5 Note tat as te dferenes between te ig demand state and ow demand state inrease, te standard deviation (wi is a measure of unertainty of market size and/or prie sensitivity inreases. Costs Regarding osts, we assume tat tere is a onstant margina ost of prodution, per unit; te retaier s margina ost is zero; te oding ost is zero, 6 and te unsod units are srapped wit no ost or vaue to eiter te manufaturer or te retaier. Anaysis We anayze te two senarios of manufaturer and retaier ownersip as a game between a manufaturer and a retaier were te manufaturer ats as te Stakeberg eader and te retaier as te foower. Te anaysis is straigtforward; te detais are omitted ere and an be found in te appendix. Te equiibrium outomes of te anaysis are given in Tabe. INSERT TABLE 5 See Marve and Pek (995 for a simiar approa for modeing unertainty. 6 A te resuts direty extend to te ase of a positive symmetri oding ost, >0. Detais are avaiabe from te autors upon request. 3
. Resuts.. Wo Soud Own te Units in a Canne? Retaining ownersip of te units in a anne unti unertainty is resoved exposes a firm to te risk of not being abe to se a te units. If te optima sae quantity turns out to be smaer tan te number of avaiabe units by Δ, ten te firm wastes money ( Δ for a manufaturer tat retains ownersip and w Δ for a retaier tat retains ownersip. On te oter and, owning te units provides a firm wit anoter degree of freedom in responding to eventua demand onditions. For exampe, a manufaturer tat owns te units an adjust te woesae prie aording to reveaed demand. If, on te oter and, ownersip is first transferred to te retaier, te manufaturer must fix te woesae prie before demand is reveaed and annot adjust it ater. Te added fexibiity is usefu te firm finds it profitabe not to se a te avaiabe units wen demand is ow. Te firm an ten restrit te quantity sod by setting a iger prie. For exampe, te manufaturer an set a iger woesae prie tat resuts in te retaier ordering (and seing fewer tan te number of units avaiabe in inventory. Tese two fores affet te manufaturer and te retaier dferenty. Te ost of wasting a unit is smaer for te manufaturer tan for te retaier sine < w. Te manufaturer aso ares more about te fexibiity afforded by ownersip sine tat is te ony way te manufaturer an respond to reveaed demand wie te retaier an aways ange te retai prie. Intuitivey, tese dferenes ead to dferent deisions by te manufaturer and te retaier regarding wen and ow mu to restrit saes in te ow-demand state. Terefore, it matters wo owns te units in a anne.
We find tat anne members deisions regarding ownersip of te units in te anne depend on te dferene in market size between te ig-demand and te ow-demand state. Let k = ; ten: ( Proposition : (A Retaier profits are greater under retaier ownersip wen tere is a arge dferene in market size ( < k and under manufaturer ownersip wen tere is an k intermediate dferene in market size ( < < k. Wen te dferene in market size is sma, retaier profits are te same regardess of ownersip ( k <. (B Manufaturer profits are greater under manufaturer ownersip wen te dferene in market size is suffiienty arge ( < ownersip wen te dferene in market size is sma ( k <. k. Manufaturer profits are te same regardess of (C Tota anne profits are greater under retaier ownersip wen te dferene in market size is arge ( < k and under manufaturer ownersip wen tere is an intermediate k dferene in market size ( < < k. Canne profits are te same regardess of ownersip wen te dferene in market size is sma ( k <. INSERT TABLE Severa important impiations derive from proposition. First, it does matter wo owns te units in a anne. Speiay, it matters wen te potentia dferene in market size is arge 5
