We address the value of quick response production practices when selling to a forward-looking consumer

Transcription

1 MANAGEMENT SCIENCE Vol. 57, No. 10, Octobe 2011, pp issn ó eissn ó 11 ó 5710 ó INFORMS Selling to Stategic Consumes When Poduct Value Is Uncetain: The Value of Matching Supply and Demand Robet Swinney Gaduate School of Business, Stanfod Univesity, Stanfod, Califonia 94305, We addess the value of quick esponse poduction pactices when selling to a fowad-looking consume population with uncetain, heteogeneous valuations fo a poduct. Consumes have the option of puchasing the poduct ealy, befoe its value has been leaned, o delaying the puchase decision until a time at which valuation uncetainty has been esolved. Wheeas individual consume valuations ae uncetain ex ante, the maket size is uncetain to the fim. The fim may eithe commit to a single poduction un at a low unit cost pio to leaning demand, o commit to a quick esponse stategy that allows additional poduction afte leaning additional demand infomation. We find that the value of quick esponse is geneally lowe with stategic (fowad-looking) customes than with nonstategic (myopic) customes in this setting. Indeed, it is possible fo a quick esponse stategy to decease the pofit of the fim, though whethe this occus depends on vaious chaacteistics of the maket; specifically, we identify conditions unde which quick esponse inceases pofit (when pices ae inceasing, when dissatisfied consumes can etun the poduct at a cost to the fim) and conditions unde which quick esponse may decease pofit (when pices ae constant o when consume etuns ae not allowed). Key wods: stategic consume behavio, quick esponse; consume leaning; picing; demand uncetainty Histoy: Received May 8, 2008; accepted Mach 15, 2011, by Matin Laiviee, opeations and supply chain management. Published online in Aticles in Advance June 20, Intoduction Long poduction and shipping lead times ae cited as key causes of supply and demand mismatches, paticulaly on poducts manufactued in an offshoe fashion (e.g., poduced in Asia and expoted to the United States o Euope). Because of these long lead times, demand foecasts and poduction decisions must be made fa in advance of the selling season, when uncetainty concening final demand is high. Thus, if lead times could be educed via, fo example, localized poduction, impoved infomation systems and foecast updating, multichannel poduction and emegency supply souces, and expedited shipping methods allowing fo a apid esponse to updated demand infomation close to (o duing) the selling season, supply and demand could be moe closely matched, educing o eliminating costly shotages and wasteful ovepoduction. Such techniques to mitigate demand uncetainty (which we efe to heeafte as quick esponse systems) can be costly because of infomation technology (IT) expenses and expedited poduction o tanspotation costs, but ae known to povide significant value to fims by bette matching supply with uncetain demand (Fishe and Raman 1996, Eppen and Iye 1997). Most existing wok on this subject analyzes quick esponse pactices using a fixed demand model; that is, maket demand (i.e., consumes) does not eact when a fim adopts quick esponse capabilities. Howeve, the consequences of a quick esponse system paticulaly lowe demand vaiability and potentially geate costs have a tangible impact on consumes by influencing measues that they diectly expeience, most notably the fill ate (faction of demand that is satisfied). Consumes, in tun, may take changes in these measues into account when making thei own puchasing decisions, and as a esult maket demand may change along a vaiety of dimensions such as the timing of puchases by consumes. Fo example, Richtel (2007) descibes how consumes leaned about the geneal scacity of the Nintendo Wii (low fill ates) and modified thei own behavio (buying any available units) in esponse; O Donnell (2006) descibes how consumes lean about and eact to inventoy availability and makdown fequency in the fashion industy; and Rosenbloom (2009) descibes how luxuy goods etailes have influenced consume behavio by educing inventoy. Thus, an impotant issue is how individual consumes may espond to the adoption of quick 1737

2 Swinney: Selling to Stategic Consumes When Poduct Value Is Uncetain 1738 Management Science 57(10), pp , 2011 INFORMS esponse techniques, and indeed whethe fims can continue to exploit the benefits of quick esponse poduction once the maket eacts optimally to this pactice. Pevious wok (Cachon and Swinney 2009, 2011) has shown that consumes may eact to quick esponse capabilities in a way that benefits the fim. Specifically, if consumes ae stategic in the sense that they anticipate potential futue pice eductions by a fim and time thei puchases accodingly, adopting quick esponse can educe the pobability of cleaance sales (by inceasing the accuacy of demand foecasts) and hence induce consumes to pay full pice fo a poduct. In this pape, we examine a scenaio in which the maket may eact to the adoption of quick esponse pactices in a negative way; that is, by employing quick esponse, a fim influences inventoy availability such that consumes will optimally eact in a manne that educes total fim demand and pofit. This setting is chaacteized by a key featue: consume value fo the poduct is initially uncetain and is leaned ove time. Valuation uncetainty may aise in consume goods in a numbe of diffeent ways. Paents inceasingly paticipate in the unfotunate itual of tying to identify the hot holiday toy fo thei childen (Slatalla 2002), tading off the isk of buying ealy and facing uncetain value fo the poduct (i.e., possibly buying a toy that tuns out to be a dud o that thei child does not want) with the isk of buying late and facing uncetain availability fo the poduct (i.e., expeiencing a stockout). Consume value may also be uncetain if the poduct is a new o innovative item (e.g., a complex poduct such as a Nintendo Wii, an Apple iphone, o an automobile); a media item (such as books, movies, music, o video games); o if the consume s equiements fo the item ae uncetain (e.g., snow skis fo a potential weekend tip in two months when weathe is unknown). A common featue of all of these examples is that ove time, consumes lean moe infomation about the poduct and gain a bette sense of its value; fo example, via channels such as pofessional poduct eviews fom websites and magazines; the eviews of fellow consumes (e.g., fom online etailes such as Amazon.com); the expeiences of fiends and family who may have puchased the same poduct; o via the esolution of intinsic uncetainty in poduct value (e.g., the weathe affecting the value of a pai of skis is known the day of the ski tip). Hence, consumes may ecognize that futue leaning will occu and may choose to delay a puchase until they have moe infomation about a poduct s value. In the spiit of these examples, ou model consists of consumes that initially have uncetain value fo a poduct, but who know that infomation about poduct value will be leaned at some point in the futue. Individual consumes in ou model thus make a decision on when and whethe to puchase the poduct: The late the custome waits to buy, the moe infomation she will have about poduct value and the geate the isk of a stockout. Specifically, in ou model consumes choose to eithe puchase ealy pio to leaning thei value fo a poduct o puchase late, afte leaning thei value. Hence, consumes in ou model may stategically delay a puchase to lean moe about poduct value athe than obtain a poduct of known value at a lowe pice, as in Cachon and Swinney (2009, 2011). Although the mechanisms diving stategic consume puchasing behavio ae simila in the two settings delaying a puchase to potentially incease net suplus the consequences fo the fim, paticulaly in how the fim values quick esponse pactices, ae vey diffeent. We show that when consumes expeience this type of time dependent leaning, geate availability esulting fom an impoved matching of supply and demand encouages consumes to delay puchasing the poduct: By educing the likelihood of a stockout, the fim deceases the isk of waiting to lean moe infomation about poduct value. As moe consumes stategically delay puchasing, total demand can decease (via mitigation of an effect known as advance selling; Xie and Shugan 2001) and pofit can be educed despite the fact that the fim can bette match supply and demand via quick esponse. Thus, in contast to pevious wok showing that the inteplay of quick esponse and consume behavio can lead to geate value fo fims in some settings, ou model demonstates that when consumes lean about poduct value ove time quick esponse capabilities can actually influence consume behavio in a way that is detimental to fim pofits. We futhe show that whethe this occus (and to what degee it occus) depends heavily on seveal chaacteistics of the selling envionment; specifically, the pice path (inceasing o deceasing ove time) and the consume etun policy (whethe efunds ae offeed to dissatisfied consumes) play a majo ole in detemining the value of matching supply and demand via quick esponse. 2. Liteatue Review Quick esponse poduction as a vehicle to help mitigate and espond to demand uncetainty has eceived a significant amount of attention in the liteatue (see, e.g., Fishe and Raman 1996, Eppen and Iye 1997). Typically, these papes model quick esponse as leading to a eduction in lead times and hence a decease in demand uncetainty. Mechanisms involved in this eduction of demand uncetainty may include extenal evelation of infomation (exogenous

