Spackling: Smoothing Make-to-Order Production of Mass-Customized. Products with Make-to-Stock Production of Standard Items

Transcription

1 pakling: moothing Make-to-Order rodution of Mass-ustomized roduts with Make-to-tok rodution of tandard Items yle D. attani he elley hool of Business, Indiana University ly Dahan Anderson hool at ULA Glen M. hmidt David les hool of Business, University of Utah Otober 30, 007 Aknowledgements: he authors thank seminar partiipants at the tanford M department and the following business shools for their helpful feedbak on this paper: W.. arey, Darden, les, ller, uqua, Haas, elley, enan-lagler, Mombs, Olin, Owen, uk, and the University of Wisonsin-Madison. orresponding author: yle attani, he elley hool of Business, Indiana University, Bloomington, IN UA. (8) kattani@indiana.edu

2 pakling: moothing Make-to-Order rodution of Mass-ustomized roduts with Abstrat Make-to-tok rodution of tandard Items onsider a mass ustomizer who produes multiple variants of a produt in make-to-order fashion, and who also produes some standard variants as make-to-stok. We evaluate priing and prodution issues from a joint marketing and operations perspetive. Marketing determines pries while operations hooses between three prodution strategies as it sets apaity. A key result is that under the logit-based assumption for our marketing model, it is optimal for all mass-ustomized produts to be pried at the same absolute dollar markup, implying all add-on options are pried at ost. Operations onsiders the following prodution strategies: ) a fous strategy where the firm produes ustom variants in a flexible plant and standard items in an effiient plant; ) a pure-spakling strategy where it produes everything in a flexible plant, first manufaturing ustom produts as demanded eah period, and then filling in, or spakling, the prodution shedule with make-to-stok output of standard produts to restok inventory; or 3) a layered-spakling strategy where it uses an effiient plant to make some of its standard items and a flexible plant where it spakles. A seond key result is to identify the optimal prodution strategy as determined by the tradeoff between the ost premium for flexible (as opposed to effiient) prodution apaity and the opportunity osts of idle apaity. We illustrate our framework with data from a messenger bag manufaturer. pakling amortizes fixed osts more effetively and thus has the potential to inrease profits from mass ustomization. eywords: mass ustomization, logit, onstant markup, spakling, flexible apaity, outsouring, offshore prodution

3 pakling: moothing Make-to-Order rodution of Mass-ustomized roduts with Make-to-tok Output of tandard Items. Introdution imbuk, a an raniso manufaturer of biyle messenger bags, has an Internet site where ustomers onfigure and order mass-ustomized bags shipped diretly from the manufaturer. he Internet hannel takes advantage of imbuk s flexible manufaturing apabilities and omplements the firm s traditional retail hannel where pre-onfigured (standard) bags are sold. imbuk s flexible an raniso fatory an produe an individual bag of any onfiguration and deliver it within days. At the time of this researh, the an raniso fatory was being used to fill demand for both the Internet hannel and the traditional retail hannel. In order to redue prodution osts, imbuk was onsidering moving prodution offshore for the standard make-to-stok (M) bags sold in its traditional hannel. While the off-shore apaity would be less expensive, it would not be able to fill demand for the mass-ustomized make-to-order (MO) bags sold in the Internet hannel in a timely manner the an raniso fatory would ontinue to produe to meet this MO demand. (We use the term M to refer to prodution in antiipation of demand, with output being added to inventory, and MO to indiate prodution that fills speifi end-ustomer orders after they are reeived.) imbuk s management team wondered what effet a shift to off-shore prodution of standard bags would have on overall osts, inluding at the flexible domesti fatory where the ustom bags would ontinue to be produed. his paper developed as we sought to analyze imbuk s situation. hould imbuk utilize effiient (off-shore) apaity? Or, should it ontinue to produe standard off-the-shelf M bags using the flexible an raniso plant, keeping a mix of MO and M in the same fatory? Under the latter option it would ontinue to employ a strategy we all spakling, where it first makes ustom MO bags At imbuk, standard and ustom produts are assoiated with retail stores and internet sales, respetively. In reality, the distribution hannel and produt type need not be linked it ould also sell standard bags diretly to ustomers and ustomized bags through retailers. he analysis would be similar.

4 as demanded eah period, and then fills in, or spakles, the prodution shedule with standard M produt, to restok inventory. 3 We were also interested in how imbuk should prie the massustomized bags. In partiular, how should the multitude of add-on options be pried? hese issues are not unique to imbuk and are strategi in nature. or example, senior managers at automobile manufaturers have been talking for a deade or more about the five-day ar, a plan for mass-ustomized ars to be produed only after orders are reeived, shipping within five days (Robison, 999). Among many detailed suggestions and analysis, Holweg (003) ites the need for volume flexibility and a build-to-order system for a five-day (or three-day) strategy to be viable. Volume flexibility is required to meet the day-to-day demand unertainty that is inherent when implementing mass ustomization, sine ustomers may prefer not to wait until orders an be bathed. Our proposed spakling strategy would assist automobile manufaturers in addressing the higher ost of this volume flexibility. As another example, onsider issues of keen interest to senior management at Dell In. Dell fouses on a single diret hannel and must determine the optimal prodution and priing strategies for its mass-ustomized desktop personal omputers. hould Dell use effiient off-shore prodution for long lead-time ustomers along with loal flexible apaity for short lead-time ustomers, or should it use loal apaity for both? How should Dell prie all the add-on options offered on its mass-ustomized units? We model these deisions from a joint marketing and operations perspetive. On the demand (i.e., marketing) side, we fous on the issue of priing the numerous produt onfigurations that arise in a mass-ustomization setting. We assume that ustomer hoie of produt onfiguration follows the logit representative ustomer framework as desribed in Ben-Akiva and Lerman (985). imilar to Anderson, et al. (99), we find the optimal priing poliy for the various onfigurations of a mass-ustomized produt is one of onstant markup. hat is, the firm adds the same dollar markup to the produt, independent of the onfiguration the ustomer has hosen (see 3 and heorem ), with the markup level 3 he Amerian Heritage Ditionary of the nglish Language: ourth dition 000 defines spakle as A trademark used for a paste designed to fill raks and holes in plaster before painting or papering. his trademark often ours in lowerase and as a verb 3