enoug (see Tabe. For intermediate dferenes in market size, te manufaturer soud retain ownersip of te units. Sine tis arrangement aso benefits te retaier, it is reasonabe to expet tat te manufaturer and retaier an rea an arrangement tat keeps ownersip wit te manufaturer. Wen tere is a arge dferene in market size, te retaier woud ike to ave ownersip of te units. However, in tis ase te manufaturer s interest dfers from te retaier s interest in tat te manufaturer prefers to retain ownersip. Sine tota anne profits are greater under retaier ownersip, tere are potentia arrangements tat woud make everyone better off and et te retaier assume ownersip. Tis may expain ases in wi we observe retaier ownersip in pratie. Of ourse, te fat tat an agreement is possibe does not mean tat te parties wi rea one, and so tere is te potentia for anne onfit under tese onditions. To iustrate te importane of tese resuts, onsider one possibe set of parameters: =0.0, =0.0, = =0.5, and =. In tis ase, expeted market size in te ow-demand state is 78% or ess tan tat of te ig-demand state, it matters wo owns te units in te anne. If te ow-demand market size is even smaer (39% or ess of te ig-demand market size, te manufaturer and te retaier wi ave opposing interests regarding ownersip of te units. Te profit impiations are substantia. For exampe, =00 and =60, te manufaturer s profit is 8% iger under manufaturer ownersip tan under retaier ownersip, but te retaier s profit is 98% iger under retaier ownersip tan under manufaturer ownersip. To understand wat drives tis resut, one must reaize tat it matters wo owns te units in te anne ony te firm tat owns te units finds it optima to restrit saes in a ow-demand 6
ase to ess tan te avaiabe inventory. 7 Obviousy, it is aways optima to se a units in igdemand onditions. If it is aso optima to se a units in ow-demand onditions, ten tere is no waste from not seing a te units and tere is no benefit from te fexibiity to reat to demand onditions wie bearing te ost of unsod units. Wen is ose enoug to ( k <, te dferene in market size is sma enoug tat it is aways optima to se a te units in bot te ow-demand and te ig-demand states (see Tabe. 8 Terefore, it does not matter wo owns te units. Next, onsider wat appens wen te dferene in market size inreases as dereases (oding onstant. Ceary tere omes a point at wi it is no onger optima to se a te units market size turns out to be sma. Te woesae prie dereases faster tan te retai prie wen dereases. Te manufaturer s margina ontribution from seing more units in te ow-demand state beomes negative for vaues of < k. Terefore, te manufaturer wants to restrit saes wen < k. To do tat, te manufaturer must ave ontro over te units in te anne and terefore wants to retain ownersip. As a onsequene, saes in te ig-demand state inrease over te optima quantity and saes in te ow-demand state derease wen te k manufaturer does not od te inventory. It turns out tat, for vaues of < < k, te added ontribution for te retaier in te ig-demand state is arger tan te oss in ontribution from te ow-demand state. Terefore, te retaier is better off (as, obviousy, is te anne under tese onditions wen te manufaturer owns te units. 7 Notie tat te prodution quantity is te same regardess of weter te manufaturer or te retaier owns te units. Terefore, it does not affet te question of ownersip. 8 Assuming optima prodution quantities. 7
Wen te dferene between te demand states is very arge, < k, te manufaturer is sti better off owning te units; owever, te retaier and te anne are better off te retaier owns te units. Wen te manufaturer owns te units, te retaier gives up some potentia ontribution in te ig-demand state (ompared to wen te retaier owns te units beause te manufaturer inreases te woesae prie wen demand is ig. Tis is ompensated by te additiona ontribution te retaier gains in te ow-demand state wen te manufaturer redues te woesae prie. However, wen < k, tis ompensation is not suffiient (tink wat appens, for exampe, wen =0; tere are no saes in te ow-demand state and te retaier gains noting from etting te manufaturer own te units and te retaier is