Lead Time, Unertainty, and Canne Deision-Making Eya Biyaogorsky Graduate Soo of Management University of Caifornia at Davis, Davis, CA 9566 eyaog@udavis.edu Oded Koenigsberg Coumbia Business Soo Coumbia University, New York, NY 007 ok08@oumbia.edu Apri 006
Lead Time, Unertainty, and Canne Deision-Making Abstrat Prodution ead time fores ompanies to make prodution deisions before te reaization of demand. Tese deisions tereafter onstrain te firms reations to anges in demand. Canne members deisions depend on te initia prodution deisions made by manufaturers and on stoking deisions by retaiers. In tis study, we anayzed ow prodution ead time affets deisions in a anne of distribution faing unertain demand. Our demand formuation is derived from miro-modeing of onsumer utiity funtions and aptures demand unertainty regarding two parameters, market size and prie sensitivity. We onsidered wi anne member, te retaier or te manufaturer, soud keep ownersip of te units in te anne and ow ead time affets pries in te anne. We find tat, in most ases, te anne, te retaier, and te manufaturer a benefit wen te manufaturer maintains ownersip over te units in te anne. However, wen tere is unertainty about market size and te differene between te possibe demand states is arge, te anne and te retaier are better off if te retaier retains ownersip of te units but te manufaturer wi sti prefer to maintain ownersip. Tus, tere is potentia for anne onfit erupting under tese onditions. In addition, we find tat te pass-troug rate varies wit te type of demand unertainty. Te pass-troug is greater tan 00% wen tere is priesensitivity unertainty and ess tan 00% wen tere is market-size unertainty. Key words: Cannes of distribution; Demand unertainty; Lead time; Priing; Passtroug.
. Introdution In a perfet word, everyone woud ave a repiator one of tose amazing gadgets depited in te Star Trek teevision sows and movies tat an instanty produe any item you want, just in time and to your exat speifiations. In our word, it takes time to manufature produts, move tem troug te suppy ain, and deiver tem to ustomers. Many industries operate suppy ains tat invove ong ead times. Fiser and Raman 996 reported tat te time between ordering and sipment of fasion merandise an be as ong as monts; in te toy industry te gap between ordering and deivery an be as ong as 8 monts. One resut of ong ead times is tat anne members manufaturers, retaiers, woesaers, distributors must make prodution and possiby ordering deisions ong before tey know te atua demand for a produt. One made, tese deisions onstrain te range of strategi and tatia reations avaiabe to partiipants as tey respond to anges in demand. For exampe, retai priing and promotion deisions an be made oser to te time a produt appears in te market, but su deisions are onstrained by te quantities aready ordered and produed and te inventories aready in pae. In a distribution anne, te need to make prodution deisions before unertainty is resoved raises te issue of wi anne member, te retaier or te manufaturer, soud retain ownersip of te units in te anne unti te demand unertainty is resoved. Grossman and Hart 986 ave sown tat ownersip an be benefiia beause it onfers to te owner te residua rigt to respond to anges in te As reported by a number of industry soures, for exampe Te Toy and Game Inventor s Handbook Levy and Weigartner 003, and te Industry Insigts FAQ at ttp://www.toysngames.om/inventors/insigt4.tm, We onsider ony made-to-stok systems in tis paper. Made-to-order systems fae a different set of issues. 3
market. A manufaturer an ange woesae pries in response to demand onditions as ong as it owns te goods, but one tite to te units is transferred to te retaier, te manufaturer an no onger ange te woesae prie. However, ownersip is potentiay osty if demand turns out to be ow. Te owner weter te manufaturer or te retaier may end up stuk wit units tat annot be sod. Tis risk may ause ea anne member to prefer tat te oter member take ownersip of te units Caon 004; Netessine and Rudi 004. Tus, it is not ear a priori wat sort of ownersip arrangement is in te best interest of te retaier, te manufaturer, and te anne and under wat onditions. Different ownersip arrangements and strutures are ommon in pratie and te potentia osts and benefits of ownersip are substantia. Here are some exampes: L.L. Bean, a diret ataog retaier, takes ownersip of its merandise fairy eary and makes fina, firm ommitments to its vendors weeks before a ataog reaes onsumers. Tese ommitments reate infexibiity tat osts te retaier $0 miion annuay due to stokouts or iquidations Siefer 993. Wa-Mart attempts to minimize te amount of time it atuay owns merandise, sometimes to as itte time as is required to eetroniay san a bar ode at ekout Cement 995. For produts su as furniture and speiaty emias, it is ommon for retaiers to operate witout any inventory at a. Retaiers essentiay operate as ataogs and order-takers wie te manufaturer maintains ownersip and keeps inventories in a entra wareouse and sips produts direty to ustomers upon order reeipt Kande 996. 4
Jonson 00 reported tat in te toy industry tere is a trend of sifting ownersip of units in te anne from retaiers to manufaturers. Appe Computer, in te span of itte more tan a year, faed bot sortages of its popuar ipod Mini payers Gibson 004 and overstoks of its new ipod Suffe payer CNNMoney 005. In response to te ipod Mini sortages, Appe inreased European pries for te ipod Mini before auning tem tere in Juy 004, prompting onsumer ompaints about te differene in pries between Europe and te U.S. Wen Toyota Motor Corp. faed suppy sortages of te Prius in te U.S. in ate 004, it raised te Prius prie by $580 Boomberg.om 004. As tese exampes eary demonstrate, ownersip an be a doube-edged sword. Firms need to understand te strategi impiations of ownersip in terms of bot potentia osts e.g., L.L. Bean s $0 miion oss and potentia benefits e.g., te abiity of Appe Computer and Toyota to raise pries in response to demand onditions. Interestingy, tese strategi onsiderations beome more prominent wit te emergene of more fexibe ontrating arrangements between anne members tat separate ownersip of te units from te atua pysia oation of te units in te anne. Many internet retaiers use drop-sipping, wereby te retaier takes ownersip but not pysia possession and units are sipped direty from te manufaturer to te fina onsumer Wa Street Journa 003; Netessine and Rudi 003. Vaentini and Zavanea 003 desribed a onsignment stok arrangement in wi a suppier keeps an agreed-upon number of units at te ustomer s wareouse. Te ustomer an draw from tat inventory aording to pries set by te suppier wi an be anged on a daiy basis. Tus, even toug te units are stored on te ustomer s premises, 5