3 Swinney: Selling to Stategic Consumes When Poduct Value Is Uncetain Management Science 57(10), pp , 2011 INFORMS 1739 fashion tends, etc.), maketing o infomation collection effots by the fim (e.g., focus goup testing), o even ealy sales data based on sample poduction in selected makets. Specifically, we adopt a stylized, two-stage appoach in which the fim is allowed an initial ode (long befoe the selling season and subject to high demand uncetainty) and a second ode (at a highe maginal cost close to the selling season with demand uncetainty vitually eliminated), simila to Cachon and Swinney (2009), Cao and Matínez-de-Albéniz (2010), and Kishnan et al. (2010). In addition, much like ou model, a numbe of these papes analyze the impact of quick esponse on nonopeational aspects of the fim such as competition (Li and Ha 2008, Cao and Matínez-de-Albéniz 2010) and etaile sales effot (Kishnan et al. 2010). The pimay distinction between ou model and pevious wok in the quick esponse liteatue is that we explicitly model the consume puchasing decision subject to consume valuation uncetainty. A numbe of ecent papes have incopoated models of intetempoal consume puchasing decisions into taditional opeational models. Examples include Su and Zhang (2008), Liu and van Ryzin (2008), and Aviv and Pazgal (2008), all of which conside consumes that stategically time puchases because pices change ove time. In contast, we conside consumes that time puchases because infomation about poduct value will be evealed ove time. Seveal papes conside a simila scenaio. DeGaba (1995) demonstates that in the absence of demand uncetainty, a fim may intentionally undestock to induce consumes to puchase when valuations ae uncetain and leaned ove time. Xie and Shugan (2001) demonstate that selling to consumes pio to the detemination of value and consumption (e.g., with advance ticket sales) can substantially incease fim pofits. Alexandov and Laiviee (2007) conside the poblem of a estauant choosing whethe to offe esevations (guaanteed seats) to customes who may o may not value dining on a given night, demonstating when esevations incease the pofit of the fim. Akan et al. (2008) discuss optimal picing to sceen heteogeneous consumes whose values ae evealed ove time. In these papes, in contast to ou model, inventoy (o capacity) is eithe infinite, exogenously set, o fixed thoughout the selling season, and hence issues of inventoy eplenishment afte eceiving updated demand infomation ae not consideed. An exception is Pasad et al. (2011), who analyze a newsvendo selling to consumes who may o may not know thei valuations and show that the optimality of advance selling (selling to consumes befoe they know thei valuations) depends on opeational measues such as the degee of demand uncetainty. Finally, a few ecent papes bidge both steams of eseach by consideing the impact of consume puchasing behavio on the value of quick esponse. In Cachon and Swinney (2009) and Cachon and Swinney (2011), consumes may delay puchasing in ode to obtain the poduct at a lowe pice duing an endof-season cleaance sale. Li and Zhang (2010) analyze the elated poblem of accepting peodes to geneate ealy demand infomation (and hence impove foecast accuacy to bette match supply and demand). In all thee papes, consumes have known value fo the poduct in question and potentially delay a puchase to pay a lowe pice; by contast, ou model focuses on valuation uncetainty as the diving mechanism of stategic consume behavio. To summaize, ou model is the fist, to ou knowledge, that consides the inteaction of stategic consume puchasing behavio with the value of quick esponse poduction pactices when consumes lean about poduct value ove time. 3. Model 3.1. The Fim and Consumes A fim sells a single poduct at an exogenous pice p to a consume population of size N ove a single selling season. Thee ae two potential poduction oppotunities fo the fim: ealy poduction (fa in advance of the selling season) and late poduction (vey close to the stat of the season). Ealy poduction is fa enough in advance of the season that maket size is unknown, though the fim does possess some foecast of demand; thus, duing the ealy poduction oppotunity, N is assumed to be a andom vaiable with positive suppot, distibution function F 4 5, and density f 4 5. The late poduction oppotunity is close enough to the stat of the selling season that maket size is known pefectly. 1 Poduction duing the ealy oppotunity incus a unit cost c 1, wheeas poduction duing the late oppotunity incus a highe unit cost c 2 c 1 because of, e.g., expedited poduction and shipping costs. Poduction at eithe point in time is assumed to be uncapacitated, and poduction duing the late oppotunity is assumed to have a shot enough lead time that all units aive befoe the stat of the selling season. The fim thus opeates in one of two potential egimes: the single pocuement (SP) egime o the quick 1 In eality, foecast updating and efinement may be the esult of an endogenous pocess that may continue even duing the selling season, e.g., monitoing ealy sales and imputing total demand, o pefoming maket eseach. To avoid issues outside the scope of this analysis e.g., demand estimation based on stochastic aivals we assume that the evelation of N is exogenous and pefect and occus just pio to the stat of the season.

4 Swinney: Selling to Stategic Consumes When Poduct Value Is Uncetain 1740 Management Science 57(10), pp , 2011 INFORMS Table 1 Fou Possible Combinations of Signal and Consume Value, and the Pobability of Each fo a Given Signal Stength Table 2 A Summay of the Distibution of Signals and Consume Types Among the Population High value Low value Signal Consume type Faction of population High signal àå 41 É à541 É Å5 Low signal à41 É Å5 41 É à5å esponse (QR) egime. In the SP egime, all poduction occus duing the ealy poduction oppotunity, wheeas in the QR egime, poduction may occu at both times. Excess inventoy emaining at the end of the selling season has zeo value. In both opeating egimes, we denote the ealy poduction quantity by q (the late poduction quantity in the QR egime is assumed to be the pofit-maximizing quantity), and the fim chooses poduction levels to maximize total expected pofit. Although the fim faces maket size uncetainty, consumes initially face uncetainty about thei own pivate valuations fo the poduct. Natue moves fist (pio to the stat of the game) and decides the type of each consume: A faction à of the population has positive value v>p fo the item, and a faction 1 É à has zeo value, whee à and v ae common knowledge. If a consume possesses value v fo the poduct, we efe to he as a high type consume, wheeas if she possesses zeo value fo the poduct, we efe to he as a low type consume. At the stat of the selling season, consumes do not know thei pivate valuation fo the poduct (thei type). At a andom time duing the selling season (i.e., unifomly distibuted thoughout the season), each consume exogenously leans he value fo the poduct (via, fo instance, poduct eviews fom pofessionals and othe consumes, expeiences with demonstation units in the stoe, etc.). Although consumes do not know thei individual valuations at the stat of the selling season, they ae not completely ignoant: Each consume eceives a noisy pivate signal that is an indication of he type. We define Å to be the quality of the signal, i.e., the pobability that the signal is coect. Fo example, a high type consume eceives a signal of high poduct value with pobability Å, and a low type consume eceives a signal of low poduct value with the same pobability. Thus, thee ae fou possible consume segments (coesponding to paiings of the two possible signals and the two possible values) summaized in Table 1. Consumes ae heteogeneous in the quality of thei pivate signals in the sense that Å is distibuted among the population (independently of consume type) accoding to the continuous distibution G4 5 and density g4 5 with suppot on the inteval 41/ Such heteogeneity in the quality of the signal may epesent, fo example, domain expetise of the population in the poduct categoy (e.g., some consumes Z 1 High value High value (coect signal) à Åg4Å5 då 1/2 Low value (incoect signal) 41 É à5 Low value High value (incoect signal) à Low value (coect signal) Z 1 1/2 Z 1 1/2 41 É à5 41 É Å5g4Å5 då 41 É Å5g4Å5 då Z 1 1/2 Åg4Å5 då ae highly technical and capable of accuately judging the quality of a new, high-tech poduct, wheeas some less sophisticated consumes eceive moe noisy signals that leave them less sue of poduct value). Thus, the total numbe of consumes in each segment depicted in Table 1 is found by integating the pobabilities in that table ove the distibution of signal stengths. The esulting distibution of consume segments aising fom this infomation stuctue is summaized in Table 2. Afte eceiving thei pivate signals, consumes aive at the fim at the stat of the selling season. Each consume updates he beliefs of poduct value via Bayes ule and calculates the expected utility of puchasing ealy (befoe knowing poduct value) and the expected utility of delaying he puchase until she leans the value of the poduct, based on he pivate signal and individual signal stength. To evaluate the expected suplus of delaying a puchase, a consume must also conside the pobability that she will be able to obtain a unit at some late point in the selling season, i.e., the consume must fom a belief about the fill ate, denoted ˆî. (Futhe details of this belief will be discussed in the next section.) Afte consumes lean thei value, they puchase if and only if they have positive suplus and the poduct is in stock, and any consume who does not obtain a unit eceives zeo suplus. Consumes ae isk-neutal expected utility maximizes who choose the puchasing stategy (befoe o afte leaning poduct value) that maximizes thei total expected suplus (expected poduct value minus puchase pice). We assume that customes who ae indiffeent between the two stategies puchase befoe leaning poduct value. To summaize, each consume knows 1. he pivate signal of poduct value (high o low) and he individual signal stength Å; 2. the common valuation distibution and its paametes (i.e., that a faction à of the population has value v); 3. the puchase pice p; and 4. he belief about the futue availability of the poduct, ˆî.