terefore better off owning te units. Te anne is better off wen te retaier owns te units beause te retaier ses more units in te ow-demand state. It is interesting tat te deision weter to own te units depends ony on te unertainty regarding market size and does not depend on unertainty regarding prie sensitivity. Te reason tat unertainty regarding prie sensitivity does not affet te ownersip deision is tat anges in prie sensitivity affet ony te prie tey do not affet te optima sae quantity. Sine ownersip matters ony a firm wants to restrit saes in te ow-demand ondition and prie sensitivity does not impat te optima saes quantity, prie sensitivity does not affet te ownersip deision. Te ritia tresod k =, wi determines wen ownersip ( matters and wen te manufaturer and retaier bot want to own te units, is te ratio of te atua prodution quantity to te number of units te manufaturer woud ike to se ex-post 8
wen market size turns out to be arge. Tus ( k an be tougt of as a measure of te redution in quantity produed beause of demand unertainty on te part of anne members. Te greater te redution in prodution, te fewer units te anne arries and, terefore, te benefit of ownersip is redued and ownersip matters ony at arger potentia dferenes in market size. Not surprisingy, demand unertainty eads to ower prodution te iger te prodution ost (, te iger te onsumers prie sensitivity eves ( and and te iger te probabiity tat onsumers are more prie sensitive. Tus, k inreases wit and dereases wit,, and... Te Effet of Lead Time on Profits As expeted, under unertain demand onditions, te presene of ead time (te situation in Figure a and b redues tota anne profits and te manufaturer profits reative to a anne witout ead time (Figure. In addition, under unertain demand onditions and in te presene of ead time, retaier profit and onsumer surpus are redued ompared to te same situation witout ead time, exept: Proposition : Wen market size is unertain, retaier profit are greater wit ead time tan witout ead time under retaier ownersip ( ( k < < and onsumer surpus are ( (3 ( ( (3 greater wit ead time tan witout ead time under retaier ownersip ( ( k < <. ( (3 ( ( (5 Surprisingy, under spei onditions, te retaier and onsumers an be better off. Te retaier is better off beause te woesae prie is ower wit ead time tan witout it wen te retaier owns te units (see Tabe. Tis ower woesae prie is obviousy benefiia to te 9
retaier. If te preeding ondition ods, tis effet is stronger for te retaier tan te ost of assuming ownersip (beause of exess inventory demand is ow wen faed wit ead time. Consumer surpus is greater beause retaier ownersip generates more saes wen market size is sma. And atoug saes are redued wen te market size is arge, te tota effet is to inrease onsumer surpus under te rigt onditions. Tis ounterintuitive resut undersores te importane of te deision about ownersip of units in te anne. It demonstrates tat, even wit te overa ineffiienies and waste resuting from ead time, onsumers and te retaier may be better off wen ead time is present wen te retaier owns te units. Tis ours beause te manufaturer in tis ase annot respond to atua demand. Terefore, some anne oordination probems are mitigated by unertainty about demand and te fat tat te retaier ontros te units in te anne. Finay, note tat neiter ownersip struture fuy soves te oordination probem in te anne. Canne profits under bot ownersip arrangements are ower tan profits from te integrated anne. Noneteess, ownersip deisions do ave an effet on tota anne profits, wi omes oser to te integrated-anne eve wen ( te retaier owns te units and < k and ( wen te manufaturer owns te units and k < < k. Under manufaturer ownersip te osses due to oordination faiure are 5%. Tese osses are ower under retaier ownersip wen te retaier prefers to own te unit. For instane, for te vaues used in te exampe in setion. ( =0.0, =0.0, = =0.5 and =, under retaier ownersip wen =60, =00, te profit oss is ony 7% ompared to 5% under manufaturer ownersip..3 Priing and Passtroug In tis setion we turn our attention to understanding ow demand unertainty and te separation of prodution and priing deisions affet priing and passtroug in te anne. Te woesae and retai pries in our mode an ange in response to atua demand onditions. 0