tey are sti owned by te suppier. Su onsignment-ike arrangements Rubinstein and Woinsky 987; Wang, Jiang, and Sen 004, as we as ertain forms of vendormanaged inventory VMI arrangements Yang, Ruben, and Webster 003, make it mu easier to sift ownersip of te units between members of a anne. Te main purpose of tis paper is to examine ownersip issues in te ontext of a simpe manufaturer-retaier anne wen demand is unertain. Speifiay, we fous on wo soud retain ownersip of te units in te anne te manufaturer or te retaier. We deveop a singe-period mode in wi a manufaturer ses its produts to a retaier tat ten ses tem to onsumers. Our demand formuation is derived from miro-modeing of onsumer utiity funtions and aptures demand unertainty regarding market size and prie sensitivity. We find tat te manufaturer aways prefers to retain ownersip, but tat te retaier under some onditions prefer te manufaturer to retain ownersip, and under oter onditions prefer to assume ownersip imsef. Te inentives for retaining ownersip depend on te nature of te demand unertainty i.e., market size or prie sensitivity and on te amount of demand unertainty faed by te anne. Wen tere is unertainty regarding market size and te possibe differene in size is arge, te manufaturer and te retaier wi disagree about wo soud ave ownersip rigts, potentiay eading to onfit in te anne. In addition, we find tat ownersip as important impiations for firms priing deisions and for onsumer surpus and soia wefare. Reated Literature Te iterature on firm beavior under demand unertainty distinguises four possibe modes of beavior tat depend on weter deisions are made before or after unertainty about demand is resoved Leand 973: A deisions are made ex 6
post after demand is known. Quantity is set ex ante before demand is known and prie is set ex post. 3 Prie is set ex ante and quantity is set ex post. 4 Bot prie and quantity are set ex ante. Unti reenty, te iterature on annes under unertainty foused on modes and 4. Tus, Gerstner and Hess 99, 995 assumed tat bot prie and quantity an be adjusted in investigating ow a anne of distribution soud use pus and pu promotions wen demand turns out to be unexpetedy ow. On te oter and, te iterature on optima prodution/inventory-repenisment pans under unertainty ommony assumes tat a deisions must be made before observing atua demand onditions Lariviere and Porteus 00. We, on te oter and, onsider te ase wen quantity is set ex ante and prie ex post mode, wi is a reasonabe desription of deision-making in annes wit reativey ong prodution ead times. Note tat te differene between tis ase and te iterature ited previousy is not just tat some deisions are made before demand is known and some after; in addition, te optimization probem is no onger a simutaneous deision on bot prie and quantity. Many industries are araterized as aving ong prodution ead times and aompanying unertainty about demand onditions. Tese inude ars, onsumer eetronis, and seasona produts ike oting and toys, Fiser and Raman 996. Even sopistiated demand foreasting systems many times annot mitigate te probems tese onditions ause. For exampe, Sport Obermeyer, a produer of ski appare tat is igy touted for its innovative use of demand foreasting, sti as to produe 50% of its merandise eary in te season before demand is known Fiser et a. 994. Intuitivey under su onditions, te abiity to wait and make deisions after demand is known soud be vauabe, ene te interest in designing proesses tat 7
aow deision postponement Van Meigem and Dada 999. Most of tat resear onentrated on produt-design strategies see, for exampe, Lee and Tang 996, but tere as been some work on te effet of different ordering arrangements between a retaier and a manufaturer. Ferguson 003 ooked at ow a retaier s postponing te ordering deision witout anging te retai prie, wi is exogenous affets te manufaturer s prodution deision. Caon 004 sowed tat offering advanepurase disounts and aowing te retaier to pae some orders before and some orders after demand is known an ep in oordinating te anne wen demand is unertain. Netessine and Rudi 003, 004 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 ange pries ex post wie prodution deisions must be taken ex ante as on anne members. Te postponement iterature points to te benefits of te abiity to deay deisions unti demand is known, but tere are indiations tat in some ases tese benefits may not be suffiient to justify deaying te deisions. Iyer and Padmanaban 000 asked wen a manufaturer soud offer fexibe terms of trade to a retaier faing demand unertainty and sowed tat tere are times wen a manufaturer wi offer rigid rater tan fexibe terms. In a setting of a singe manufaturer and mutipe ompeting retaiers, Iyer, Narasiman, and Niraj 003 investigated ow improved information affets te manufaturer s preferene regarding were to keep te 8