5 effetively set by the produt onfigurations most highly valued by the ustomer. Assuming the massustomized produt variants an be thought of as some base onfiguration plus a set of add-on options (suh as would be identified on the window stiker of a new ar), this priing poliy means all add-on options should be pried at ost (with all margin effetively inluded in the prie of the base onfiguration). On the operations side, we find the optimal levels for effiient and flexible apaities, a deision whih defines the firm s use of one of three possible strategies: fous, pure spakling, or layered spakling. A fous strategy (see the top frame in igure ) uses both types of apaity in a speialized (foused) manner: the flexible fatory meets daily (or other time period) demand for ustom produts using an MO proess, requiring enough apaity to meet a high daily demand realization, while the effiient fatory meets demand for standard produts via an M proess. Demand for standard items is realized at the end of some planning period, at whih time overage and underage osts are assessed. With the layered-spakling strategy (depited in the middle frame in igure ), the firm again uses two fatories, a flexible one and an effiient (e.g., overseas) fatory. With spakling, the firm s first priority in the flexible fatory is to produe ustom produts via MO. However, orders for ustom produts are uneven (unertain), yielding an undesirable prodution profile ompared to smooth shedules that would allow for higher apaity utilization. he firm spakles (smoothes) the prodution shedule by using the same (flexible) prodution apaity to first produe all ustom produts and then using the remaining apaity to produe standard produts in M fashion. With layered-spakling, in addition to the flexible fatory (that employs spakling) the firm also uses an effiient fatory to produe additional standard produts in M fashion. he result is that MO prodution in the flexible fatory losely traks demand for ustomized produts, while M prodution of standard produts equals the sum of the daily surplus of flexible apaity plus another layer of output from the effiient fatory. M prodution traks demand for standard produts not over the short-run but rather over the longer-run, with some inventory temporarily built-up, and meets the level of demand determined by the ritial fratile of a newsvendor problem that we develop herein. 4

6 igure ous, Layered pakling, and ure pakling trategies. ous: One flexible fatory produes ustom produts, and one effiient fatory produes standard produts. apaity rodution apaity and output lexible atory Unused flexible apaity Daily output of ustom Realized daily produts = daily demand demand for ustom produts Days (or other time period) rodution apaity and output ffiient atory ntire demand of standard produts is realized after days, with underage and overage osts. Daily prodution of standard produts = apaity Days (or other time period) Layered pakling: One flexible fatory produes ustom produts and fills any remaining apaity by produing standard produts (left); and one effiient fatory produes only standard produts (right). apaity rodution apaity and output lexible atory Daily prodution of standard produts Daily prodution of ustom Realized daily produts = daily demand demand for ustom produts Days (or other time period) rodution apaity and output ffiient atory ntire demand of standard produts is realized after days, with underage and overage osts. Daily prodution of standard produts = apaity Days (or other time period) ure pakling: One flexible fatory produes ustom produts and fills remaining apaity by produing standard items. apaity rodution apaity and output Daily prodution of standard produts Daily prodution of ustom Realized daily produts = daily demand demand for ustom produts Days (or other time period) Avg. daily prodution of standard produts (entire demand for standard produts is realized after days, with overage and underage osts) Avg. daily output of ustom produts = avg. realized demand of ustom produts Under a pure-spakling strategy, the firm utilizes only one flexible fatory (see the bottom frame of igure ). imilar to the layered-spakling strategy, eah day the flexible fatory first produes the ustom produts demanded that day, and then fills any remaining apaity with prodution of standard 5

7 produts. he firm sets total apaity of this one flexible fatory to meet a ritial fratile of a newsvendor problem (again, as desribed herein). With both the layered and pure spakling strategies, the level total prodution output allows for higher utilization of the flexible apaity and improved effiieny. A ontribution of this paper is to identify the onditions under whih the various strategies of fous, layered spakling, and pure spakling are optimal. We applied the model to imbuk s situation. We gathered data on ustomer preferenes to use diretly in the marketing model, while on the operations side we used ost and demand information provided by imbuk to gain insights as to the best use of effiient and flexible apaity. Beause it promised short lead times, imbuk planned to ontinue to make its mass-ustomized produts in its domesti fatory. hould imbuk ontinue to use a pure-spakling strategy, produing all ustom and standard produts in the flexible domesti fatory? Alternatively, should it adopt a layered-spakling strategy (with some standard produts made overseas, in addition to the ones made domestially via the spakling strategy)? Or, finally, should it go to a fous strategy (with ustom produts made domestially and with standard produts made stritly overseas)? imbuk s management ould alulate readily the diret unit ost savings the fous strategy proffered from the use of effiient prodution (redued unit ost times units produed). In ontrast, the ounter-benefits that spakling yielded by making better use of apaity resulted in lower amortized fixed ost per unit whih were less apparent. urprisingly, we found that under a reasonable senario, the urrent pure-spakling strategy remained optimal imbuk should not move any prodution offshore, in spite of the available lower prodution osts. In we frame our work in the ontext of other work related to ahieving mass ustomization. We then build our model in 3 we develop the marketing model assuming osts are known, and then feed the resulting pries into the operations model in 4. o illustrate some of the insights our model offers, in 5 we use the results to analyze imbuk s situation. We onlude with a disussion and summary in 6. 6

