Closed-Loop Supply Chain Models with Product Remanufacturing

OriginalClosed-Loop Supply Chain Models with Product Remanufacturing R. CananSavaskan Kellogg School ofManagement, Northwestern University, Evanston, Illinois 60208, r-savaskan@kellogg.northwestern.edu ShantanuBhattacharya,LukN.

OriginalVanWassenhove Technology Management,

OriginalINSEAD,

OriginalBoulevard deConstance, 77305 Fontainebleau, Cedex, France {shantanu.bhattacharya@insead.edu, luk.van-wassenhove@insead.edu} The importanceof remanufacturing used productsintonew ones hasbeenwidely recognizedin the literature T and in practice.Inthis paper,we addressthe problemof choosingthe appropriatereversechannelstructure for the collectionof used products from customers.Specifically,we consider a manufacturerwho has three options for collectingsuch products:(1) she can collect them herselfdirectlyfromthe customers,(2) she can providesuitableincentivesto an existingretailer(who alreadyhas a distributionchannel)to inducethe collection,or (3)she cansubcontractthe collectionactivityto a thirdparty.Basedon our observationsin the industry, we model the threeoptions describedabove as decentralizeddecision-makingsystems with the manufacturer being the Stackelberg leader.Whenconsideringdecentralizedchannels,we find that ceterisparibus,the agent, who is closerto the customer(i.e., the retailer),is the most effectiveundertakerof productcollectionactivity for the manufacturer.

OriginalIn addition,we show that simple coordinationmechanismscan be designed such that the collectioneffortof the retailerand the supply chainprofitsareattainedat the same level as in a centrally coordinatedsystem.

OriginalKeywords:supply chainmanagement;reverselogistics;remanufacturing;

Originalchannelstructure History:Acceptedby ChristopherTang,formerdepartmenteditor;receivedOctober24, 2003.Thispaperwas with the authors26 monthsfor 3 revisions.

Original1. Introduction

OriginalThe importance of the environmental performance of products and processes for sustainable manufacturing and service operations increasingly is being recognized. While legislation introduced in Europe, North America, and Japan encourages this awareness, many corporations have proactively taken measures in anticipation of evolving environmental performance requirements.

OriginalIncreasingly, manufacturers of durable and nondurable goods are establishing economically viable production and distribution systems that enable remanufacturing of used products in parallel with the manufacturing of new units.

OriginalRemanufactured products are typically upgraded to the quality standards of new products, so that they can be sold in new product markets. In this paper, we consider product categories in which there is no distinction between a remanufactured and a manufactured product, and we refer to the distribution systems, which use a combination of manufacturing and remanufacturing, as closed-loopsupply chains.

OriginalThe prospect of remanufacturing poses interesting questions with respect to the design and management of closed-loop supply chains. The goal of this paper is to develop a detailed understanding of the implications that a manufacturer's reverse channel choice has on forward channel decisions and the used-product return rate from the customers.

OriginalIn current practice, we find a variety of reverse channel formats deployed by manufacturers. In some cases, manufacturers collect their used products directly from the customers.

OriginalFor instance, Xerox Corporation provides prepaid mailboxes so that customers can easily return their used copy or print cartridges to Xerox without incurring any costs. The company also remanufactures high-value, endof-lease copiers (Xerox Corporation 2001).

OriginalThe used copiers are collected directly by Xerox as new ones are installed. Overall, the green remanufacturing program saves the company 40%-65% in manufacturing costs through the reuse of parts and materials (Ginsburg 2001).

OriginalSimilar activities are undertaken by Hewlett Packard Corporation for computers and peripherals, and by Canon for print and copy cartridges. Manufacturers of consumer products such as single-use cameras and mobile phones utilize retailers for collecting their used products.

OriginalFor instance, Eastman Kodak Company receives single-use cameras from large retailers that also develop film for customers. On average, 76% of the weight of a disposed 239 This content downloaded from 142.12.73.66 on Mon, 22 Apr 2013 14:09:08 PM All use subject to JSTOR Terms and Conditions Savaskan,Bhattacharya, and VanWassenhove:Closed-Loop SupplyChainModels

Original240 Management

OriginalScience50(2),pp. 239-252,D2004INFORMS camerais reusedin the productionof a new one. Each time a camera is returned to Kodak, the retaileris reimburseda fixedfee per cameraand the transportation costs.