inventory. Tey found tat, wit more reiabe information, te manufaturer prefers to od te inventory ony if te retai market is very ompetitive. 3 Te work most osey reated to te urrent study is a working paper by Tayor 005. Tayor, independent of us, studied a setting tat is simiar to our mode. Among te questions posed by Tayor was wen soud a manufaturer se to a retaier 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-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 C of Proposition in Setion 4, 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 differ from Tayor in viewing te ownersip deision as a strategi oie for te anne rater tan just for te manufaturer. Tus, we onsider issues affeting inentives for te retaier wie Tayor s mode inudes a onstraint tat te retaier as to be no worse off under manufaturer ownersip tan under retaier ownersip. Tis enabes us to sow tat tere are situations in wi anne members an agree tat te retaier soud retain ownersip even if te 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 te presene of ead time affets priing and promotion deisions and ow te nature of te demand unertainty affets tese issues. 3 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 9
Sifting ownersip of units in te anne from te retaier to te manufaturer and vie versa aso means sifting te risk from one to anoter. Tis bears some simiarity to meanisms su as return poiies Mantraa and Raman 999; Marve and Pek 995; Padmanaban and Png 997 and guaranteed profit margins Mantraa, Basuroy, and Gajanan 005 tat provide risk-saring between retaiers and manufaturers. Tese meanisms, owever, provide for risk-saring witout sifting a partiipant s rigt to make deisions about te units in te anne. In ontrast, anging ownersip sifts bot risks and deision rigts, and it is te question of wo soud od tose deision rigts tat is entra to tis study.. Mode We onsider a biatera anne in wi a risk-neutra manufaturer ses its produt to a risk-neutra retaier tat ses to onsumers. In order to ave te units ready and on store seves in time, te firms must make many deisions we in advane of te seing time. In partiuar, firms in many industries must ommit to te prodution quantity very eary in te panning ye. For exampe te ead-time between te start of unit prodution and avaiabiity of tose units for sae reaes as mu as 8 monts in te toy industry Ekert 00, and monts in te fasion industry Fiser and Raman 996. Oter deisions, ike priing, an be made mu oser to te seing season or during te seing season. 4 Canne members are unertain about demand onditions. Tey take steps ike market resear by wi tey try to earn about te true demand onditions. As a resut, te amount of unertainty tey ave about demand is redued over time. Tus, manufaturer wi vountariy offer a return poiy. 4 Even in te ase of diret ataog retaiers ike L.L. Bean, priing deisions are finaized mu oser to te sipping of ataogs tan are prodution deisions. 0
te firms ave ess unertainty wen making te priing deisions tan wen making te prodution deisions. Te earier prodution deisions must be made, te more unertain firms wi be about demand. Tis is beause of te potentia for anges in eonomi onditions and onsumer tastes and beause onsumers are notoriousy bad at prediting teir future beavior Morwitz 997. Given tese onditions, it is natura to ask wo in te anne, te manufaturer or te retaier, soud ave ownersip over te units produed unti te priing deisions ave to be made. If te manufaturer retains ownersip, it an adjust te woesae prie in response to te ower demand unertainty but aso risks being stuk wit units tat annot be sod or an be sod ony at deepy disounted pries. Te retaier an aways adjust te retai prie as it earns more about demand. If te retaier takes ownersip over te units, tat oks in te woesae prie arged by te manufaturer and te retaier reaps most of te windfa if demand turns out be ig, at te ost of getting stuk wit unwanted units if demand turns out to be ow. To apture tis situation and te fores invoved, we used a simpe mode in wi tere are two states of firms knowedge about demand: In te beginning, te manufaturer and retaier ea ave some symmetria and exogenous unertainty about demand. Ten, at a ater point, tey earn te true demand in te market. Prodution deisions must be made before te firms earn te true demand state. Priing deisions an be made after te firms earn about demand. Te assumption tat tere are ony two possibe states of knowedge about demand is eary a simpifiation of te rea-word proess in wi partiipants knowedge of demand deveops over time, aowing tem to adjust prodution and marketing aordingy. However, tis mode aptures te primary aspets operating in
tis situation: prodution deisions are made under onditions of more severe unertainty tan are priing deisions, and at a ertain point, te anne must ommit to a prodution pan. Canging te 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 Seifer 993. We furter assume tat tere is a onstant margina ost of prodution, per unit, and tat te retaier s margina osts are zero. Unit-oding osts are zero 5 and unsod units are srapped wit no ost or vaue to eiter te manufaturer or te retaier. We distinguis between two possibe ases. In te first ase Figure A, te retaier takes deivery of ordered units wen demand is sti unknown and assumes ownersip upon deivery. 6 Te time ine in tis ase is as foows: Te manufaturer sets te woesae prie wie tere is sti unertainty regarding demand, and te retaier orders produts. Te units are produed and deivered to te 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. In te seond ase, te retaier paes orders wit te manufaturer ony after earning wat te true demand in te market is. However, te ead time needed for prodution fores te manufaturer to produe units in antiipation of retai orders and atua prodution takes pae wie tere is sti unertainty about demand. In tis ase, te time ine is as foows see Figure B: Te manufaturer deides ow many units to produe. After te firms earn te true demand onditions, te manufaturer sets te woesae prie and te retaier paes orders wit te manufaturer and sets te retai 5 A te resuts direty extend to te ase of a positive symmetri oding ost, >0. Detais are avaiabe from te autors upon request. 6 Deivery and ownersip transfer do not ave to appen at te same time. Te ritia assumption ere is tat ownersip is transferred to te retaier before demand is known.