8 . Related Literature A firm using mass ustomization strives to produe many variants of the produt so that eah ustomer s needs are individually met while maintaining/retaining the low ost of mass prodution. trategies for ahieving these (historially) diverging objetives (of ustomization and low ost) have been a topi of muh reent attention. pakling (in either the pure or layered form) is one tool the firm an employ to supply a wider variety of produts at low ost in the fae of unertain demand. Our notion of spakling ontributes to the body of researh that demonstrates the benefit of flexible resoures. In seeking the optimal mix of less ostly, dediated apaity and more expensive, flexible apaity, our researh builds on the model of Van Miegham (998).. In his model the firm deides between prodution using only dediated apaity, only flexible apaity, or a mix of both, as determined by the marginal ost of flexible apaity. All prodution is MO, in that apaities are alloated to produts after demand is observed. Van Mieghem finds that it may be advantageous to invest in more expensive flexible resoures even with perfetly positively orrelated produt demands. We also find support for expensive flexible resoures but in a different framework: we assume that prodution an be MO or M and that both fixed and variable osts are a funtion of the type of prodution. In our setup, flexible resoures an improve apaity utilization through prodution smoothing. ostponing produt differentiation is another form of prodution flexibility that an redue the risk of under-produing or over-produing varied produt onfigurations. Graman and Magazine (00) show that if postponement involves even only a relatively small fration of prodution, the benefits are nearly as great as if the firm ould delay differentiation for all units. Gupta and Benjaafar (00) show that postponement helps reonile the needs of high variety and quik response time. In our setting, risks of under- or over-produing are partly eliminated by the firm s offering of ustom produts. However, ustom produts require more expensive apaity, and there is a risk of aquiring too muh or too little. Our proposed spakling strategy mitigates this risk. ynan and Rosenblatt (995) study the tradeoff between lower-ost M prodution and higher- 7

9 ost MO (or assemble-to order, AO) prodution for a single standard produt. Rudi (000) also assumes a single produt and onsiders the tradeoff between low-ost, long-lead time M prodution in the ar ast and higher-ost loal prodution with short lead times and pre-positioning of omponents (AO). Mukstadt, et al. (00) investigate the use of MO prodution for items (alled B/-type) with highly errati demand while using M prodution for more preditable A-type items. hey develop a omputationally effiient approah for setting inventory base-stok levels and for alloating apaity, omparing performane to an alternative where inventory and apaity deisions are made prior to observing demand (M). In ontrast to the above artiles, our model onsiders a mass-ustomized produt in addition to a standard produt, and only the standard produts might benefit from lower-ost off-shore prodution. he ustomer hooses either a standard produt that an be M or a ustom MO produt, and we determine the appropriate prodution strategy. By produing both standard and ustom produts using flexible apaity, the firm more effiiently utilizes the flexible apaity that is needed to produe the ustom produts. Arreola-Risa and Deroix (998) study the optimality of a strit MO poliy versus a strit M poliy for a ompany produing multiple heterogeneous produts at a shared manufaturing faility. hey model demands as independent oisson proesses with different arrival rates and derive optimality onditions for MO versus M poliies onsidering tradeoffs in inventory holding and bakordering osts. hey onsider whether a speifi produt should be built MO or M. Rajagopalan (00) also onsiders the firm s portfolio of produts using a model to determine whih produts should be made to order and whih should be made to stok. We fous on a different problem: determining whether effiient apaity should be employed to produe M items. In our setting, standard produts are always produed as M and ustom produts as MO. he idea of dediated apaity and reative apaity, as put forth by isher and Raman (996), is also related to our approah. arly in the prodution season, apaity is dediated to produts having low demand variability (essentially, prodution is M). apaity used late in the season an reat to loserto-atual demand (essentially, prodution is MO). In isher and Raman, the fous is on the prodution 8