5 Swinney: Selling to Stategic Consumes When Poduct Value Is Uncetain Management Science 57(10), pp , 2011 INFORMS 1741 To simultaneously model both stategic (fowadlooking) and nonstategic (myopic) customes, we intoduce a paamete Ñ that is analogous to a discount facto: if Ñ = 0, customes do not anticipate the oppotunity to puchase afte leaning poduct value, wheeas if Ñ = 1, they do The Consume Decision: Wait o Buy? We now analyze the consume decision: whethe to wait o buy. In analyzing the consume decision, the elevant unit of analysis is a consume who aives at the stat of the selling season, finds a unit in stock, 2 and consides puchasing the poduct immediately (which ensues that a unit will be obtained, but not that value will be high) o delaying the puchase decision until she leans he valuation (which ensues that the consume will only puchase if she has high value fo the poduct but does not ensue that she will successfully obtain a unit). 3 The expected suplus of an immediate puchase is É s 4Å5v Ép, whee É s 4Å5 is the posteio pobability that the consume has high value fo the poduct, conditional on a signal s 2 8l1 h9 (i.e., low o high value) and signal stength Å. Fo a consume eceiving a high value signal, this posteio pobability is É h 4Å5 = = P4high type and high signal5 P4high signal5 Åà Åà + 41 É Å541 É à5 0 (1) Note that É h 4Å5 is inceasing in Å. Similaly, if the consume eceives a signal indicating that the poduct is low value, the posteio pobability is É l 4Å5 = 441 É Å5à5/441 É Å5à + Å41 É à55. Note that É l 4Å5 is deceasing in Å. If É l 4Å5v É p>0 fo some Å, consumes eceiving a low signal may eceive positive suplus fom an ealy puchase, wheeas if É l 4Å5v É p<0, all low signal consumes eceive negative 2 If any consume finds the fim out of stock, the game is essentially ove; because of ou assumption that the fim s QR ode aives pio to the stat of the selling season, if a consume finds the fim out of stock, all subsequent consumes will as well, egadless of the opeating egime. 3 Technically, the consume chooses between puchasing befoe leaning he value and afte leaning he value, both of which could potentially be at any time duing the selling season. Howeve, conditional that a consume decides to puchase befoe leaning he value, the optimal time to puchase is immediately at the stat of the season (as this minimizes the isk of a stockout). Similaly, conditional on puchasing afte leaning poduct value, the optimal puchase time is at the moment she ealizes he value fo the poduct, as this too minimizes the isk of a stockout. Hence, the consume effectively chooses between an immediate puchase at the stat of the season and a puchase at the moment she leans he valuation. Note that subgame pefection of the consume stategy is not an issue, as consumes do not obseve inventoy diectly and hence cannot update beliefs about demand, supply, o fill ates as the season pogesses. suplus. In the following analysis, we assume that the latte case holds fo all Å. 4 Because of this assumption, all consumes eceiving a low signal have negative expected suplus fom puchasing befoe leaning thei valuation. It follows that all such consumes will delay puchasing until afte leaning thei valuations, and only those consumes who eceive a high signal will conside a puchase pio to leaning thei valuations. The expected suplus fo a high signal consume fom an ealy puchase is É h 4Å5v É p, wheeas the expected suplus fom a delayed puchase is Ñ ˆîÉ h 4Å54v É p5. Note that if É h 4Å5 = 1 ealy suplus is geate than late suplus (because Ñ1 ˆî apple 1), wheeas if É h 4Å5 = 0 late suplus is stictly geate than ealy suplus. It intuitively follows that consumes puchase ealy if É h 4Å5 is high, a fact that leads to ou fist peliminay esult chaacteizing consume actions in any possible equilibium in which consumes have identical beliefs about the fill ate: Lemma 1. In any equilibium with identical consume beliefs ˆî, thee exists a unique citical Å such that all consumes who eceive a high value signal and have Å Å puchase befoe leaning poduct value, wheeas all consumes with Å < Å wait until afte leaning poduct value. Poof. All poofs appea in the appendix. Lemma 1 shows that in any equilibium (the pecise fom of which we have not yet specified beyond equiing identical beliefs ˆî), consumes who eceive a signal of high poduct value and who have high signal quality (accuately judge poduct value) will puchase befoe leaning thei valuations, wheeas consumes who have low signal quality (pooly judge poduct value) will delay until afte leaning poduct value. Thus, we may chaacteize the equilibium behavio of the consume population by a single paamete, the citical signal stength Å. In equilibium, the citical signal stength is detemined by calculating the suplus fom an immediate puchase by a consume who aives at the stoe and finds a unit in stock and equating that suplus with the expected suplus of delaying the puchase until leaning poduct value, solving fo Å and yielding Å = 41 É à5p 41 É à5p + à4v É p541 É Ñ ˆî5 0 (2) 4 Equivalently, àv É p<0, i.e., a custome with a completely noninfomative signal will not puchase the poduct befoe leaning its value. This assumption allows us to ignoe customes who eceive a low value signal in all futhe equilibium discussion, because thei dominant action is to delay puchasing. If we elax this assumption, we must account fo low signal customes in each equilibium, but the qualitative effects of the model emain unchanged. É

6 Swinney: Selling to Stategic Consumes When Poduct Value Is Uncetain 1742 Management Science 57(10), pp , 2011 INFORMS 4. The Inventoy-Puchase Timing Game Consumes and the fim thus take pat in a game: Consumes choose when to puchase (eithe befoe o afte leaning poduct value), and the fim chooses how much inventoy to poduce (eithe in the single ealy poduction oppotunity in the SP egime, o in both poduction oppotunities in the QR egime). We fist analyze the SP and QR egimes sepaately, then conside fim pofit in each scenaio to detemine fim pefeence between the two opeational capabilities. The sequence of events in the quick esponse egime is summaized in Figue 1. The sequence in the SP egime is identical, except thee is no second poduction oppotunity. We assume that the fim cannot cedibly commit to an inventoy level; that is, consumes do not diectly obseve the inventoy level of the fim pio to making thei puchasing decisions. This is a typical assumption (Su and Zhang 2008, Cachon and Swinney 2009) eflective of the fact that pecise inventoy infomation is often obscued fom common consumes and, moeove, it is difficult fo the fim to cedibly convey infomation about inventoy (e.g., the fim always has incentive to tell consumes thee is less inventoy than actually is available in ode to engende a sense of scacity). Similaly, we assume that the consume population cannot cedibly commit to a citical signal stength that detemines equilibium puchase timing, hence the fim must fom beliefs about the citical signal stength (which we label ˆÅ) and make optimal inventoy decisions given these beliefs. Such beliefs may deive fom past expeience with simila poducts, fom maketing eseach o fom a detailed undestanding of the consume valuation stuctue. Fom a modeling pespective, this means the game is one of simultaneous moves between the consume population and the fim. In othe wods, consumes optimally time thei puchases given a fixed belief about inventoy availability ( ˆî), wheeas the fim optimizes inventoy given a fixed belief about consume puchase timing ( ˆÅ), and the simultaneous solution to these optimization poblems foms the Nash equilibium to the game. As a final step, we assume that both fim and consume expectations ae ational, i.e., consistent with the equilibium outcomes (Su and Zhang 2008, Cachon and Swinney 2009, Huang and Van Mieghem 2009). Rational expectations ae a esult of both consumes and the fim possessing beliefs that do not systematically deviate fom eality; moe discussion of this assumption follows below. The equilibium will thus be chaacteized by values of q (the fim s inventoy level) and Å (the citical signal stength of the consume population). Let the supescipt * denote a geneic equilibium paamete (eplacing * with sp o q when efeing specifically to the single pocuement o quick esponse case). We then fomally define the equilibium as follows: Definition 1. A Nash equilibium (q 1Å ) with ational expectations to the game between the fim and the consume population satisfies the following: 1. The fim chooses an initial inventoy level q (and, in the QR egime, a second inventoy pocuement) to maximize total expected pofit, conditional on beliefs about consume behavio ˆÅ. 2. The consume population detemines the citical signal stength Å, conditional on beliefs about poduct availability ˆî. 3. Fim beliefs ae ational, i.e., ˆÅ = Å 0 4. Consume beliefs ae ational, i.e., ˆî = î4q 1Å 5, whee î4q1 Å5 is the fill ate given initial inventoy q and citical signal stength Å. We emphasize hee that although we have explicitly modeled beliefs and imposed ationality on those beliefs, the end esult is identical to the Nash equilibium of a simultaneous move game with full infomation. This also implies that we implicitly assume consumes ae awae of the opeating egime of the fim (eithe single pocuement o quick esponse) as, in geneal, these two egimes will have diffeent Figue 1 Sequence of Events with Quick Response Consumes aive, obseve pivate signals of poduct value, and choose to puchase immediately o wait to lean poduct value. The initial poduction oppotunity (pio to leaning maket size, N). The second poduction oppotunity (afte leaning maket size, N). Consumes who waited unifomly lean thei pivate valuation fo the poduct, and puchase if thei suplus is positive. Selling season