One way to tink about tese prie anges is in te spirit of Gerstner and Hess (99 as te stati anaog of a dynami mode of promotions. 9 Tus, te ange in retai and woesae pries between demand states an be interpreted as te offering of onsumer and trade promotions, respetivey. We find tat: Proposition 3: Retai and woesae prie disounts are deeper in a anne wit ead time tan in a anne witout ead time. Te presene of ead time as two effets on priing deisions: ( beause te quantity produed is smaer tan te desired sae quantity wen demand is strong, te prie wen demand is strong is iger under ead time tan under no ead time; and ( te prodution ost is sunk wen te firm makes te priing deision. Terefore, te saes quantity wen demand is weak is iger and te orresponding prie is ower wit ead time tan witout ead time. Obviousy, te dferene in prie between situations of strong and weak demand is arger wit ead time tan witout ead time. We now turn our attention to understanding ow te passtroug rate is affeted by te nature of te demand unertainty faing te anne. We find tat: Proposition : (A In te absene of unertainty regarding prie sensitivity (i.e., wen te anne faes ony market-size unertainty, te passtroug is ess tan 00%. (B Wen tere is unertainty regarding prie sensitivity, te passtroug rate inreases as te potentia dferene in prie sensitivity inreases, and, for suffiienty arge dferenes in prie sensitivity, te passtroug rate is iger tan 00%. Tis resut sows tat te passtroug rate depends on ow mu prie sensitivity in te market an ange. Te more tat prie sensitivity an ange, te iger te resuting passtroug rate and, importanty, tis an ead to passtroug rates tat exeed 00%. To understand tis resut, onsider te effet tat market-size and prie-sensitivity unertainties ave on te demand funtions. If prie sensitivity is known, unertainty regarding 9 One su mode is of perisabe produts wit iid demand over periods.
market size eads to te demand funtion being steeper (rotated ounterokwise in te owdemand state tan in te ig-demand state (see Figure, top pane. As a resut, for te same number of units to be sod, te woesae prie must ange more tan te retai prie and passtroug is ess tan 00%. In ontrast, market size is known, unertainty regarding prie sensitivity eads to te demand funtion being ess steep (rotated okwise in te ow-demand state tan in te ig-demand state (see Figure, bottom pane. In tat ase, for te same number of units to be sod, te woesae prie must ange ess tan te retai prie and passtroug is greater tan 00%. Te passtroug rate wen tere is unertainty regarding bot market size and prie sensitivity is a ombination of tese two effets. As te potentia dferene in prie sensitivity inreases, te prie-sensitivity effet beomes more dominant and te passtroug rate inreases unti at a ertain point it passes 00%. Insert Figure 5. Conusion One of te deisions faed in organizing a anne of distribution is assignment of ownersip of te inventory of units in te anne. Previous resear on tis question onentrated on ost and effiieny onsiderations reated to te pysia oation of te inventory in te anne. We instead fous on te deision rigts tat ownersip provides and suggest tat te assignment of tese deision rigts is anoter important aspet tat firms soud onsider wen determining ownersip. Te deision rigts onferred by ownersip an benefit a firm beause it provides fexibiity in ow te firm an respond to anges in market onditions. We sow tat tis fexibiity is indeed vauabe and may ead firms to seek ownersip wen te benefits of su fexibiity exeed te potentia osts of ownersip.