10 sequene given the apaity (i.e., whih produts should be produed at eah stage of the season) while we fous on the optimal struture of the apaity. Additionally, we require MO prodution for a subset (i.e., the mass-ustomized segment) of our demand. Variety and lead-time are pertinent issues in our setting. Lanaster (990) offers a broad survey of papers addressing the variety issue. Li (99) disusses lead-time issues. If ustomers were always willing to wait, all items would be produed as MO without any risk. He finds a boundary between M and MO as refleted in newsvendor type results. alvador, et al. (00) disuss how manufaturing harateristis affet the appropriate type of modularity in produt family arhiteture and omponent souring to mitigate the negative impat of produt variety. hey suggest that when the desired level of produt variety is low relative to total prodution volume, omponent swapping modularity helps to maximize operational performane. We present an additional strategy to maximize operational performane when there is a mix of high variety ustom produts along with standard produts. Blakburn et al. (99) suggest that offering inreased variety and shorter response times yields strategi advantages. or a firm that has hosen to offer high variety and quik response at a speifi level, our researh analyzes alternate strategies by whih a firm an fill its orders most effiiently. We address the variety issue by giving the ustomer a hoie between standard and ustom produts, using the logit framework; the issue of ustomer willingness-to-wait is folded into a produt s reservation prie. Alptekinoglu and orbett (007) study ompetition between a mass ustomizer and a mass produer in a game-theoreti setting where ustomers have heterogeneous preferenes on a single taste attribute. he mass produer an hoose to invest in more flexible apaity (ultimately being able to math the mass ustomizer s flexibility). hey find that the mass produer faing ompetition from a mass ustomizer hooses to offer lower produt variety ompared to a monopolist. While our researh is not in a ompetitive setting, we present a strategy to help a mass ustomizer apitalize on the heterogeneous ustomer preferenes for both standard and ustom produts. Our researh also ontributes to a growing literature that touhes on the integration of marketing and operations management deisions; f., hase (996), liashberg and teinberg (993), armarkar 9

11 (996), Lovejoy (998), van Ryzin and Mahajan (999), and Verma, et al. (00). Our fous solution is similar to van Ryzin and Mahajan (999) who use the multinomial logit model in a newsvendor setting and show that the optimal set of stoking levels has a simple struture. 3. Marketing Model for riing Mass-ustomized Units In this setion, we onsider the priing deision for a mass-ustomized produt where the ustomization arises through options added or subtrated from a base produt. (We refer to these as addon options). We use a standard logit formulation to develop a marketing model whih yields optimal pries for eah produt variant. he resulting produt margins for the mass-ustomized produts, along with exogenous parameters for the standard produts, are fed into the operations model (see 4) whih determines the optimal apaities. We apply the integrated marketing and operations models to the ase of imbuk in 5. We aept as given the base produt and the menu of ustomizable features (i.e., add-on options) the firm offers on the produt. We assume the firm has measured eah ustomer s willingness-to-pay for eah produt attribute, saled into dollars. his might be done, for example, through onjoint analysis and user design, as desribed by Dahan and Hauser (00). hus we an find eah ustomer s dollar-saled utility for any of the ustomized onfigurations available. Let produt j denote a speifi onfiguration of a mass-ustomized produt, with p j denoting its prie. ee able for a summary of notation used in the marketing model. Let r i j denote ustomer i s expeted dollar-equivalent utility for produt j, exluding prie: We refer to r i j as ustomer i s reservation prie for produt j. If viewed deterministially, then given the hoie of buying produt j or buying nothing, ustomer i buys at a prie below r i j. ee hmidt and orteus (000) and mith (986) for a similar approah. ah ustomer s net utility is saled by a prie-sensitivity parameter β i, suh that the net dollar value ustomer i attahes to produt j is β i (r i j p j ) ξ i j where ξ i j is a random error term assumed to be distributed Gumbel, i.e., double exponential, suh that ξ i j ξ k j is distributed logistially; hene the 0

12 standard logit formulation applies. Let q i j denote ustomer i s probability of purhase for produt j; q i j is a funtion of pries. If the ustomer has the hoie of buying one of w produt onfigurations, along with the option to buy nothing from the firm (for this buy nothing hoie we assume r i j p j = 0), then ustomer i s probability of purhase of produt j is given by the logit formulation as: q i j i i exp( β ( r )) j p j = w i i exp( β ( r )) k pk k = () able. Notation Used in the Marketing Model, 3 (in the order defined in the text) p j ales prie of ustomized produt j. r i j he maximum ustomer i is expeted to pay for produt j (her reservation prie). β i rie sensitivity parameter for ustomer i, assumed onstant over all i. ξ i j Random error term. q i j ustomer i s probability of purhase of produt j. β, r j q j he representative ustomer s parameters. j rodut j s unit ost, assumed onstant over volume. m j he markup on produt j, m j = p j j. W he number of ustomized produts offered. d j he maximum markup at whih the ustomer would buy produt j, d j = r j j. Π M xpeted profit, a funtion of pries p through p w. μ he number of ustomers. m he optimal markup, onstant aross all produts. We adopt the representative ustomer approah, whereby the parameters for a single ustomer are used to approximate the aggregate harateristis of the population. Ben-Akiva and Lerman (985) desribe this approah in their disussion of aggregate foreasting tehniques, and Anderson, et al. (99) further disuss its validity. One interpretation is that ξ i j is not a random error term, but rather aounts for ustomer preferene heterogeneity. hat is, the representative ustomer approah is valid if eah ustomer s hoie is deterministi and the variations in ustomer evaluations of a given produt are distributed Gumbel. rom here on, we simply use β and r j (without supersripts) to denote the harateristis of the representative ustomer, and use q j to denote the representative ustomer s purhase probability for produt j. he ustomer will hoose between buying any one of the possible produt onfigurations or nothing at all.