7 Swinney: Selling to Stategic Consumes When Poduct Value Is Uncetain Management Science 57(10), pp , 2011 INFORMS 1743 equilibium fill ates. This assumption is motivated by seveal consideations. Fist, ou pimay focus in this pape is on how the value of quick esponse is impacted by consumes esponding optimally to this pactice. This is not to say that it is impossible fo fims to mask opeational capabilities fom consumes, but athe that the egime of inteest fo this analysis is pecisely the scenaio in which consumes do coectly infe and optimally espond to the fim s opeational capabilities. Second, although the pecise manne in which consumes lean about fim opeational capabilities is outside the scope of this pape, quick esponse has tangible outcomes fo consumes (e.g., the impact on poduct availability) and one might easily imagine that consumes epeatedly patonizing fims may lean ove time that fim A has a geate inventoy availability than fim B (i.e., fim A uses quick esponse wheeas fim B does not). Thus, it is easonable to assume that even if a consume does not explicitly know that a fim uses quick esponse pe se, the consume becomes awae of the consequences of this stategy by obseving measues tangible to he (like fill ates). 5 In addition to anecdotal evidence, ecent empiical studies suggest that consumes o at least some faction of any paticula consume population ae both fowad looking and capable of developing ational expectations theeby coectly infeing futue fim actions, even if such actions ae pobabilistic. Isael (2005), using data fom the automotive insuance industy, estimates that about 20% of individuals ae fowad looking and fom ational expectations of futue insuance pices. Osadchiy and Bendoly (2010), in an expeimental setting, detemine that about 38% of subjects ae fowad looking, and the extent of stategic behavio inceases as moe infomation about futue pobabilistic events is given to consumes. Soysal (2008) assumes that consumes do fom ational expectations of pices and in inventoy availability in a fashion appael setting, and then uses stuctual estimation to deive a demand model and detemine that expectations of futue inventoy availability plays a significant ole in cuent peiod sales. Chevalie and Goolsbee (2009), in an empiical investigation of the college textbook maket, find 5 Fo instance, consumes have come to expect that video game manufactue Nintendo is incapable of apid inventoy eplenishment to meet demand (Richtel 2007) and hence futue availability is low. On the othe hand, consumes have come to expect that Geneal Motos (GM) will satisfy demand on hit poducts and hence futue availability is high, a belief that GM is now actively tying to change (Stoll 2007). Moe fomally, see Su and Zhang (2009) and Kalai and Lehe (1993) fo a discussion and analysis of how consume leaning ove time in a simila setting can convege to the equilibium of a single-shot game with ational expectations. stong suppot that consumes ae capable of foming ational expectations of the pobability that a new edition of a textbook is eleased (which impacts the esale value of the cuent edition of a text). Although none of these papes empiically demonstate that consumes fom ational expectations in pecisely ou setting, 6 the esults do povide evidence that consumes ae both fowad looking and capable of foming such expectations in geneal, be it egading pice (Isael 2005, Osadichy and Bendoly 2010); inventoy availability duing cleaance sales (Soysal 2008); o othe pobabilistic fim actions (such as intoducing new poducts, Chevalie and Goolsbee 2009). Thid, a numbe of papes in the liteatue employ simila assumptions in which consumes ae awae of high-level fim stategy (quick esponse o no quick esponse; display all inventoy o display one unit at a time; obtain advance demand infomation o not), although consumes cannot diectly obseve low-level tactical decisions like pecise inventoy amounts. In these models, and in ous, the intent is to conside the equilibium consume esponse to an opeational pactice once consumes have become awae of, and eacted to, that pactice. 5. Equilibium and the Value of Quick Response Having defined the equilibium that we will analyze, we now poceed to calculate the equilibium and exploe the value of quick esponse in the next section. We must fist pove that an equilibium to the game exists (and that such an equilibium is unique) in ode to discuss its popeties; the following lemma accomplishes this fo the SP egime. Lemma 2. When the fim opeates in the single pocuement egime, an equilibium 4q sp 1Å sp 5 exists and is unique. The equilibium total demand to the fim is Z 1 D = N à + 41 É à5 41 É x5g4x5 dx 0 (3) Å sp Fom (3), the equilibium demand of the fim is deceasing in Å sp. It is appaent, then, that the fim pefes moe consumes to puchase ealy as this inceases total demand. This esult is sometimes efeed to as the advance selling phenomenon (see Xie and Shugan 2001) in which a fim exploits consume valuation uncetainty by inducing some consumes to puchase the poduct befoe leaning thei value that will ultimately be dissatisfied (have low valuation). 6 Indeed, an inteesting diection fo futue eseach would be to empiically veify whethe consumes fom ational expectations of fim opeational capabilities such as quick esponse.

8 Swinney: Selling to Stategic Consumes When Poduct Value Is Uncetain 1744 Management Science 57(10), pp , 2011 INFORMS We next move to the game in which the fim opeates in the QR egime. Recall that when detemining the numbe of units to poduce using quick esponse, the fim chooses an inventoy level that maximizes total pofit. As a esult, if the fim has quick esponse capabilities, the optimal action is to pocue enough inventoy in the quick esponse ode to satisfy all demand, conditional on a fixed belief about consume behavio (fixed ˆÅ). Because fim expectations about ˆÅ ae ational, this means the fim pocues enough inventoy to satisfy all demand it eceives, and hence consumes believe that the fill ate at that fim is equal to 1; afte leaning the tue value of demand, the fim cannot cedibly commit to satisfying anything less than the total demand it eceives. Quick esponse thus inceases the expected suplus of consumes who delay thei puchase by inceasing the expected fill ate, and so stengthens the incentive fo consumes to wait. All else being equal, this will shift demand to late times, which will in tun decease the amount of advance selling that occus. The stoy does not end with the effect of quick esponse on consume behavio; QR also offes value by bette matching supply and demand unde uncetainty. Thus, it emains to be seen how QR affects the pofit of the fim in equilibium. Befoe we answe this question, we must fist demonstate that an equilibium exists and is unique when the fim opeates in the QR egime. The following lemma does this, in addition to compaing the equilibium outcomes (citical signal stength and inventoy level) to the single pocuement egime. Lemma 3. When the fim opeates in the quick esponse egime, an equilibium 4q q 1Å q 5 exists and is unique. In equilibium, moe consumes delay thei puchases (Å sp apple Å q ) and the fim sets a lowe inventoy level (q q apple q sp ) than in the single pocuement egime. Having demonstated that equilibia exist and ae unique in both egimes, we may now addess the value of quick esponse: the incemental incease in pofit because of the adoption of a quick esponse system. Ou fist esult demonstates how the value of quick esponse is affected by stategic custome behavio: Theoem 1. (i) The incemental equilibium value of quick esponse (è q É è sp ) is smalle if consumes ae stategic (Ñ = 1) than if they ae nonstategic (Ñ = 0). (ii) The incemental equilibium value of quick esponse (è q É è sp ) is stictly deceasing in the cost of quick esponse (c 2 ), and if c 2 = p, è q apple è sp. In othe wods, pat (i) of Theoem 1 shows that quick esponse yields less value to the fim when consumes ae stategic than when they ae nonstategic. This is because stategic behavio by consumes educes the total demand to the fim: When customes ae stategic (Ñ = 1), all individuals intentionally delay thei puchase, and inevitably some of these customes will not buy the poduct once they lean thei valuation. As a esult, the value of matching supply and demand is lowe (thee is less potential demand to match). How much is the value of quick esponse educed by stategic behavio? Can it eve be negative? Pat (ii) of Theoem 1 addesses these questions, yielding a supising esult: Quick esponse may educe the pofit of the fim even if the maginal pocuement cost is stictly less than the selling pice. This stands in contast to the existing liteatue on quick esponse: With nonstategic consumes (e.g., Fishe and Raman 1996) o with stategic consumes in the absence of leaning (Cachon and Swinney 2009), quick esponse always povides nonnegative value if the magin on a unit pocued using quick esponse is weakly positive (i.e., if c 2 apple p). Theoem 1 shows that this need not be the case when consumes lean about thei valuations ove time: It is possible fo quick esponse to yield a positive magin on each unit sold while simultaneously yielding lowe expected pofit to the fim than the single pocuement egime. The key to both theoems lies in the dual effects of quick esponse: shifting demand and matching supply with demand. These two effects pull the equilibium pofit of the fim in opposite diections. Shifting demand (fom ealy puchases to late puchases) educes pofits by deceasing the amount of advance selling. Matching supply with demand inceases pofits by eliminating lost sales all demand is captued, albeit at a highe unit pocuement cost and educing the chance of ovestock. Hence, the fim only values quick esponse so long as the cost of shifting demand is exceeded by the gain fom bette matching supply with demand; see Figue 2. 7 Theoem 1 demonstates that the value of both effects is highe when consumes ae nonstategic (Ñ = 0) than when they ae stategic (Ñ = 1). When consumes ae nonstategic, the demand shifting effect is eliminated. Futhemoe, total demand to the fim is highe, so the value of matching supply and demand fo any given c 2 is highe than when consumes ae stategic. Thus, when Ñ = 0, all thee cuves depicted in Figue 2 ae highe, as Figue 3 demonstates. Although we have shown that the value of quick esponse is lowe if consumes ae stategic and lean about poduct value ove time, this is not to say 7 In Figue 2 and all othe gaphical examples, v = 18, p = 10, c 1 = 5, and à = 0075, N is gamma distibuted with mean 10 and standad deviation 5, and Å follows a beta distibution with both paametes equal to 5 condensed to lie in the inteval 41/21 15.