We onsider te situation of a monopoisti anne onsisting of a manufaturer and a retaier tat are unertain a priori about demand onditions in te market. Wen tere is a arge degree of unertainty regarding market size (te potentia dferene in market size is arge, we find tat te manufaturer and te retaier ea prefer to own te units in te anne, wi an ead to onfit. Wen te degree of unertainty is intermediate bot members of te anne prefer to ave te manufaturer own te units. Furter, wen te dferene is sma or te unertainty is ony regarding prie sensitivity, it does not matter wo owns te units. We aso find tat unertainty affets te passtroug rate in te anne. Te passtroug rate is beow 00% wen firms know te onsumers prie sensitivity. Te rate inreases wit te eve of unertainty regarding prie sensitivity and an even exeed 00% te degree of unertainty regarding prie sensitivity is ig. Tese findings ave important manageria and teoretia impiations. Tey point to te importane of te deision about wo wi own te units in te anne. Tey tus provide anoter important expanation for wy we observe dferent arrangements regarding ownersip of units in annes and under wat onditions tose arrangements soud be used. Our mode demonstrates tat ownersip, wie potentiay osty, aso onfers vauabe added fexibiity in deision-making. Indeed, we find tat te manufaturer prefer to retain ownersip even toug it is osty and tat, under some onditions, te retaier wants to ave ownersip as we. Tese resuts suggest tat strategi onsiderations are important in addition to any ost and/or effiieny onsiderations in deiding wo soud own te units in a anne 0. If te manufaturer s and retaier s osts do not dfer greaty, strategi onsiderations may dominate and te manufaturer (at east may be better off it maintains ownersip. 0 Obviousy, in ase of asymmetri osts (inventory oding osts and savage vaue te firm tat is more effiient as iger inentives to maintain ownersip. 3
Our mode resuts aso provide anoter expanation for te empiria penomenon of passtroug rates tat range from ess tan 00% to mu greater tan 00%. Empiria resear on passtroug rates as reported vaues ranging from 0% to more tan 00% (Cevaier and Curan 976; Waters 989; Armstrong 99. Previous studies expained te arge range of observabe pass-troug rates and, in partiuar, te ess intuitive vaues of rates greater tan 00% as resuting from dferent demand-funtion sapes for dferent produts (Buow and Pfeiderer 983; Battberg and Nesin 990; Tyagi 999. We provide a ompementary expanation by sowing tat te amount of unertainty regarding onsumer prie sensitivity affets te passtroug rate and tat a arge amount of unertainty an resut in passtroug rates tat exeed 00%. Te basi tension in our mode is between te benefit ownersip onfers troug greater fexibiity in deision-making and te potentia ost of ownersip in te form of overstoks and inventory risks. Tus, our mode is suited for situations in wi diret variabe osts are substantia, making te potentia ost of ownersip arge. Tis is true for produts su as ars, durabe onsumer goods, otes, and toys. On te oter and, te mode does not effetivey apture situations in wi diret variabe osts are reativey sma or even nonexistent, as is te ase for woy digita produts. In tose situations, te ost of overstok is very ow and, terefore, issues assoiated wit making te prodution deision before demand is known are not as important. We assume in te mode tat tere is ony one prodution run tat takes pae before te firms earn about demand. Tis orresponds we to situations in wi repenisment orders annot be fufied during te seing season (see, for exampe, Fiser et a. (99 and Moon (00 but it is eary a simpiation of situations in wi firms an pae repenisment Nesin, Powe, and Stone (995 aso expained rates greater tan 00% using a oss eader argument.