13 Let j denote produt j s per-unit ost, assumed to be onstant over volume. In reality, osts j are a funtion of the firm s prodution strategy (be it one of fous, pure spakling, or layered spakling); for simpliity of exposition we ignore this subtlety. (A possible extension of the analysis would be to iterate between the marketing model desribed here in 3 and the operations model in 4 to find the onvergent outome in terms of marketing s priing deision and operations apaity deision.) Let m j p j j denote the firm s dollar markup on produt j, and let w denote the number of produts marketed suh that j {,,, w}. Define d j r j j as the representative ustomer s disriminating markup for produt j; it is the markup the firm ould ahieve in selling produt j if it ould perfetly prie disriminate at the individual ustomer level (to the first degree), under deterministi ustomer hoie. he ustomer s net utility from buying produt j at prie p j is (r j p j ) = (d j m j ), sine d j r j j and m j p j j. he expression (d j m j ) replaes the expression (r j p j ) in (), and allows us to highlight the role of markup m, leading to a powerful result. Given osts for eah produt, marketing s optimization problem is to set pries (and therefore markups) to maximize expeted profit, denoted by Π M (p, p,, p w ). he marketing model does not onsider demand unertainty and thus assumes all demand is met from the population of µ possible ustomers. (Overage and underage osts ould be aounted for by iterating between the marketing and operations models.) Given the logit representative ustomer approah desribed earlier, and realling that q j is the representative ustomer s probability of purhase of produt j: w w (,,..., ) = ( ) = Π p p p μ p q μ m q M w j j j j j j= j= () Marketing s optimal priing strategy is stated in heorem, representing a version of the onstant absolute markup property that follows from this formulation. his property is noted in Anderson, et al. (99), p. 5, in a different ontext. We inlude in Appendix I a proof in the setting of our model.

14 HORM. If the representative ustomer is hoosing between buying any one of w produts offered by a single firm or buying nothing from the firm, the firm should prie all w produts at the same absolute dollar markup, denoted by m. he impliit solution for m, whih exists and is unique, is given by: m = β q j k = w j= q j, where: ( β ( j )) ( β ( dk m )) ( β j ) exp d m exp d = =. w βmexp ( βm ) exp (3) (4) heorem demonstrates that when applying the representative ustomer approah, the firm finds it optimal to prie any onfiguration of its produts at a onstant absolute dollar markup (but not at the same perent margin). If it deviates from m by, say, inreasing the markup of produt j, there are several ompeting onsequenes. It gets higher margin on produt j, but redues j s expeted unit sales (i.e., its probability of purhase). In turn, it inreases the expeted unit sales (and profit) derived from eah of the other produts, but diminishes total expeted unit sales. It is not lear a priori whih effet will dominate. heorem proves there is always a profit loss by deviating from m. Next, onsider the firm s priing strategy when its produt assortment is reated by adding or deleting individual features (i.e., add-on options) from a base unit, as in a mass-ustomization setting. or example, automobile manufaturers typially suggest a retail prie for a base onfiguration, along with pries for individual options. (he firm may also quote dedutions from the base prie if ertain features are deleted.) We assume additive osts: the ost of any finished unit is equal to the ost of the base unit plus the ost of the supplemental features. OROLLARY. Applying heorem to a strategy for priing add-on options, it is optimal for the firm to prie the base unit at ost plus m, and prie eah option to be added or deleted at ost. 3

15 orollary provides guidane to firms as they prie add-on options in a mass-ustomized setting. o the extent their demand meets the assumptions of the logit model, orollary shows that the firm need not optimize the prie of eah individual option, but only the prie of the base unit. he markup m that is inluded in the base-unit prie aounts for the desirability of the assortment of ustomized produts, whih depends to some extent on the menu of upgrade options. In other words, this result should not be interpreted to mean that the firm does not make any money on desirable options. he more desirable the add-on options, the higher the optimal markup m. onversely, if the firm eliminated all add-on options, then m would go down; otherwise ustomers would walk away without buying. ustomers always have a no-buy alternative. A further key assumption is that the prie sensitivity (b) for eah ustomer is not different aross the various produt onfigurations available. his is reasonable only if the resulting produt hoies are relatively similar. While the notion of priing all add-on options at ost seems ounterintuitive, some examples of this type of priing might be an auto dealer that advertises any ar on the lot for $99 over invoie, or a fast-food restaurant that will super-size your meal for $0.39, where $0.39 is the inremental ost of supersizing. Another example is a warehouse lub whose profits are roughly equal to the sum of its annual membership fees: the base produt is the membership and the add-on options are the goods purhased by a ustomer throughout the year, whih are effetively sold at ost. Improving the seletion of goods inreases the optimal membership fee and/or the number of members. he onstant-markup priing solution is an intriguing result, and while outside the sope of this paper, further investigation is merited as to the range of situations in whih suh priing is optimal. he onstant-markup result has powerful impliations for priing options in a mass-ustomization setting. o the extent that ustomer demand is onsistent with a logit framework, and produt onfigurations are additive variations to a base unit, then the onstant-markup result provides a simple priing struture at optimality: from the optimal markup for a base unit, options are added or deleted at ost. 4