9 Swinney: Selling to Stategic Consumes When Poduct Value Is Uncetain Management Science 57(10), pp , 2011 INFORMS 1745 Figue 2 Incemental value of quick esponse The Incemental Value of Quick Response 4è q É è sp 5 as a Function of the Cost of an Expedited Pocuement 4c 2 5 When Ñ = 1, Sepaated into Component Factos Total value Supply/demand matching Demand shifting Unit cost of a second pocuement (c 2 ) that quick esponse is always hamful to the fim in this setting. As Theoem 1 and Figue 2 demonstate, quick esponse can incease the pofitability of the fim if, all else being equal, c 2 is small enough. Nevetheless, a esult of Theoem 1 is that it may be in the best inteests of the fim to fogo quick esponse tactics and the option to pocue additional inventoy, and futhe to ensue that consumes ae awae of this opeating egime. Paticulaly in light of additional fixed costs that inevitably accompany the adoption of any quick esponse system (e.g., shipping and fulfillment infastuctue, IT systems, and poduction capacity o esevation costs), it is clea that the fim is less likely to benefit fom a quick esponse system when customes ae stategic and lean about poduct value ove time. This elates, in pat, to the ationing isk esults in the liteatue on stategic consume puchasing. In contast to the mee eduction of inventoy descibed in this liteatue, Theoem 1 implies that the fim may be bette off with an entiely diffeent opeating policy (single pocuement vesus quick esponse) when consumes ae stategic by opeating without quick esponse, the fim s inability to eact to updated demand infomation in a timely and esponsive way can benefit the fim by geneating a cedible mismatch between supply and demand and inducing moe consumes to puchase pio to leaning thei value. Figue 3 Incemental value of quick esponse The Incemental Value of Quick Response 4è q É è sp 5 as a Function of the Cost of an Expedited Pocuement 4c 2 5 When Ñ = 0 Total value Supply/demand matching 5 Demand shifting Unit cost of a second pocuement (c 2 ) 6. Consume Retuns The peceding analysis assumed that a consume who puchased an item ealy had no ecouse if he value fo that item tuned out to be low that is, the possibility that a consume could etun a poduct if she is dissatisfied was excluded. In some industies, this assumption is appopiate. Fo example, with most types of media (e.g., movies, music, video games, o compute softwae) etuns ae fobidden once an item has been opened (often because of feas of piacy), and Amazon.com does not allow etuns on lage televisions because of the logistical challenges of etun shipping. In some cases, howeve, poduct etuns ae a common and impotant component of fim stategy. Satisfaction guaantees abound in many settings (clothing, electonics, etc.), with fims encouaging customes to ty new poducts isk fee and pomoting geneous etun policies. 8 Such policies incease the consume incentive to puchase ealy by educing the consequences of buying a poduct that is not valued. Retuns policies have eceived attention in the liteatue: see, fo example, Davis et al. (1995), Su (2009), Liu and Xiao (2008), and Shulman et al. (2009). Howeve, these papes do not conside the impact of consume etuns policies on a fim s incentives to adopt a quick esponse stategy. We assume that etuns ae allowed thoughout the selling season, and each etun is fo a full efund minus a consume estocking fee, c 0 (i.e., the net efund is p É c ). We pesent ou esults fo geneal c to include the case in which the estocking fee is established by the nom of the industy (e.g., no fee may be customay fo competitive easons), and we discuss the fim s choice of optimal estocking fee below. Retuns occu immediately afte a consume who puchased ealy leans he valuation (e.g., unifomly thoughout the selling season). We assume that etuned poducts ae esalable that is, the fim may immediately epackage and esell any etuns that it eceives. Futhemoe, we assume that any consume who wishes to puchase and finds the fim out of stock costlessly waits to see if any etuned poducts become available to puchase duing the selling season. Consumes who make a etun incu a hassle cost h 0 deiving fom, fo instance, the tavel cost of etuning to a stoe. Retuns ae also costly to the fim, incuing an intenal fim estocking fee of f 0 on each etuned item (due to, fo example, epackaging costs o the cost of employee time). We assume that p ÉhÉ c 0, i.e., a dissatisfied consume benefits 8 At both Amazon.com and the electonics etaile Best Buy, fo example, etuns ae allowed fo full efunds on most items within a 30-day peiod; duing the holidays this etun window is extended up to a maximum of 90 days.

10 Swinney: Selling to Stategic Consumes When Poduct Value Is Uncetain 1746 Management Science 57(10), pp , 2011 INFORMS fom a etun. This implies that if É h 4Å5v É p 0, then É h 4Å5v É p + 41 É É h 4Å554p É h É c 5 É h 4Å5v É p 0, i.e., with etuns, high signal consumes have geate incentive to puchase ealy than without etuns. We assume also that etuns ae enough of a hassle (h+ c is lage enough) that low signal consumes still do not puchase befoe leaning thei valuations. 9 We ae inteested in how the addition of the descibed etun policy changes the esults of 5, specifically the esults povided in Theoem 1. By inceasing expected suplus fom an ealy puchase, etuns encouage moe consumes to puchase befoe leaning thei values. Although this would seem to benefit the fim, the incease in advance puchasing comes at a pice: Consumes who puchase ealy and ae dissatisfied can be costly to the fim, because each etuned unit costs the fim the pice of the efund minus the chaged consume estocking fee, p É c, and the intenal fim estocking fee, f. Thus, the value of quick esponse pactices which, as we have aleady mentioned, shift demand by lessening the availability isk associated with delaying a puchase will depend upon the magnitude of these estocking fees, as the following theoem shows. Theoem 2. If consume etuns ae allowed: (i) If f c, equilibium fim pofit (in eithe egime) and the incemental value of quick esponse ae geate with stategic customes than with myopic customes, and the incemental value of quick esponse is always positive. (ii) Othewise (if f < c ), equilibium fim pofit (in eithe egime) and the incemental value of quick esponse ae geate with myopic customes than with stategic customes, and the incemental value of quick esponse may be positive o negative. The peceding theoem yields seveal intiguing esults. Fist, the theoem shows that unde consume etuns, if f c, fim pofit in eithe egime is geate if customes exhibit stategic behavio than if they ae nonstategic. The key to this esult lies in the fact that if f c, etuns (a) ae costly to the fim on a maginal basis and (b) ensue that no consume who does not value the poduct eceives the poduct, theeby eliminating the value of advance selling effect and guaanteeing that fim demand (net of etuns) is always àn egadless of the value of Ñ. Thus, thee is no benefit to selling a unit to a consume who ultimately possesses low value fo the poduct; on the contay, this is costly to the fim because of the estocking costs. The fim seeks to minimize the numbe etuns, and the numbe of etuns is lowe when consumes ae stategic (and hence wait to lean about poduct value befoe puchasing) than when they ae nonstategic (blindly puchasing befoe knowing thei eal valuation, only to 9 Specifically, this implies àv É p + 41 É à54p É h É c 5 < 0. etun the item late). If, on the othe hand, f < c, then the fim chages customes moe fo a etun than its own intenal costs associated with a etun; in this case, the fim pofits fom each individual etun and so, just as in the model without consume etuns, pefes if customes puchase befoe leaning thei valuations. Consequently, the fim pefes a nonstategic custome population that is moe apt to puchase ealy. Theoem 2 also shows that if f c, quick esponse always inceases fim pofit. Just as in pat (i) of the theoem, the fim benefits fom minimizing the numbe of costly etuns; hence, the tendency of quick esponse to shift demand also inceases fim pofit. When f < c, howeve, this may o may not be the case; just as in the model without etuns, the fim is hut by demand shifting as it educes advance selling and pofitable etuns. Finally, Theoem 2 shows that if f c the esult of Theoem 1 is evesed: the value of quick esponse is geate if customes exhibit stategic behavio than if they ae nonstategic. Intuitively, the ability of a quick esponse system to induce demand shifting (which is pofitable if f c ) is most effective when consumes ae stategic (indeed, when consumes ae completely nonstategic, quick esponse induces no demand shifting at all). Hence, the value of quick esponse is geatest unde fowad-looking custome behavio. Altenatively, when f < c, we again have a esult simila to Theoem 1: quick esponse is less valuable when customes ae stategic because it geneates demand shifting and causes the fim to lose pofitable etuns. The esults of Theoem 2 ae due to the inclination of consumes to hoad inventoy: given that etuns ae possible, a consume would athe puchase an item ealy and un the isk of having to etun the poduct, as opposed to delaying the puchase and isking a stockout. Two ways to educe hoading ae to incease availability (e.g., adopt quick esponse) and make consumes stategic (incease Ñ fom 0 to 1). If f c, then hoading is costly to the fim and so both stategic behavio and quick esponse help to minimize this negative behavio. This implies that if Figue 2 wee plotted fo the case of costly etuns ( f c ), the demand shifting potion of the gaph would have positive value. Lastly, conside the scenaio if the fim is capable of choosing whethe to offe etuns and may set the consume estocking fee c to maximize pofit. Given ou assumptions, the optimal consume estocking fee is c = p É h, i.e., the geatest possible estocking fee that will induce consumes to etun the poduct. The fim will clealy not offe etuns if c < f because etuns ae individually costly and also esult in a decease in total sales. Thus, pat (i) of Theoem 2 cannot hold if the fim can choose whethe to