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. Insert Figure Demand Unertainty We mode demand and demand unertainty in te foowing manner: Let φ be onsumers vauation of te servie provided by te produt. We assume tat φ is distributed uniformy 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. 7 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 onsumers 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,. 7 Tese assumptions ead to a inear demand funtion formuation. We aso onduted an anaysis using an exponentia demand formuation. A te resuts of te inear ase od for te exponentia ase as we. Detais are avaiabe from te autors upon request. 3
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. We mode unertainty in demand as a disrete two-state distribution. Demand an be eiter ig wit probabiity or ow wit probabiity were is known. We denote parameters reated to te ig-demand state wit a subsript and parameters reated to te ow-demand state wit a subsript. In one ase, we assume tat anne members are unertain about onsumers prie sensitivity and know for ertain te market size. Prie sensitivity an be strong or weak wit >. In a seond ase, we assume tat anne members are unertain about te number of potentia onsumers in te market but know for ertain teir prie sensitivity. Market size an be arge or sma wit >. 8 Te tird ase we onsider is wen firms ave substantia unertainty regarding bot market size and prie sensitivity. 8 See Marve and Pek 995 for a simiar approa for modeing unertainty. 4
3. Anaysis In tis setion, we anayze a game between a manufaturer and a retaier in a distribution anne were te manufaturer ats as te Stakeberg eader and te retaier as te foower. 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 sine 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 figuring out weter more ompex arrangements su as side payments and noninear pries are aed for. Witin tis anne struture, we examine two senarios one in wi te retaier owns te units and bears te ost of unsod inventory and a seond in wi te manufaturer owns te units. In a ases we appy te proper parameter restritions to ensure tat demand is strity positive and bot te retaier and te manufaturer ave non-negative expeted profits. 3. Market-Size Unertainty In tis setion, we anayze te ase were anne members do not know te exat market size,. Wit probabiity, demand is ig ; wit probabiity, demand is ow. Te prie sensitivity,, is known and fixed. Tabe reports te equiibrium outomes for te tree possibe regimes: te retaier owns te units and <, te manufaturer owns te units and, and eiter te manufaturer or te retaier owns te units and 5
>. Tabe aso sows as a benmark te outomes wen te anne does not fae ead time. We next desribe ow te equiibrium outomes were derived. 3.. Retaier Owns te Units Wen te retaier assumes ownersip of te units Figure A, te manufaturer determines te woesae prie based on urrenty avaiabe unertain information regarding demand onditions. Te retaier orders units from te manufaturer based on te same demand information and te quoted woesae prie. After demand is reveaed, te retaier sets te retai prie. To find te subgame perfet equiibrium, we sove tis game bakward and start wit te retai prie deision. At tat point, te retaier aready knows te exat market size i i=, and tus faes te foowing demand funtion: q = i p. Remember tat te retaier ods units tat it aready ordered and annot reeive any additiona units in time beause of prodution ead time. Obviousy, te retaier annot se more tan te Q units it aready ods. Terefore, te retaier s maximization probem is Max p i s. t. p q, p, i q, p Q. i i i i 3 Tere are two possibiities; te optima prie may impy eiter tat te onstraint in Equation 3 is binding and a Q units are sod or tat te onstraint is not binding and ony some of te units are sod and te rest are srapped rea tat we assumed tat srapping is ostess. We sow in te Appendix tat te soution for tis optimization probem eads to two possibe ases. First, if is suffiienty arge, te optima retai 6
prie is set at a eve su tat a units are sod regardess of te demand ondition. Oterwise, te optima prie is set at a eve su tat a units are sod if demand is ig but ony some of te units are sod if demand is ow. Te equiibrium outomes are given in Tabe and te derivation of te soutions an be found in te Appendix. Here, for te sake of brevity, we desribe fuy ony te atter ase in wi te retaier s poiy is to se a units wen demand is ig but ony some wen demand is ow. In tis ase, te retaier s optima priing deision is given by: p i Q if i =, = i =. 4 Next, we onsider te retaier s ordering deision. Te retaier makes te ordering deision before knowing te exat demand state. Terefore, te retaier determines te order quantity, Q, tat soves te foowing optimization probem: Max Q E ] = wq π π, 5 [ R H L were π L π H is te profit if te market size is sma arge and is given by πl = [ ], and Q Q πh = [ ]. 6 Tis optimization probem yieds: w Q =. 7 We now turn to te manufaturer s woesae priing deision. We assume tat te manufaturer is a Stakeberg eader and orrety inorporates te retaier s optima 7
reation funtion. Terefore, te manufaturer determines te woesae prie tat soves te foowing optimization probem: Max w = w Q. 8 M Te first-order ondition wit respet to w yieds: w =. 9 Comparing te retaier s profits under tis poiy wit its profits from te poiy of seing a te units in bot demand onditions, we find tat tis poiy is optima wen <. 3.. Manufaturer Owns te Units In tis senario, te manufaturer makes te prodution deision before demand is reveaed and before reeiving orders from te retaier. After demand is reveaed, te manufaturer sets te woesae prie, te retaier paes its orders, te units are deivered to te retaier, and te retaier sets te retai prie. We find tat tere are two different regimes. First, for vaues of >, te entire prodution quantity is sod independent of atua market size. For vaues of, te manufaturer s optima poiy is to se a of te units produed wen market size is arge and se ony a portion of te avaiabe units wen market size is sma. Note tat in tis ase it is te manufaturer not te retaier wo deides wat portion to se sine te manufaturer owns te units and an adjust te woesae prie in response to demand onditions. Te equiibrium outomes are given in Tabe and te derivation an be found in te Appendix. 8