16 4. Operations Model In this setion we develop an operations model to gain insight into the tradeoffs inherent in the deision between fous and spakling. In this setion the term spakling will apply to either pure- or layered-spakling. ounter to our intuition, we find that with spakling the optimal level of effiient apaity an be zero, even when there is a unit ost advantage to produing standard units in an effiient fatory. When the optimal effiient apaity under spakling is zero, then the result is pure spakling; otherwise it is layered spakling. We assume that demands are realized over a single period, orresponding to the lead time of the firm s standard retail orders (e.g., a month), and that this period has subperiods (e.g., days). At the start of the period, prior to the realization of demands in eah subperiod, the firm must determine the level of eah type of apaity (flexible and effiient) to aquire in order to meet the demands expeted over this period. In making its apaity deisions, the firm minimizes expeted osts. At the beginning of the period (but after the apaity deision), the firm reeives an order for standard produts, due at the end of the period. At the beginning of eah subperiod (e.g., eah day), the firm reeives orders for ustomized produts due by the end of that subperiod. We denote (x) and (x) as the distribution funtions for subperiod demand for ustom units and period demand for standard units, respetively, with densities f (x ) and f (x ). Demand for ustom units is distributed normally with mean μ and standard deviation σ. We assume that demand for standard units in a period is independent of demand for ustom units and is distributed normally with mean μ and standard deviation σ. hus, total demand is also distributed normally with density f (x ), mean, and standard deviation. ee able for a summary of notation used in the operations model. he firm s deisions for prodution apaities of effiient and flexible resoures are denoted and, respetively, where one unit of apaity an make exatly one unit of produt per subperiod. Let θ denote the fixed ost per subperiod for a unit of effiient apaity (whih is used only to make 5

17 standard units) and let θ denote the fixed ost per subperiod for a unit of flexible apaity (whih an be used to make a ustom unit under the fous strategy, or to make either a standard or ustom unit under either spakling strategy), and let and denote the variable prodution osts per unit for effiient and flexible apaities, respetively. ffiient apaity is assumed to be fully utilized (i.e., units will be built independent of demand), while flexible apaity is assumed to be utilized only to the extent that there are orders. Under a spakling strategy, where flexible apaity is used to produe both ustom and standard orders, we assume that in eah subperiod ustom orders are produed first, with any remaining apaity used to fill standard orders. able. Notation Used in the Operations Model, 4 (in the order defined in the text) Τ Number of subperiods in the period. Distribution funtion for subperiod demand of ustom units (density x ) ~Normal(μ, σ ). δ x Realization of demand for ustom units in subperiod. Distribution funtion for period demand of standard units (density ) ~Normal(μ, σ ). Distribution funtion for period demand of both standard and ustom units (density ) ~Normal(μ μ, ). Deision variable: rodution apaity (per subperiod) of effiient fatory. Deision variable: rodution apaity (per subperiod) of flexible fatory. ixed ost per subperiod for a unit of effiient apaity. ixed ost per subperiod for a unit of flexible apaity. Variable ost per subperiod for a unit of effiient apaity. Variable ost per subperiod for a unit of flexible apaity. enalty ost of baklogged standard order (but avoids ost of ), >θ. enalty ost of baklogged standard order (but avoids ost of ), > θ. G( ) xpeted period osts, inluding prodution and penalty osts. n i ( ) Loss funtion: expeted number of baklogged sales for demand with distribution. L(zi) tandard normal loss funtion with standard variate z i. We assume baklogging, with penalty osts as follows. Baklogged orders of standard units are shipped at the higher (penalty) ost per unit instead of the usual θ per unit (and to ignore the trivial senario, we assume >θ ). his assumption orresponds to a senario where bakorders of standard units are leared after the last period, inurring a high penalty ost but avoiding apaity or unit osts. (his might be prodution from a subontrator, for example.) Baklogged orders of ustom units inur a penalty of in addition to the usual variable prodution osts while avoiding fixed osts for 6

18 apaity of θ per unit (and, we assume > θ ). he ustom units are bakordered aross subperiods, and so this assumption essentially is that the bakorder will onsume existing flexible apaity and the usual variable prodution osts in the next subperiod, but with a bakorder penalty. We assume no salvage values (for M prodution) and that all osts are greater than zero. With no salvage values, overage osts arise from fixed prodution osts. We first analyze the firm s optimization problems given that it hooses the fous strategy, and then given that it hooses a spakling strategy. In the ase of fous, prodution of standard produts is eah subperiod, while prodution of ustom produts in eah subperiod is the minimum of demand and apaity. If the firm hooses the fous strategy, expeted period osts G( ) are determined as follows: ( ) = ( θ ) n ( ) and ( ) = [ θ μ n ( )] G G where n ( ) = ( x ) f ( x) dx = σ L( z ) and n ( ) ( x ) f ( x) dx = σ L( z ) the relevant loss funtions, with and = are. otal ost is the sum ( ) G( ) G. In the ase of spakling denoted with a supersript s in eah of the subperiods exatly standard units are produed using effiient apaity while units are produed using flexible apaity. he flexible prodution is used first to meet demand for max( x δ, ) units of ustomized produts, where δ x is the realization of demand for ustom units in subperiod δ. he remaining apaity max( x δ, ) is used to produe standard produts. hortfalls of ustom units in a subperiod inur a penalty of. A shortfall of standard units arises and inurs a penalty ost of per unit if total period demand (for all produts) is greater than total apaity. otal expeted ost over the period for the spakled-prodution ase is:, where,, and, and, and. he term aounts 7

19 for the prodution of standard units built using flexible apaity (sine there is insuffiient effiient apaity), while and aount for period shortages of standard and ustom produts, respetively. We determine optimal apaities for standard and ustom produts through first and seond order onditions on the ost funtions for the foused- or spakled-prodution ases. All proofs are in the Appendix. HORM. ase A (ous): he optimal apaities and are: = ( μ z σ ) and = μ z σ where the standard variates z = Φ [( θ ) ] and = Φ [( θ )( )] z. ase B (pakle): he optimal apaities and in the spakling ase are:. layered spakling ( 0) and (5) (6) with Φ. pure spakling ( 0) and Φ = ( μ z σ ) [ ( )] θ ' with z = Φ. (7) We note that the optimal solutions in the fous ase are standard newsvendor, and thus losedform, expliit funtions. In ontrast, while the optimal solutions for the spakle ase also have a 8