11 Swinney: Selling to Stategic Consumes When Poduct Value Is Uncetain Management Science 57(10), pp , 2011 INFORMS 1747 offe etuns, because clealy the fim will not offe etuns if they ae costly. 10 The fim may offe etuns if c > f, in which case individual etuns ae pofitable and pat (ii) of the theoem holds. In eithe case, if the fim can choose whethe and how much to chage fo etuns, the model with consume etuns mios ou base model, suppoting all of ou oiginal esults. The fact that in some cases stategic custome behavio can be good fo the fim (and fo the value of quick esponse) uns contay to the vast majoity of the stategic consume liteatue. This is because, in ou model, fowad-looking behavio esults in actions that benefit customes (due to the avoidance of hassle costs and consume etun fees) and the fim (due to the avoidance of intenal fim estocking costs). Thus, ou model demonstates how the inteaction of two effects consume leaning and costly poduct etuns can lead the fim to benefit fom both quick esponse pactices and a vey stategic custome population. 7. Picing In this section, we endogenize picing in ou oiginal model and addess how the value of quick esponse is affected. We conside two types of picing: fixed picing (in which the etaile sets a single pice fo the entie selling season) and intoductoy picing (in which the etaile may set a diffeent pice duing the initial o intoductoy elease of the poduct, e.g., when consume valuations ae still unknown). Unlike the inventoy level, pice is diectly obseved by consumes, and hence the fim acts as a leade in the pice game. Thus, the model with fixed picing entails a fist stage in which the fim sets the (constant) selling pice, and a second stage which behaves identically to the games analyzed in 3 5. As a esult, given a paticula pice, the pevious esults continue to hold (notably the equilibium existence esults) in the second stage of the game, and we need only analyze the fim s choice of the selling pice by compaing expected pofits in the inventoy/puchasing subgames using vaious pice levels. The following theoem confims that the esult of Theoem 1 quick esponse may decease fim pofit continues to hold even when the fim may set a (constant) pice level. In what follows, we use the subscipt to denote equilibium values (pofits, 10 Nevetheless, it is impotant to keep in mind that in pactice fims may offe etuns policies even if etuns ae individually costly; in many industies (e.g., etailing) the vast majoity of etuns ae fo full (o nealy full) efunds because of competitive pessue, and ae subsequently costly to fims see Stock et al. (2006) fo a discussion of how fims actively attempt to minimize etuns. If this is the case, pat (i) of the theoem holds. quantities, signal stengths) in a model with fixed endogenous picing. Theoem 3. The incemental equilibium value of quick esponse with fixed picing is stictly deceasing in the cost of quick esponse (c 2 ), and if c 2 = v, è q apple èsp. The key to this esult is the following: When pices ae fixed acoss time, egadless of the optimal pice level, adopting quick esponse inceases the consume incentive to wait and hence deceases advance selling and fim pofit. The feedom to set the pice is of little value in the quick esponse egime when c 2 is lage, because the fim s optimal pice lies in the inteval 6c 2 1 v7; if the pice is lowe than c 2, then quick esponse is neve used, hence the fim essentially moves to the single pocuement egime. In the single pocuement egime, the fim emains fee to pice anywhee in the inteval 6c 1 1 v7. When the cost of quick esponse is lage, the quick esponse egime has two detimental effects to the fim: picing is constained and moe consumes delay puchasing because of highe availability. As a esult, the single pocuement egime becomes even moe attactive than in the exogenous pice case. Thus, Theoem 3 mios the esult of Theoem 1: it is possible fo quick esponse to decease pofit even when the magin is positive (c 2 apple p apple v). In the intoductoy picing case, we assume that the fim chages two diffeent pices: an intoductoy pice and a egula pice. The intoductoy pice is valid only at the stat of the selling season (e.g., the fist week, o fo peodes) when consumes make thei initial decision on when to puchase, wheeas the egula pice is valid theeafte. Consumes develop ational expectations of futue pices; that is, they coectly anticipate the egula pice (o, equivalently, the fim cedibly announces the egula pice along with the intoductoy pice). We fist note that if the fim is fee to set diffeent pices but is constained only to mak pices down ove time, Theoem 3 continues to hold. 11 If the fim can aise pices ove time, howeve, a diffeent pictue emeges. Let p 1 and p 2 be the intoductoy pice and the egula pice, espectively. Note that the optimal egula pice is p 2 = v; all consumes know thei values when puchasing at the egula pice, and possess values equal to v o 0 fo the poduct. Hence, the fim extacts all suplus fom consumes puchasing afte leaning the poduct s value by chaging the valuation of the high type consumes. Consequently, all 11 It is neve optimal in the cuent model to set an intoductoy pice that is highe than the egula pice; the lowe egula pice would only encouage moe consumes to delay puchasing and hence decease the amount of advance selling. Thus, a fim constained to mak down ove time chooses to set a constant pice, and the model educes to the fixed picing case analyzed above.

12 Swinney: Selling to Stategic Consumes When Poduct Value Is Uncetain 1748 Management Science 57(10), pp , 2011 INFORMS consumes have zeo suplus fom delaying a puchase (both high and low types, egadless of whethe they successfully pocue a unit), and all consumes with positive expected suplus fom an ealy puchase will choose to buy befoe leaning thei valuations. In geneal, the optimal intoductoy pice satisfies p 1 apple v, i.e., the fim chages a lowe intoductoy pice to induce some advance selling among consumes. Because all consumes have identically zeo suplus fom a delayed puchase, if the fim adopts quick esponse and aises the consume expectation of poduct availability ( ˆî), the fim does not aise the expected suplus to any consumes fom a delayed puchase. Thus, quick esponse no longe shifts demand; the only effect emaining is matching supply and demand, hence quick esponse always has positive value. The following theoem summaizes this esult. Theoem 4. The incemental equilibium value of quick esponse with intoductoy picing is always positive if c 2 apple v. The key to Theoem 4 is that inceasing pices ove time povides consumes with geate incentive to puchase ealy, shifting demand fom late puchases to the ealie puchases. This effect counteacts the tendency of quick esponse to shift demand in the opposite diection. Thus, intoductoy picing and quick esponse ae complimentay in the sense that they enhance one anothe s value: inceasing pices educes costly demand shifting because of quick esponse, and quick esponse eliminates costly supply/demand mismatches (mismatches that ae paticulaly costly unde intoductoy picing because of the highe egula pice). Because of the assumption that consume values follow a two-point distibution, intoductoy picing in the pesent model completely eliminates stategic waiting in the sense that all consumes eceive zeo suplus fom a delayed puchase and hence consumes puchase ealy if and only if they have positive expected suplus (e.g., as if they wee nonstategic). Should consumes have moe than one positive valuation, in geneal intoductoy picing will not eliminate all stategic waiting. In that case, the adoption of quick esponse once again shifts demand to late times and deceases advance selling; nevetheless, inceasing pices ove time continues to educe the amount of stategic waiting that occus and hence minimizes the negative aspects of demand shifting because of quick esponse. Thus, although stategic waiting will not in geneal be eliminated by adopting intoductoy picing if consumes have a moe complicated valuation distibution, it will be educed by intoductoy picing, a fact that inceases the value of quick esponse elative to the fixed picing case. 8. Discussion Quick esponse systems o, moe geneally, leadtime eduction and apid inventoy eplenishment ae often suggested as potential panaceas to the ill effects of supply and demand mismatches. In this pape, we show that such stategies ae less valuable to the fim when consumes ae fowad looking and have uncetain value fo a poduct about which they lean ove time. Futhemoe, even if the fixed cost of implementing a quick esponse system is zeo, it is possible that the option to eceive additional inventoy afte a foecast update deceases the fim s pofit once the consume esponse to inceased availability is taken into account. In that egad, ou base model epesents a wost case scenaio fo the fim. In this scenaio, stategic customes that ae awae of and espond optimally to the fim s opeating stategy quick esponse can decease, and even make negative, the value of this opeational stategy. This is because the tangible outcome of quick esponse to consumes influences puchasing incentives in pecisely the wong way (fom the fim s point of view). 12 Manageially, these esults ae impotant fo thee easons. Fist, a fim may not wish to adopt quick esponse in this setting, because of the eduction in value caused by the optimal consume esponse to the fim s opeational capabilities. Second, ou model illustates that in cetain cases the fim may wish to mask its opeational capabilities fom consumes, i.e., to pevent them fom eacting optimally. Thid, these esults show that context mattes specifically, the chaacteistics of consumes and of the poduct when a fim detemines whethe to invest in opeational flexibility and whethe to publicize that investment. It is also woth noting that quick esponse is an opeational poxy fo (moe geneically) infomation. Taken in that context, ou esults on the value of quick esponse ae essentially esults on the value of accuate infomation concening poduct demand. The fact that quick esponse sometimes yields negative value suppots the maxim that ignoance can be bliss; the lack of accuate infomation about demand can seve as a commitment mechanism to keep inventoy scace and incease advance selling. 12 Indeed, even if the fim can cedibly commit to any abitay fill ate in eithe opeating egime, it is possible to show that the optimal action is to commit to identical fill ates in the quick esponse and single pocuement egimes (details available fom the autho upon equest). In this case, consumes ae ignoant to the use of quick esponse, and hence the demand shifting effect is eliminated; as a esult, pat (ii) of Theoem 1 no longe holds (i.e., the value of quick esponse cannot be negative) but pat (i) continues to hold (the value of quick esponse is educed by stategic consume behavio). So even in the best case scenaio in which consumes ae oblivious to the use of quick esponse, its value is loweed because of fowad-looking consume behavio when valuations ae uncetain.