INSERT TABLE 3. Prie-Sensitivity Unertainty In tis setion, we anayze te ase were anne members are unertain about prie sensitivity in te market. Wit probabiity, onsumers are not very prie sensitive and terefore demand is ig. Wit probabiity, onsumers are more prie sensitive, so demand is ow. Te potentia market size,, is known and fixed. Su a setup orresponds we, for exampe, to te effet of eonomi onditions on demand. If te eonomy turns sout, aggregate prie sensitivity in te automobie market soud inrease. Te potentia market size, on te oter and, soud not be affeted. Demand for free ars, ten, woud be te same regardess of eonomi onditions. As before, we anayze and ompare two possibe senarios. In one, te retaier owns te units. Te retaier paes orders wit te manufaturer before te unertainty is resoved and te manufaturer produes ony te amount ordered by te retaier. In te seond, te manufaturer owns te units and deides ow mu to produe before te unertainty is resoved wie te retaier paes orders ony after te unertainty is resoved. We find te optima deisions for te manufaturer and retaier by working bakward, as we did for te ase of market-size unertainty see Setion 3., and derive te subgame perfet equiibrium for ea of te senarios. Tabe reports te equiibrium outomes for tree different ases: te retaier owns te units, te manufaturer owns te units, and a benmark of te resuts wen te anne does not fae prodution ead time see te Appendix for te detais of deriving tese resuts. Tis ase turned out to be somewat simper tan te one for market-size unertainty 9
beause te fu prodution quantity is sod under a senarios due to te fixed market size. INSERT TABLE 3.3 Combined Market-Size and Prie-Sensitivity Unertainty Te anaysis for ombined market-size and prie-sensitivity unertainty is very simiar to te anaysis desribed in Setion 3.. In te interest of brevity, we ave omitted te detais ere, but tey are avaiabe from te autors. 4. Resuts 4.. Wo Soud Own te Units in a Canne? Retaining ownersip over te units in a anne 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 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 transferred to te retaier, te manufaturer as to fix te woesae prie before demand is reveaed and annot adjust it ater aording to te reveaed demand. Te added fexibiity is usefu if 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 differenty. Te osts of wasting a unit are smaer for te manufaturer tan for te retaier sine < w. Te 0
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 differenes ead to different 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. Next we present te resuts desribing ow demand unertainty affets te manufaturer and retaier deisions regarding ownersip of te units in te anne. 4.. Market-Size Unertainty We define k= as a tresod eve su tat for any vaues of k < neiter te manufaturer nor te retaier find it optima to od inventory 9. Wen market size is unertain, we find tat tere are tree different regimes depending on te size of te unertainty. Ten, Proposition : Wen market size is unertain, A Tota anne profits are greater under retaier ownersip if te differene in market size is arge < k and under manufaturer ownersip if te differene is k intermediate < < k. Canne profits are te same regardess of ownersip if te differene in market size is sma k <. B Retaier profits are greater under retaier ownersip if te differene in market size is arge < k and under manufaturer ownersip if te differene is intermediate
k < < k. Retaier profits are te same regardess of ownersip if te differene in market size is sma k <. C Manufaturer profits are greater under manufaturer ownersip if te differene in market size is not too sma < ownersip if te differene in market size is sma k <. k. Manufaturer profits are te same regardess of INSERT FIGURE Tere are severa important impiations stemming from Proposition. First, it does matter wo owns te units in a anne. Speifiay, it matters wen tere is unertainty about market size and te potentia differene in market size is arge enoug see Figure. For intermediate differenes in market size, te manufaturer soud retain ownersip over te units, and sine tis is aso in te interest of te retaier, it is reasonabe to expet tat te manufaturer and retaier an rea an arrangement tat keeps ownersip wit te manufaturer. For arge differenes in market size, te retaier woud ike to ave ownersip of te units. However, in tis ase te manufaturer s interest differs 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 of te units. Tis may expain ases were we observe retaier ownersip in pratie. Of ourse, te fat tat an agreement is possibe does not mean tat te parties 9 Note tat wen < ten k < 0 < and bot firms woud never arry units in inventory.
wi rea one, and terefore tere is potentia for anne onfit to arise under tese onditions. To iustrate te importane of tese resuts, onsider one possibe set of parameters were =0.04, =0.5, and =4. In tis ase, if expeted market size in te ow-demand state is 68% or ower of te ig-demand state, it matters wo owns te units in te anne. If te ow-demand market size is even smaer 34% or ower of te ig-demand market-size, te manufaturer and te retaier wi ave opposing interests regarding ownersip of te units. Te profit impiations are aso substantia: for exampe, if =00 and =60, te manufaturer s profits are 64% iger under manufaturer ownersip tan under retaier ownersip, but te retaier s profits are 48% iger under retaier ownersip tan under manufaturer ownersip. To understand wat drives tis resut, one as to reaize tat it matters wo owns te units in te anne ony if te firm tat owns te units finds it optima to restrit saes in te ow-demand ase to ess tan te avaiabe inventory. 0 Obviousy, it is aways optima to se a units in ig-demand 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. Tis is exaty wat appens wen k <. In tat ase te differene in market size is sma and te optima poiy is aways to se a te units see Tabe. Terefore, it does not matter wo owns te units. Next, onsider wat appens wen te differene in market sizes inreases as dereases oding onstant. Ceary tere omes a point at wi it is no onger 0 Notie tat te prodution quantity is te same weter te manufaturer or te retaier owns te units. Terefore, it does not affet te question of ownersip. 3
optima to se a te units if demand turns out to be ow. 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 needs to 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 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. Wen te differene 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 if 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 terefore te retaier is better 4