orders. Te abiity to ave an additiona prodution run in response to atua demand may affet ownersip oies as we as oter deisions, su as te initia quantity ordered by te retaier. Mutipe prodution runs aso may ead to situations in wi te manufaturer and te retaier simutaneousy own some of te units. For exampe, te manufaturer may, in su situations, try to imit te number of units te retaier an order before te unertainty is resoved. In tis paper, we oneptuaize ownersip of te units in te anne as a simpe eiter/or onstrut. Our mode uses te ommon assumption tat firms are risk-neutra (or at east tat tey soud be risk-neutra. It is interesting to onsider ow dferent risk attitudes migt affet te resuts. Ex ante, for te manufaturer (retaier, te dferene in profit between te two demand states varies more wen te manufaturer (retaier owns te units. Tus, risk-averseness tends to redue te expeted benefit of ownersip. As a onsequene, one woud not expet tere to be a region of indferene regarding ownersip firms are risk-averse. Instead, in tat ase, bot firms wi prefer not to own te units. In addition, it wi require greater benefit from ownersip for firms to prefer to own te units. Tus te regions in wi te manufaturer and retaier bot want to own te units wi be at iger eves of unertainty in te risk-averse ase tan in te risk-neutra ase (te ritia tresod k wi be ower. A fu anaysis of te effet of risk attitude is beyond te sope of te paper; noneteess, it appears tat risk-averseness, wie weakening te resuts somewat, does not affet te overa struture of te findings. A natura foow-up question is weter te manufaturer or te retaier wi atuay retain ownersip of te units in te anne, espeiay in ases were teir interests dfer. 3 Sine te anne s profits are greater under retaier ownersip wen bot te retaier and te manufaturer want to retain ownersip, te effiieny riterion suggests tat te retaier wi assume Te effets for a risk-seeking firm are te opposite of tose for te risk-averse firm. 5
ownersip. Indeed, one aows side payments between te retaier and te manufaturer, it is easy to onstrut an arrangement tat makes everyone better off under retaier ownersip, tus guaranteeing it. Atoug te effiieny riterion is appeaing in teory, in pratie it may not be so easy to rea su arrangements. For exampe, it is we known in te iterature addressing te doube marginaization anne-oordination probem tat two-part tarfs an oordinate te anne (Moorty 987 but su arrangements are not ommony observed in pratie (exept in franising; see Desai and Srinivasan (996. Tus, it is not ear wi anne member wi atuay retain ownersip wen te retaier and manufaturer inentives dfer. It appears tat te ownersip question presents anoter oordination issue for anne members. Tese issues, as we as oter questions reating to te effet of ompetition and risksaring arrangements (su as return poiies on ownersip deisions, require additiona foowup resear. Tis paper provides te beginnings of an understanding of te impiations of ownersip for te anne and of te effets of te presene of ead time and demand unertainty on deision-making by anne members. 3 Our mode obviousy does not direty address tis question sine we do not mode te deision witin te anne regarding ownersip, ony te inentives of te anne members to retain ownersip. 6
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30 ( ( < ( ( 3 ( 3 ( ( < ( ( > ( 3 ( 3 3 3 ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( 3 3 3 3 ( ( ( ( Tabe : Equiibrium Outomes Retaier Ownersip Manufaturer Ownersip Indferene No Lead Time Prie (arge market size Prie (sma market size Woesae prie (arge market size Woesae prie (sma market size NR Saes (arge market size ( ( ( ( ( Saes (sma market size ( ( (
3 i i i 3 ( 8 ( i i i ( i i i 6 ( Prodution (ordering quantity ( ( ( ( ( Retaier profit R Π R Π ( ( 6 ( Manufaturer profit ( 8 ( ( M Π ( ( 8 ( Consumer surpus CS CS ( ( 3 ( Were, ( 6 ( ( ( ( R = Π, ( 3 ( ( 5 ( ( ( CS =, ( 6 ( ( ( ( R = Π, ( 8 ( ( ( ( M = Π and ( 3 ( ( ( ( CS =.
Tabe : Ownersip Struture Preferenes < k k < < k k < Manufaturer s preferene Manufaturer ownersip Manufaturer ownersip Retaier s preferene Retaier ownersip Manufaturer ownersip Tota anne profit Retaier ownersip Manufaturer is greater under ownersip Indferent Indferent Indferent 3
Figure a: Retaier Ownersip Retaier orders produt Retaier sets retai prie Retaier sraps unsod units t Manufaturer sets woesae prie Figure b: Manufaturer Ownersip Retaier orders produts and sets retai prie t Manufaturer produes units Manufaturer sets woesae prie Manufaturer sraps unsod units Figure : No Lead Time Case Retaier orders produts and sets retai prie t Manufaturer produes units & sets unit prie Unertainty resoved 33
P,w Figure : Pass-troug and Demand Unertainty Retaier Reation Curve Δ P Δ w Consumer Demand P,w * q q Δ P Retaier Reation Curve Δ w Consumer Demand * q q 3