13 Swinney: Selling to Stategic Consumes When Poduct Value Is Uncetain Management Science 57(10), pp , 2011 INFORMS 1749 These esults povide insight into when a fim should adopt a fast supply chain that allows action on impoved demand infomation. Quick esponse is most valuable in settings with known o easily detemined poduct value, wheeas it is less valuable if the poduct has difficult to ascetain o uncetain value to consumes. This suppots the application of quick esponse in industies such as fashion appael (Fishe and Raman 1996, Fedows et al. 2004) ove industies with moe complicated o innovative poducts such as electonics (Fishe 1997, Kishnan et al. 2010). Quick esponse can be paticulaly valuable if paied with intoductoy picing ( 7) but may be less valuable if consume etuns ae allowed and ae costly to the fim ( 6). As we have shown, the value of matching supply and demand depends not only on the eduction of lost sales and excess inventoy, but also on the stategic esponse of the fim s customes to inceased poduct availability. This esponse can be hamful (if advance selling deceases as a esult), beneficial (if costly etuns ae allowed and hoading is an issue), and even diminished o eliminated by the appopiate picing stategy (inceasing pices ove time in the optimal manne). Acknowledgments The autho thanks the depatment edito, associate edito, and two efeees, as well as Géad Cachon, Mashall Fishe, Haikesh Nai, Seguei Netessine, Tava Olsen, Avind Tipathi, and Senthil Veeaaghavan, and semina paticipants at the Univesity of Pennsylvania, the Univesity of Texas at Dallas, the Univesity of Rocheste, the Univesity of Washington, New Yok Univesity, London Business School, Washington Univesity in St. Louis, Nothwesten Univesity, the Univesity of Chicago, Columbia Univesity, Duke Univesity, Stanfod Univesity, and the INFORMS 2007 Annual Meeting in Seattle fo numeous comments and suggestions. Appendix. Poofs Poof of Lemma 1. Consumes who eceive a high value signal puchase ealy if É h 4Å5v É p 0 and if the expected suplus fom puchasing ealy is geate than the expected suplus fom delaying, i.e., if É h 4Å5v É p Ñ ˆîÉ h 4Å54v É p5. Because Ñ ˆî apple 1, it is tue that expected suplus fom a delay is inceasing in Å at a slowe ate than expected suplus fom an immediate puchase. Futhemoe, if Å = 1, then ealy suplus is v É p and late suplus is Ñ ˆî4v É p5, i.e., ealy suplus is weakly geate than late suplus. If Å = 1/2, the opposite elationship holds (fom ou assumption that É l 41/25v É p<0). Thus, thee exists some (unique) citical Å such that, fo all Å > Å, the inequality above is stict, wheeas fo Å < Å, the inequality is violated. É Poof of Lemma 2. Given the fim s belief ˆÅ concening the citical signal stength, ealy demand is composed of two consume segments: those with high value and coect signals and those with low value and incoect signals. Let é 1 4 ˆÅ5 = à R 1 xg4x5 dx + 41 É à5r 1 41 É x5g4x5 dx. The ˆÅ ˆÅ total demand fom these consumes is thus N é 1 4 ˆÅ5. All consumes with signal stengths less than ˆÅ delay puchasing, and only those with high value will puchase the poduct. Late demand is thus consumes who have high value and eceived a low value signal, and consumes who have high value, eceived coect signals, and chose to delay thei puchase. Let é 2 4 ˆÅ5 = à R 1 41 É x5g4x5 dx + à R ˆÅ xg4x5 dx, 1/2 1/2 such that the total demand fom these consume segments is N é 2 4 ˆÅ5. The total fim demand is thus D = N é4 ˆÅ5, whee é4 ˆÅ5 = é 1 4 ˆÅ5 + é 2 4 ˆÅ5. The fim s expected pofit is è4q5 = 6p min4q1 D5 É c 1 q7, which is a concave function of q yielding an optimal inventoy level satisfying P4D < q5 = 4pÉc 1 5/p. Substituting fo D, we see that the best eply function is q4 ˆÅ5 = é4 ˆÅ5F É1 44p É c 1 5/p5. We may now deive the equilibium by imposing the ational expectations hypothesis, which implies ˆÅ = Å sp and ˆî = î4q sp 1Å sp 5. With a andom allocation ule, the actual second fill ate fo any 4q1 Å5 is given by î4q1 Å5 = 6min44q É é4å5n é4å5n 5/é4Å5N 7. Substituting the fim s optimal inventoy level, we see that in any equilibium, î4q1 Å5 = Z F É1 44pÉc 1 5/p5 0 Z à + F É1 44pÉc 1 5/p5 f 4x5 dx F É1 44p É c 1 5/p5 É x x f 4x5 dx1 which is independent of Å. Next, note that the left-hand side of (2) is inceasing in Å with a slope of one, and the ighthand side is inceasing independent of Å in any equilibium because î4q1 Å5 is independent of Å in equilibium. Hence, thee clealy exists a unique Å that satisfies (2), and thus the equilibium to the game is unique. É Poof of Lemma 3. Because the fim opeates in the QR egime, the only ational belief of the consume population is that ˆî = 1; because the quick esponse pocuement is subgame pefect, the fim will satisfy all demand. Hence, the consume best eply is independent of any fim actions, and is dictated by the solution to (2) with ˆî = 1, which implies Å q = 41 É à5p/441 É à5p + à4v É p541 É Ñ55. It follows that Å sp apple Å q fo any equilibium fill ate in the single pocuement egime. The fim s pofit function is è4q5 = 6pDÉ c 1 q É c 2 4D É q5 + 7, whee D = N 4é 1 + é 2 5 and é 1 and é 2 as ae in the poof of Lemma 1. It follows that the fim s best eply R exists and is unique, given by q4å q 5 = 4à + 41 É à5 1 Å q41 É x5g4x5 dx5f É1 44c 2 É c 1 5/c 2 5, hence the equilibium existence and uniqueness esults follow. This futhemoe implies 41 É à5 R 1 Å sp41 É x5g4x5 dx 41 É à5r 1 Åq41 É x5g4x5 dx, and it follows that total equilibium demand to the fim is geate in the SP egime than in the QR egime, yielding q q apple q sp. É Poof of Theoem 1. (i) Let = è q É è sp be the incemental equilibium value of quick esponse. Recall that é4å q 5N is the equilibium total demand in the QR egime, and é4å sp 5N is the demand in the SP egime,

14 Swinney: Selling to Stategic Consumes When Poduct Value Is Uncetain 1750 Management Science 57(10), pp , 2011 INFORMS whee é4å 5 = à + 41 É à5 R 1 41 É x5g4x5 dx and Å = Å 41 É à5p/441 É à5p + à4v É p541 É Ñî 55. Fom the expession fo Å, Å sp Ñ=0 = Åq Ñ=0 = 41 É à5p/441 É à5p + à4v É p55 apple Åsp Ñ=1 apple Å q Ñ=1, whee, e.g., Åsp Ñ=0 denotes the equilibium citical signal stength in the SP egime when Ñ = 0. Because é 0 4Å 5 < 0, é4å q Ñ=15 apple é4åsp Ñ=15 apple é4åq Ñ=0 5 = é4åsp Ñ=05. The equilibium fim pofit is, in the SP egime, è sp = é4å sp 5 6p min4n 1 F É1 44p É c 1 5/p55 É c 1 F É1 44p É c 1 5/p57, and in the QR egime, è q = é4å q 5 6p min4n 1 F É1 44c 2 É c 1 5/c 2 55 É c 1 F É1 44c 2 É c 1 5/c p É c 2 54N É F É1 44c 2 É c 1 5/c In each expession, the tem inside the backet is the maximum expected pofit without stategic customes (i.e., a taditional newsvendo and a newsvendo with quick esponse, espectively). Denote the backet tem in egime R by B R, R = sp1 q. Note that B q B sp. The incemental value of QR is thus = é4å q 5B q É é4å sp 5B sp. When Ñ = 0, this implies Ñ=0 = é4å sp Ñ=0 54Bq É B sp 5, and when Ñ = 1, Ñ=1 = é4å q Ñ=1 5Bq É é4å sp Ñ=1 5Bsp apple é4å sp Ñ=1 54Bq É B sp 5 apple Ñ=0, which poves the esult. (ii) Define è q 4q5 = 6pD É c 1 q É c 2 4D É q5 + 7, whee D is the total demand at the fim (a function of Å q ). Let è q be the equilibium pofit of the fim with quick esponse, and let è sp be the equilibium pofit without QR. Diffeentiating è q with espect to c 2, we have dè q dc 2 = èq 4q5 = É P4D>q q 5 = É1 + c 2 É c 1 < 00 c 2 q=q q c 2 Thus, the equilibium pofit of the fim is deceasing in c 2. In the limit as c 2! p, the magin on each unit sold that is pocued via QR goes to zeo. The fim s pofit effectively becomes the same as if it did not have QR capabilities, except in equilibium, moe consumes will delay puchasing than if the fim did not have QR. Thus, lim c2!p è q = è sp ó Å=Å q apple è sp ó Å=Å sp. É Poof of Theoem 2. We use the subscipt to denote equilibium values with etuns. The poofs of equilibium existence and uniqueness ae simila to Lemmas 2 and 3, and ae omitted. With consume etuns, any consumes who puchase ealy and ae dissatisfied with the poduct will etun the item. Because we assume that these poducts ae esalable, the total demand to the fim is simply àn. Thus, the expected pofit (without quick esponse) is è sp 4q5 = 6pàN É p4àn É q5 + É c 1 q É 4 f É c 541 É à5n R 1 Å sp 41 É x5g4x5 dx7, whee Å sp efes to the equilibium citical consume signal stength with etuns, detemined by equating ealy puchase and late puchase suplus, yielding Å sp = 4h + c 541 É à5/44h + c 541 É à5 + à4v É p541 É Ñ ˆî55. Diffeentiating è sp 4q5, we see dè sp 4q5 dq = p41 É F 4q/à55 É c 1 and dèsp 4q5 = Épf 4q/à50 dq Hence, è sp 4q5 is concave in q and yields an optimal inventoy level equal to q sp = àf É1 4p É c 1 /p5. Note that the optimal inventoy level is independent of the citical signal stength, Å sp, and as a esult so is the fill ate, which we denote î sp. Thus, dè sp /dñ = 4 f É c 541 É à5 å41 É Å sp 5g4Å sp 54dÅ sp /dñ5. Because då sp dñ = Åsp à4v É p5î sp 4h + c 541 É à5 + à4v É p541 É Ñî sp 5 > 01 it follows that dè sp /dñ 0 if f c (and dè sp /dñ apple 0 if f apple c ). Similaly, in the quick esponse egime, as in the case without etuns, quick esponse induces ˆî = 1, hence Å q = 4h + c 541 É à5/44h + c 541 É à5 + à4v É p541 É Ñ55 and Å sp apple Å q fo any equilibium belief concening the fill ate in the SP egime. The expected pofit with quick esponse is è q 4q5 = 6pàN É c 2 4àN É q5 + É c 1 q É 4 f É c 5 41 É à5n R 1 41 É x5g4x5 dx7. Diffeentiating è q 4q5, we see dè q 4q5 dq Å q = c 2 41 É F 4q/à55 É c 1 and dèsp 4q5 = Éc dq 2 f 4q/à50 Pofit è q 4q5 is thus concave in q and yields an optimal inventoy level equal to q q = àf É1 44c 2 É c 1 5/c 2 5. Again, the optimal inventoy level is independent of the citical signal stength, Å q, and as a esult so is the fill ate, î sp. As befoe, whee dè q dñ = 4 f É c 541 É à5å41 É Å q 5g4Å q då q 5 dåq dñ 1 dñ = à4v É p5 Åq 4h + c 541 É à5 + à4v É p541 É Ñ5 > 01 hence dè q /dñ 0 if f c and dè q Next, let Á sp è sp = 6pàN É p4àn É q sp = Á sp É 4 f É c 541 É à5å R 1 Å sp /dñ apple 0 if f apple c. 5 + É c 1 q sp 7 such that 41 É x5g4x5 dx, and let Á q = Á q É 4 f É c 5 be defined analogously such that è q 41Éà5å R 1 Å q 41Éx5g4x5 dx. Note that Á sp and Á q ae the optimal pofits (without and with quick esponse, espectively) of a newsvendo facing demand àn, hence Á q both ae independent of Ñ. Thus, è q If f É è sp = Á q É Á sp + 4 f É c 541 É à5å c, then clealy è q Å q and thus è q because Å sp apple Å q then because Å sp É è sp, è q Z Å q Å sp Á sp and 41 É x5g4x5 dx0 è sp. Lastly, if Ñ = 0, then Å sp = = Á q É Á sp. If Ñ > 0 and f c, then É è sp Á q É Á sp. If Ñ > 0 and f apple c, apple Å q, è q É è sp apple Á q É Á sp. É Poof of Theoem 3. The subscipt denotes equilibium values with fixed endogenous picing. The existence of an equilibium is immediate, because we have aleady shown an equilibium exists to the inventoy/puchasing subgames and the fim s expected payoffs ae bounded (by 0 and N 4v É c 1 5) and its stategy space is a compact inteval 6c 1 1 v7 in the picing game (6c 2 1 v7 when using quick esponse; if the pice is less than c 2 but geate than c 1, the fim will neve use QR and evets to the SP egime). Let è q, pq, and qq be the equilibium pofit, pice, and inventoy of the fim with quick esponse and fixed picing, and let è sp be the equilibium pofit without QR. Diffeentiating è q with espect to c 2, we have dè q q q = è + è dc 2 c 2 p dp q q + è dc 2 Å då q q apple è 0 dc 2 c 2 Obseve that eithe è q / p = 0 (the fim pices at an inteio optimum) o dp q /dc 2 = 0 (the fim pices on the bounday, i.e., c 2 o v). Unlike the case without picing, då q /dc 2 in geneal does not equal 0. This is because dp q /dc 2 0 and då q /dp 0 in othe wods, highe costs of quick esponse lead to highe pices (a natual esult) and highe pices lead to moe consumes waiting, see Equation (2). Because