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. Insert Figures 3 and 4 Figure 3 depits ow, under market-size unertainty, ownersip is impated by te prodution ost. Te regions in wi retaier ownersip or anne onfit ours and were a prefer te manufaturer to own te units are argest wen te prodution ost is zero. As inreases, tose regions diminis in size and eventuay disappear, at wi point it does not matter wo owns te units. Tis refets te fat tat te optima prodution quantity dereases wit. At ow prodution eves, a units are sod regardess of te demand state and it does not matter wo owns te units. As te optima prodution eve inreases, te possibiity of being stuk wit unsod units in te owdemand state inreases and ownersip beomes important. 4.. Prie-Sensitivity Unertainty As an be seen from Tabe, under prie-sensitivity unertainty, a units are sod even in te ow-demand state. Tus, ike te ase of sma differenes in market size, ownersip does not matter. Indeed, omparing te resuting profits between te ases of manufaturer ownersip and of retaier ownersip, we find tat Proposition : Wen prie sensitivity is unertain, te manufaturer, te retaier, and te anne are indifferent to weter te manufaturer or te retaier owns te units in te anne. Te reason tat it is optima to se a te units even under ow-demand onditions wen firms are initiay unertain about prie sensitivity is tat te market s size is known and fixed. Sine te firm aready as te units wen te priing deision is made, te reevant margina ost is zero as a te osts are aready sunk. Terefore, Wie expeted profits are te same, teir distribution over te demand states differs depending on ownersip. Tus, te resut ods ony for risk-neutra parties. 5
tere is aways a positive prie at wi it is optima to se a te units regardess of te demand ondition and it does not matter wo owns te units. 4..3 Combined Market-Size and Prie-Sensitivity Unertainty In most ases, firms wi be unertain about bot market size and prie sensitivity. Te findings from te ase of market-size unertainty od in tis ase as we. Briefy, tis ours beause te effets of market-size unertainty and priesensitivity unertainty on te ownersip deision are ortogona to ea oter. In partiuar, prie-sensitivity unertainty does not ange te ownersip deision and, terefore, te driving fore beind te ownersip deision is market-size unertainty even if tere is some prie-sensitivity unertainty. 4.. Te Effet of Lead Time on Profits As expeted, under unertain demand onditions, te presene of ead time redues te tota anne profits and te manufaturer profits ompared to a anne witout ead time. In addition, under unertain demand onditions and in te presene of ead time, te retaier earns ess profits and Consumer surpus are ower tan te profits and onsumer surpus witout ead time, exept: Proposition 3: wen market size is unertain, te retaier owns te units in te [ ] k anne, and < <, in wi ase retaier profits and onsumer 3 surpus are greater wit ead time tan witout ead time. Surprisingy, under speifi 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 retaier. If te preeding ondition ods, tis effet is stronger tan te ost of assuming ownersip beause of exess inventory if demand is 6
ow and faing ead time for te retaier. Te reason onsumer surpus is iger is tat retaier ownersip generates a iger eve of saes in te ow-demand ondition; and atoug saes are ower in te ig-demand ondition, te tota effet is to inrease onsumer surpus under te rigt onditions. Tis ounterintuitive resut undersores te importane of te deision about ownersip over te 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 if te retaier owns te units. Tis ours beause te manufaturer annot respond to te atua reveaed demand wen te retaier owns te units. Terefore, some anne oordination probems are mitigated by te unertainty about demand and te fat tat te retaier ontros te units in te anne. 4.3 Priing Deisions One feature of our mode is te possibiity of state-dependent pries. Retai and sometimes woesae pries may depend on te atua demand state. In a monopoy setting, intuition suggests tat pries soud be ower in te ow-demand state tan in te ig-demand state. Te foowing resut sows tat tis is not aways te ase and tat prie disounting depends on te nature of te demand unertainty and te presene of ead time in te anne: Proposition 4: Pries retai and woesae are ower in ow-demand states tan in ig-demand states if: a. prie sensitivity is stoasti, or b. market size is stoasti and tere is prodution ead time. As prie sensitivity inreases, te optima prie dereases. Tus, wen tere is prie-sensitivity unertainty, we expet to observe redued pries if demand drops. On In a ompetitive setting, tis is not as ear sine te temptation to ut pries may be stronger wen demand is ig Rotemberg and Saoner 986. 7
te oter and, it is not aways optima to redue pries in te ase of market-size unertainty. Te reason is tat, under market-size unertainty, te number of onsumers varies but te onsumers wiingness-to-pay stays te same aross demand onditions. Terefore, witout prodution ead time, a firm woud aways arge te same prie and adjust te quantities produed and sod aording to te size of te market. However, wit prodution ead time, te firm annot adjust te prodution quantity after demand is reveaed. Tis eads to more inventory on and wen demand drops ompared to te ase witout ead time. As a resut, tere are ony some onditions under wi it is optima to offer prie disounts in te ow-demand state given a priori market-size unertainty and ead time in te anne. Anoter way to tink of Proposition 4 is to reinterpret our mode in te spirit of Gerstner and Hess 99 as te stati anaog of a dynami mode of promotions. 3 Tus, te ange in retai and woesae pries between demand states an be interpreted as te offering of onsumer and trade promotions, respetivey, and Proposition 4 states wen promotions wi be offered as a resut of demand unertainty. Proposition 5: Retai and woesae prie disounts are deeper wit prodution ead time tan witout prodution ead time. Prodution ead time as two effets on priing deisions: beause te quantity produed is smaer tan te desired sae quantity in te ig-demand state, te reguar prie 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 in te owdemand ase is iger and te orresponding prie is ower wit ead time tan witout ead time. Obviousy, te differene between te reguar prie and te promotiona prie is arger wit ead time tan witout ead time. 8
4.4 Pass-troug Rate We now turn our attention to understanding ow demand unertainty and te presene of prodution ead time affet pass-troug by te retaier of redued woesae pries by te manufaturer. Proposition 6: Pass-troug is ess tan 00% wen market size is unertain. Pass-troug is greater tan 00% wen prie sensitivity is unertain. Tis resut omes from te opposite effets tat market-size and prie-sensitivity unertainties ave on te demand funtions. Market-size unertainty eads to te demand funtion in te ow-demand state being steeper rotated ounter okwise tan in te ig-demand state see Figure 5, 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, prie-sensitivity unertainty eads to te demand funtion in te ow-demand state being ess steep rotated okwise tan in te igdemand state see Figure 5, bottom pane. As a resut, for te same number of units to be sod, te woesae prie must ange ess tan te retai prie and pass-troug is greater tan 00%. 5. Disussion Insert Figure 5 5. Ownersip and Deision Autority in a Canne Lee, Padmanaban, and Wang 997 demonstrated in an infuentia paper tat unertainty is magnified as we move furter away from te onsumer in a suppy ain. Based on tis, onventiona wisdom is tat, to te extent tat information asymmetries annot be addressed by better information systems, deision autority soud be 3 One su mode is of perisabe produts wit iid demand over periods. 9