20 newsvendor struture, they are losed-form, impliit funtions that inlude the optimal apaity on the right hand side of the equation as well as on the left hand side. Given that the ost funtion in the spakle ase is well-behaved (see the proof of heorem in the Appendix), the optimal solution an be found easily via a searh algorithm. ase A orresponds to fous (effiient apaity for standard produts and flexible for ustom) while ase B orresponds to spakling (flexible apaity in a dual role with part of it responding to ustom orders while the remainder produes standard items to inventory). In the ase of fous, optimal apaities are determined through traditional newsvendor formulations with net unit underage osts of θ ' and θ for flexible and effiient apaities, respetively, and overage osts of and θ, respetively. In the spakling ase, the θ optimal apaity is determined impliitly through equations (5) and (6) or through equation (7) for the layered- and pure-spakling ases, respetively. afety apaities for the two ases are for the fous ase and for the spakling ases. z σ z σ he optimal solutions in ase B are impliit with underage and overage osts interpreted as follows. he underage ost for flexible apaity,, inludes the penalty ost for a missed sale of a ustom order less the premium for flexible versus effiient apaity. he premium is adjusted for the probability that the flexible apaity will be used to fill standard orders,, sine shortages of effiient apaity will be filled using flexible apaity. he overage ost is the probability-adjusted premium for flexible versus effiient apaity. he underage ost for effiient apaity,, inludes the penalty ost for a missed sale of a standard unit adjusted by the (sunk) ost of apaity less the expeted variable ost of produing the unit using existing flexible apaity,. he expetation is determined again from the probability that the flexible apaity will be needed, i.e., r. he interpretation of ase B is similar. 9

21 pakling shifts some (or all) of the prodution of standard units from the effiient faility to the flexible faility. hus, flexible apaity will be greater (or equal) under spakling vis-à-vis fous, i.e.,. imilarly, effiient apaity will be lower (or equal) under spakling, i.e., 0. It is interesting to note, that the optimal level of effiient prodution an be zero (i.e., pure-spakling may be optimal) even when effiient prodution has a lower unit ost than flexible prodution. In other words, it is not always the ase that at least some units should be produed in an effiient faility. Having found the optimal apaities and resulting expeted osts with the fous and spakling strategies, the optimal strategy (of fous versus spakling) is found by simply hoosing the one with the lower expeted ost. In the next setion we offer some examples to gain further insight into the tradeoffs inherent in this hoie. 5. mpirial Analysis and xamples In this setion, we desribe briefly our analysis of imbuk s situation. In order to address the marketing onerns, we aquired imbuk s ustomer-related data in a three-stage study. In stage one, 97 MBA students at MI partiipated in an adaptive onjoint survey, as desribed by oubia, et al. (003). he onjoint survey involved prie plus nine other attributes, inluding size (medium or large), olor (red or blak), type of losure of the laptop sleeve (a full flap or a small tab), and six on-off attributes either the bag inluded the attribute or laked it namely, an MI logo, a holder for a ell phone, a holder for a personal digital assistant, a laptop sleeve, a mesh poket, a bottom boot, and a arrying handle separate from the shoulder strap. rom the onjoint study we were able to determine dollar-saled part-worths for eah attribute. In the seond stage, eah student was given $00 to spend on a self-onfigured ustom bag. If a student onfigured a bag pried below $00, she reeived the differene in ash. he third stage onsisted of a follow-up survey in whih a student indiated the probability that she would have atually purhased her ustomized bag, and identified her delay penalty for having to wait for the MO bag. rom this data, we determined eah ustomer s expeted dollar- 0

22 equivalent utility for eah produt and option, exluding prie, and estimated the prie-sensitivity parameter. Based on this information, we ould determine the optimal markup (heorem ). On the operations side, we used imbuk s produt ost and demand data to determine the optimal prodution strategy. At the time of this researh, imbuk was produing everything in its flexible an raniso fatory using a pure-spakling strategy, and was onsidering moving to a fous strategy where standard units would be produed overseas, or to a layered-spakling strategy where some prodution of standard goods would remain in the flexible domesti fatory. We sought to quantify the effets of eah strategy. We used our stylized model to gain insights into the tradeoffs imbuk faed. While imbuk s setting was an ongoing rather than a single-period problem, its situation ould be viewed approximately as a sequene of monthly problems with monthly deisions for effiient apaity (prodution of standard bags in the offshore faility) and flexible apaity. We assumed a subperiod to be one day and a period to be one month ( = 30). imbuk estimated that effiient off-shore prodution would ost approximately $3 per bag ($ labor and $ material) while bags produed in an raniso ost approximately $8 per bag ($6 labor and $ material). Leadtime and shipping osts made it impratial to produe mass-ustomized bags overseas. In partiular, shipping bags by sea took four weeks but ost a negligible $0.0 per bag. Air shipments of bags would result in satisfatory leadtimes, but air shipments ost approximately $5 per bag, whih was muh greater than the ost savings of overseas prodution. We assumed that the fixed ost for the flexible apaity was the labor ommitment for the upoming month while the variable ost was the material used in eah bag. rodution osts were thus θ = $3 and $8 for effiient and flexible apaities, respetively. We used penalty osts equal to the average pries in eah hannel. Approximately 0% of demand at imbuk was for ustom bags; daily demand for ustom bags was approximately 40 bags while daily demand for standard bags was approximately 60. he oeffiient of variation in subperiod demand was approximately 33%.