15 Swinney: Selling to Stategic Consumes When Poduct Value Is Uncetain Management Science 57(10), pp , 2011 INFORMS 1751 è q / Å apple 0 (the moe consumes that wait, the lowe the fim s pofits), it follows that the 4 è q / Å54dÅq /dc 25 apple 0. Finally, because dè q q apple è = É P4D>q q dc 2 c 5 = É1 + c 2 É c 1 < 01 2 c 2 we find that pofit is deceasing in c 2, pecisely as in the case without picing, and è q É èsp is similaly deceasing in c 2. In the limit as c 2! v, the fim s optimal pice with QR goes to v, and magin on each unit sold that is pocued via QR goes to zeo. Hence, the fim s pofit effectively becomes the same as if it did not have QR capabilities, with two caveats: it is constained to pice at v (in the SP egime, the fim can pice anywhee in the inteval 6c 1 1 v7), and in equilibium, moe consumes will wait than if the fim did not have QR because QR natually shifts demand. In othe wods, if c 2 = v, è q É èsp = èq ó p=v É max p26c1 1v7 è sp apple è q ó p=v É è sp ó p=v apple 0, whee the last inequality follows fom Theoem 1. É Poof of Theoem 4. The poof is omitted; because consumes have zeo suplus fom a delayed puchase they ae essentially myopic. É Refeences Akan, M., B. Ata, J. Dana Revenue management by sequential sceening. Woking pape, Nothwesten Univesity, Evanston, IL. Alexandov, A., M. A. Laiviee Ae esevations ecommended? Woking pape, Nothwesten Univesity, Evanston, IL. Aviv, Y., A. Pazgal Optimal picing of seasonal poducts in the pesence of fowad-looking consumes. Manufactuing Sevice Ope. Management 10(3) Cachon, G. P., R. Swinney Puchasing, picing, and quick esponse in the pesence of stategic consumes. Management Sci. 55(3) Cachon, G. P., R. Swinney The value of fast fashion: Quick esponse, enhanced design, and stategic consume behavio. Management Sci. 57(4) Cao, F., V. Matínez-de-Albéniz The impact of quick esponse in inventoy-based competition. Manufactuing Sevice Ope. Management 12(3) Chevalie, J., A. Goolsbee Ae duable goods consumes fowad-looking? Evidence fom college textbooks. Quat. J. Econom. 124(4) Davis, S., E. Gestne, M. Hagety Money back guaantees in etailing: Matching poducts to consume tastes. J. Retailing 71(1) DeGaba, P Buying fenzies and selle-induced excess demand. RAND J. Econom. 26(2) Eppen, G. D., A. V. Iye Impoved fashion buying with Bayesian updating. Ope. Res. 45(6) Fedows, K., M. A. Lewis, J. A. D. Machuca Rapid-fie fulfillment. Havad Bus. Rev. 82(11) Fishe, M What is the ight supply chain fo you poduct? Havad Bus. Rev. 75(2) Fishe, M., A. Raman Reducing the cost of demand uncetainty though accuate esponse to ealy sales. Ope. Res. 44(1) Huang, T., J. A. Van Mieghem Ae you willing to click? Advance demand infomation and pice discimination unde stategic consume behavio. Woking pape, Nothwesten Univesity, Evanston, IL. Isael, M Who can see the futue? infomation and consume eactions to futue pice discounts. Woking pape, Nothwesten Univesity, Evanston, IL. Kalai, E., E. Lehe Rational leaning leads to nash equilibium. Econometica 61(5) Kishnan, H., R. Kapuscinski, D. A. Butz Quick esponse and etaile effot. Management Sci. 56(6) Li, C., F. Zhang Advance demand infomation, pice discimination, and peode stategies. Woking pape, Univesity of Connecticut, Stos. Li, Q., A. Ha Reactive capacity and inventoy competition unde demand substitution. IIE Tans. 40(8) Liu, Q., G. van Ryzin Stategic capacity ationing to induce ealy puchases. Management Sci. 54(6) Liu, Q., W. Xiao Selling to heteogeneous customes with uncetain valuations unde etuns policies. Woking pape, Hong Kong Univesity of Science and Technology, Clea Wate Bay, Kowloon. O Donnell, J Retailes ty to tain shoppes to buy now. USA Today (Septembe 25), industies/etail/ sales-shopping-usat_x.htm. Osadchiy, N., E. Bendoly Ae consumes eally stategic? Implications fom an expeimental study. Woking pape, Emoy Univesity, Atlanta. Pasad, A., K. E. Stecke, X. Zhao Advance selling by a newsvendo etaile. Poduction Ope. Management 20(1) Richtel, M A yea late, the same scene: Long lines fo the elusive Wii. New Yok Times (Decembe 14), Rosenbloom, S Luxuy stoes tim inventoy and discounts. New Yok Times (Novembe 18), Shulman, J. D., A. T. Coughlan, R. C. Savaskan Optimal estocking fees and infomation povision in an integated demand-supply model of poduct etuns. Manufactuing Sevice Ope. Management 11(4) Slatalla, M Hot holiday toys: A paent s stategy. New Yok Times (Novembe 14), 11/14/technology/online-shoppe-hot-holiday-toys-a-paent-s -stategy.html?pagewanted=2. Soysal, G The dynamics of demand in seasonal goods industies: An empiical analysis. Ph.D. thesis, Nothwesten Univesity, Evanston, IL. Stock, J., T. Speh, H. Shea Managing poduct etuns fo competitive advantage. Sloan Management Rev. 48(1) Stoll, J. D How GM handles a hit: Build fewe. Wall Steet Jounal (Octobe 31), SB html. Su, X Consume etuns policies and supply chain pefomance. Manufactuing Sevice Ope. Management 11(4) Su, X., F. Zhang Stategic consume behavio, commitment, and supply chain pefomance. Management Sci. 54(10) Su, X., F. Zhang On the value of inventoy infomation and availability guaantees when selling to stategic consumes. Management Sci. 55(5) Xie, J., S. M. Shugan Electonic tickets, smat cads, and online pepayments: When and how to advance sell. Maketing Sci. 20(3)