reegated to te member of te anne osest to te onsumer i.e., te retaier 4 wit te notion being tat everyone benefits wen te member wit te best information makes te deision. Sine te owner of te units in a anne as te residua deision rigts regarding te units, tis impies tat it is te retaier tat soud assume ownersip. Tere is, owever, some anedota evidene in te popuar business press tat suggests tat foowing tis presription and pusing te deision autority down in te anne as been ess benefiia to manufaturers tan expeted. Our resuts suggest tat etting te retaier ave te deision autority indeed may not be in te best interest of te manufaturer. In addressing te issue of deision autority in te anne, anne members soud onsider te strategi benefits of making te deision as we as te information asymmetries. In our mode wi does not ave any information asymmetry, ownersip, wie potentiay osty, aso onfers added fexibiity in deision-making. Tis fexibiity is vauabe, and indeed we find tat te manufaturer prefers to retain ownersip and tat, under some onditions, manufaturer ownersip is aso in te interest of te retaier. However, under oter onditions te retaier prefers to assume ownersip. Tese resuts suggest tat strategi onsiderations are important in addition to any information asymmetry in deiding wo soud ave te deision autority in a anne. If te information asymmetries in te anne are not too great, strategi onsiderations may dominate and manufaturers at east may be better off if tey ave te deision autority. 4 Note tat Lee, Padmanaban, and Wang 997 did not make tis aim. Tey foused instead on information saring as teir reommendation. 30
Te ownersip issue may aso impat te retaier s inination to sare information wit te manufaturer. Foowing Lee et a. 997, many studies investigated wen information saring in a anne is benefiia see, for exampe, Gavirneni, Kapusinski, and Tayur 999; Gaur, Gioni, and Sesadri 005; and Yang et a. 003. Obviousy, wen te retaier prefers tat te manufaturer own te units in te anne tere are inentives for te retaier to sare information wit te manufaturer in order to improve its deision-making. But wat appens wen te retaier does not want te manufaturer to own te units? Migt witoding te information atuay ead to deisions tat are more profitabe to te retaier? And an witoding of information be used to more easiy onvine te manufaturer to agree to retaier ownersip? 5. Pass-troug Empiria resear on pass-troug rates reports vaues ranging from 0% to more tan 00% Cevaier and Curan 976; Waters 989; Armstrong 99. Retaier opportunism in te form of ow pass-troug rates is a vexing probem for manufaturers, and understanding its auses and ow to inrease pass-troug rates is an important resear question Kumar, Rajiv, and Jeuand 00. 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 different demand-funtion sapes for different produts Buow and Pfeiderer 983; Battberg and Nesin 990; Tyagi 999. 5 Te approa taken by tese studies was to ompute te optima reation by te retaier to anges in te woesae prie. Te assumption was tat te motivation for te ange in te woesae prie is exogenous to te retaier onsumer 5 Nesin, Powe, and Stone 995 aso expained rates greater tan 00% using a oss eader argument. 3
demand in partiuar remains te same and, terefore, te ony effet te retaier noties is te ange in woesae prie. Tus Tyagi 999, for exampe, onsidered anges in te manufaturer s input osts and an inrease in ompetitive intensity at te manufaturer eve. Our resuts provide a different rationae for pass-troug rates tat are ess tan or greater tan 00%. We ave sown tat, wen te woesae prie anges in response to anges in demand onditions, te nature of te demand unertainty determines weter te pass-troug is more or ess tan 00%. Speifiay, we ave sown tat, for a inear demand funtion, te pass-troug rate is greater tan 00% wen tere is prie-sensitivity unertainty and ess tan 00% wen tere is market-size unertainty. We ave demonstrated different pass-troug rates by reying not on different demandfuntion sapes but on te type of demand unertainty faing te anne. Terefore, it is feasibe to observe different pass-troug rates for te same produt over time if te nature of te unertainty regarding demand anges over time. In our mode, anges in demand onditions drive priing deisions and, as a resut, te retaier reats not ony to a ange in woesae prie but aso to te atua ange in demand onditions. A seond important differene from te previous iterature is tat in our ase prie disounts invove anging prie between two demand urves ig and ow demand. In te previous iterature, prie anges were aong te same demand urve. 6. Conusions In tis paper we ave ooked at te question of weter te manufaturer or te retaier soud ave ownersip of te units in a anne wen demand is unertain. In our setting, prodution and possiby ordering must take pae before anne members earn of te atua demand onditions wie pries an be adjusted to atua demand 3
onditions. Te presene of prodution ead time raises new issues regarding te reationsip between manufaturers and retaiers and as a profound effet on our understanding of anne beavior. Ownersip over te units in te anne matters under su onditions, and anne members priing deisions differ from tose taken wen tere is no ead time. Wen tere is unertainty regarding market size and te possibe differene in size is arge, te manufaturer and te retaier ea prefer to own te units in te anne. Wen te differene in te possibe market size is not as arge, a members of te anne prefer to ave te manufaturer own te units. And wen te differene is sma or te unertainty is ony regarding prie sensitivity, it does not matter wo owns te units. We aso find tat retai and woesae prie disounts are deeper, reguar pries are iger, and promotiona pries are ower wen tere is prodution ead time tan wen tere is no ead time. Finay, te nature of te unertainty affets te pass-troug rate. Te pass-troug rate is ess tan 00% if tere is market-size unertainty and greater tan 00% if tere is prie-sensitivity unertainty. Tese findings ave important manageria and teoretia impiations. Tey point to te importane of te deision regarding wo wi ave ownersip of te units in te anne. Tey provide an expanation for wy we observe different arrangements regarding ownersip of units in annes and under wat onditions tose arrangements soud be used. In order to make informed deisions regarding ownersip, firms need to understand te nature and amount of unertainty tey fae in different situations. Musi CDs, for exampe, ave a fairy we known prie eastiity based on arge quantities of istoria data avaiabe to te industry, but te popuarity and terefore avaiabe 33