23 Reall that management was onsidering going to a strategy of fous or one of layered spakling. Given a predominane of standard demand, and with effiient overseas prodution offering nearly 30% in (fixed plus variable) ost redution, it is not surprising that a layered spakling strategy would be preferred over pure spakling. igure shows the expeted osts for the three strategies over a range of osts for the effiient prodution. As expeted, layered-spakling dominated the strategies with a lower total expeted ost aross all values. We note that a fous strategy would be preferred to imbuk s purespakling strategy if the unit osts of effiient apaity were $6.50 or less about 8% lower than the unit osts of the $8.00 per unit flexible apaity. igure. Given 0% ustom roduts, Layered pakling was the referred trategy xpeted osts for ure pakling, ous, and Layered pakling xpeted osts $0 $5 $0 $05 $00 $95 $90 pure spakling fous layered spakling =30 p =50 p '=00 μ /Τ=60 μ =40 v=0.33 θ =$6 =$ $85 $3 $4 $5 $6 $7 $8 Unit ost of ffiient rodution: θ. urrent level = $3. Note in partiular the ost benefit that layered spakling offers over the fous strategy. ven though ustom produts represent only about 0% of the prodution volume, layered spakling redues overall ost by approximately 5% as ompared to the fous strategy. Another way of looking at this is that layered spakling redues the effetive ost of the ustom units by about 0%. (his is alulated by multiplying the expeted daily demand for ustom items of 40 by the variable plus fixed ost of $8 yielding a monthly ost of $,600. Meanwhile, the urrent unit ost of effiient prodution of $3 saves

24 $93,493 $89,386 = $4,07.) imbuk an signifiantly redue the effetive ost of mass-ustomization via the layered spakling strategy. Interestingly, imbuk s inreasing emphasis on mass ustomization ould signifiantly hange the piture. etting all parameter values at urrent levels exept the fration of total demand that is ustom produt, we examined in igure 3 what happened to expeted osts and optimal apaities as the fration of ustom prodution inreased from 0%. he total expeted ost gap between layered and pure spakling narrowed rapidly with an inrease in the fration of output that is ustom produt, and was effetively eliminated at just over 70%. In other words, moving offshore to take advantage of effiient prodution ould be a fleeting savings if mass-ustomized produts were to beome a more prominent fration of the produt mix. igure 3. ure pakling Beomes avorable as the % of Orders that are ustom Grows xpeted osts for Layered vs ure pakling xpeted osts $30 apaities 300 Optimal apaities for Layered vs ure pakling $0 pure spakling 50 pure spakling: optimal flexible apaity () $0 $00 $90 $80 layered spakling =30 p =50 p '=00 μ μ /=00 v=0.33 θ =$6 =$ θ =$3 0% 0% 40% 60% 80% 00% % of orders that are ustom: μ /(μ μ /Τ). urrently 0% but growing layered: optimal flexible apaity () layered: optimal effiient apaity () 0% 0% 40% 60% 80% 00% % of Orders that are ustom: μ /(μ μ /). urrently 0% but growing. igure 3 onfirmed that at the then urrent ratio of ustom to total demand of around 0%, imbuk had signifiant inentive to move to offshore prodution and use layered spakling. But if the ratio of ustom orders were to inrease, as had been the trend to date, this inentive would diminish and ompletely disappear when ustom orders omprised 70% or more of total demand. Above 70%, it would be optimal to use a pure-spakling strategy essentially the then urrent strategy of utilizing just one flexible domesti fatory. 3

25 ummarizing the mmbuk results, the layered-spakling strategy offered signifiant savings for imbuk over the fous strategy that they were onsidering, reduing overall osts by 4.4% (and reduing effetive osts for ustom produts by about 0%). he layered-spakling strategy was attrative given the high (80%) fration of output that was urrently assoiated with standard produts. However, as mass-ustomized demand ontinued to grow, pure-spakling ould beome optimal. If over 70% of prodution were to be alloated to ustom demand, the firm would no longer find signifiant advantage for overseas prodution even though it was nearly 30% less ostly per unit. 6. onlusion Motivated by the experienes of imbuk, we gain insight into a ouple of issues arising with mass ustomization. irst, in a marketing model, we find that if ustomer demand fits into a logit framework, then optimal priing is ahieved through a onstant markup. he onstant-markup result has powerful impliations: when mass ustomization is ahieved by adding options to a base unit, then the base unit should inorporate the full optimal markup, and options should be added or deleted at ost. However, the firm does have an inentive to offer desirable options beause they inrease the markup ommanded by the base unit. or example, at the time of this researh, imbuk was harging ustomers $5 for hoosing a different logo olor than the standard olor. he sewing mahine that added the logo had numerous olors of thread mounted to the mahine, and there was no differene in ost between adding the standard olor or any of the other olors mounted on the mahine. A signifiant fration of ustomers paid the $5 for a ustomized logo olor, suggesting this was a desirable option. Assuming the logit model fairly represented their demand, our model suggested that offering the ustom logo olors at no extra ost and inreasing the prie of the base bag (by some amount determined by the marketing model) would inrease imbuk s total profit (and possibly their sales) as ompared to their urrent priing strategy. On the operations side, we analyze the benefits of spakling, a proess involving the use of a flexible prodution faility to produe both standard and ustomized produts. We ompare spakling to 4