market size for an individua CD are igy unertain. Many onsumer eetronis goods ave we-defined prie points and te main unertainty for new modes is market potentia. On te oter and, in many mature produt ategories, firms may fae greater prie-sensitivity unertainty and itte market-size unertainty. A firm introduing a sigty improved diswaser mode wi expet demand for diswasers to depend on te need for repaement purases and te number of new ouseods reated wit te eve of demand unaffeted by introdution of a new mode. Te main unertainty for te firm wi be te prie premium it an arge for te improved mode. Competey new produts woud generay fae substantia unertainty regarding bot market size and prie sensitivity. It is aso important to understand wat eads to unertainty about demand. For exampe, ead time itsef is a ause of unertainty wit onger ead times generating greater unertainty. Tus, one migt expet to see a iger inidene of anne onfit in annes wit ong ead times. Consequenty, an additiona benefit of sortening ead times oud be a redution in anne onfit. Managers and researers must be aware and take into aount tat priing deisions in te presene of prodution ead time differ from te norma presriptions of modes tat do not onsider prodution ead time. For exampe, empiria resear in te NEIO tradition may use teoretia soutions to derive knowedge regarding unobserved information su as woesae pries see, for exampe, Sudir 00, but tose teoretia soutions woud vary depending on te existene of prodution ead time in te anne. Our mode resuts aso provide an expanation for te empiria penomenon of pass-troug rates tat range from ess tan 00% to mu greater tan 00%. We ave 34
sown tat te nature of te demand unertainty determines te pass-troug rate and tus an expain wy a brand an ave different pass-troug rates at different times. Finay, te resuts demonstrate ow te type of unertainty tat firms fae an ave a major impat on teir deisions. Te basi tension in our mode is between te benefits ownersip onfers troug greater fexibiity in deision-making and te potentia osts of ownersip in te form of overstoks and inventory risks. Tus, our mode is suited for situations in wi diret prodution osts are substantia and terefore te potentia ost of ownersip is arge. Tis is true for produts ike ars, durabe onsumer goods, otes, and toys. On te oter and, te mode does not apture we situations in wi diret prodution osts are reativey ow or even nonexistent, as for ompetey digitized produts. First, in tose situations te ost of overstok is very ow. Terefore, te issues assoiated wit making te prodution deision before demand is known are not as important. Seond, wen prodution osts are reativey ow, oter osts, wi we assumed to be zero in our mode, beome more signifiant in te deision proess. For exampe, retaiers inur a seing ost wit te sae of ea unit. If tese seing osts are substantia reative to prodution osts, Proposition about te indifferene to ownersip wen tere is priesensitivity unertainty no onger ods. As ong as prodution osts are suffiienty ig, owever, seing osts do not affet te resuts and Proposition ods. 6 We assume in te mode tat tere is ony one prodution run tat takes pae before 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. 994; and Moon 00 but it is eary a simpifiation of situations were 6 Detais of tis anaysis are avaiabe from te autors upon request. 35
firms an pae repenisment orders. Te abiity to ave an additiona prodution run in response to atua demand onditions may affet ownersip oies as we as oter deisions, su as te initia quantity ordered by te retaier. Mutipe prodution runs may ead to situations in wi bot te manufaturer and te retaier own units at te same time. In tis paper, we oneptuaized ownersip over te units in te anne as a simpe eiter/or onstrut. 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 differ. 7 Sine tota anne profits are iger under retaier ownersip wen bot te retaier and te manufaturer want to retain ownersip, te effiieny riterion suggests tat te retaier wi assume ownersip. Indeed, if 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 and tus guarantees retaier ownersip. Atoug te effiieny riterion is teoretiay appeaing, it may not be so easy to rea su arrangements in pratie. For exampe, it is we known in te iterature on te doube marginaization anne oordination probem tat two-part tariffs an oordinate te anne Moorty 987. Yet 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 differ. 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 risk-saring arrangements ike return poiies on ownersip deisions, require additiona 7 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. 36
foow-up resear. Tis paper provides te beginnings of an understanding of te impiations of ownersip for te anne and of te effets of prodution ead time and demand unertainty on deision-making by anne members. 37
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Tabe : Equiibrium Outomes Market-Size Unertainty Prie ig demand Retaier Ownersip Manufaturer Ownersip Indifferene No Lead Time < 3 4 3 4 > 4 4 3 4 4 [ ] Prie ow demand 3 4 4 3 4 4 [ ] 3 4 Woesae prie ig demand [ ] Woesae prie ow demand Saes ig demand Saes ow demand Prodution ordering quantity Retaier profit Manufaturer profit Consumer surpus > > 4 4 4 6 8 4 3 4 4 4 6 8 3 > [ ] 4[ ] 4[ ] 4[ ] 6 [ ] 8 [ ] 3 [ ] 4 4 4 i 6 8 i [ ] 3 Tis is te equiibrium soution for te ase wen te manufaturer arries te inventory and and te ase wen te retaier arries te inventory and.tus, wen, it does not matter wo arries te inventory. i 4
4 3 4 4 3 4 3 4 3 4 3 4 4 4 4 6 8 3 4 4 4 4 4 6 8 6 8 3 3 4 3 4 Tabe : Equiibrium Outomes Prie-Sensitivity Unertainty Retaier Ownersip Manufaturer Ownersip No Lead Time Prie ig demand Prie ow demand Woesae prie ig demand Woesae prie ow demand NR Saes ig demand Saes ow demand ig demand Prodution ordering quantity ow demand Retaier profit Manufaturer profit Consumer surpus
Figure A: Retaier Ownersip Retaier orders produt Prodution Retaier takes deivery Retaier sets retai prie Retaier sraps unsod units t Manufaturer sets woesae prie Figure B: Manufaturer Ownersip Manufaturer produes units Manufaturer sets woesae prie Retaier orders produts and sets retai prie Manufaturer sraps unsod units t Unertainty resoved 43
Figure Manufaturer LEGEND Indifferent Retaier Manufaturer ownersip 3 Retaier ownersip Canne k / k / r 44
Figure 3: Ownersip as a Funtion of Manufaturing Cost / Indifferent / Manufaturer Ownersip Retaier Ownersip/ Canne Confit 0 C 0 / 45
Figure 4: Ownersip as a Funtion of = 0. 0.9 0.8 Indifferent 0.7 0.6 Manufaturer assumes risk 0.5 0.4 0.3 0. Canne onfit 0. 0 0.0 0. 0. 0.3 0.4 0.5 0.6 0.7 0.8 0.9 teta 46
P,w Figure 5: 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 47