OriginalIn the auto industry,independentthirdparties(i.e., dismantlers) are handling used-product collection activities for the original equipment manufacturers (OEMs).Recently,the "bigthree"auto manufacturers in the United Statesstartedto invest in jointresearch and remanufacturingpartnershipswith dismantling centers to benefit from their scale economies and experience (Bylinsky 1995).

OriginalThird parties such as GENCO Distribution System are also preferredby some consumer goods manufacturersfor their experiencein used-productcollection(Hickey2001). To investigate how reverse channel choice affects the forwardchannel decisions and the used-product returnrates,we considera two-echelonsupply chain and model a single manufacturer-retailer dyad with product remanufacturing.1Based on observations from currentpractice and the extant literature,we consider three reverse channelformats:(1) manufacturercollecting used products directlyfrom the customers (Model M), (2) manufacturercontractingthe collectionof used productsto the retailer(ModelR), and (3) manufacturercontracting the collection of used products to a third party (Model 3P).

OriginalWe contrast the results for the decentralizedchannels with the centrallycoordinatedsystem (Model C) to illustratepotentialsources of inefficienciesin closed-loop supply chains.

OriginalMorespecifically,we addressthe followingresearch questions: (1) How are the wholesale price, the retail price, and the total channelprofitsaffectedby the choice of the reversechannelstructure?

Original(2) How do the closed-loopsupply chainstructures influencethe incentivesto invest in used-productcollection and the productreturnrates? Some of the key results of this paper demonstrate that in a closed-loop supply chain, the retailerhas an importantdual role due to his proximity to the market.Theanalysisshows thatwhen pricesaresensitive to changes in unit production costs, by being closer to the final demand, the retailer can efficiently reflect unit cost savings from remanufacturing to the final price of the product, and jointly optimize the investment in used-product collection.

OriginalThe manufacturer is at a disadvantage in coordinating pricing and used-product return rates, because she faces double marginalization in the forward channel. The thirdparty model is the least-preferred option because the payments made to the third party for undertaking collection become a direct cost to the supply chain, do not induce incentivesto increasethe finaldemand and, therefore, reduce the profitability of product remanufacturing.The model also demonstratesthat the manufacturercan furtherimprove the profits of the R Model to the level of a centrally coordinated system by using a single two-parttariff.Becausewe define the two-part tariffcontingent on the product returnrate, it not only coordinatesthe pricing decision of the retailerin the forwardchannelbut also the collectioneffortin the reversechannel.

OriginalOn a broaderlevel, this paper contributesto our understandingaboutthe interactionsbetween reverse and forwardchanneldecisions, as well as the incentives of the agentsto invest in used-productcollection in differentreversechannelstructures.

OriginalThe rest of this paper is organized as follows. In the following section, we briefly discuss the current literature and the contribution of this paper. Section 3 is devoted to the conceptualizationand formulationof the model.Followingthe developmentof the model, the analyticalresults for the optimal closedloop supply chainstructuresarepresentedin s4.

OriginalSection 5 examines channel coordination mechanisms with used product collection.We outline the limitations of this work and possible directionsfor future researchin s6.

Original2. Literature

OriginalThis paper draws on and contributes to several streams of literature, each of which we review below. A growing literaturein operations management addresses reverse logistics managementissues for remanufacturable products.

OriginalWe refer the reader to Fleischmannet al. (1997)and Guide et al (2000) for completeliteraturereviews. Thebasic underlying assumption in these papers is that the planning of closed-loopsupply chainoperations,such as network design (Krikke1998),shop-floorcontrol(Guideet al.

Original1997),and inventory control (van der Laan 1997)is done by a central decision maker to optimize total system performance.By adapting a game-theoretic approach,we relax the centralizedplanner assumption and model the independent decision-making process of each supply chain member.

OriginalSpecifically, we examine the interaction between pricing decisions in the forward channel and the incentives to collect used products under different reverse channel structures.

OriginalThere is a growing number of research papers on reverse logistics that use game theory to model remanufacturing decisions. Majumder and Groenevelt (2001) examine how third-party remanufacturing can induce competitive behavior when the recycled products cannibalize the demand for the original product.

OriginalDebo et al (2002) model the durability choice 1 Throughout this paper, we adopt the convention of using the pronoun "she" to refer to the manufacturer. All other supply chain members are refered to by the pronoun "he." This content downloaded from 142.12.73.66 on Mon, 22 Apr 2013 14:09:08 PM All use subject to JSTOR Terms and Conditions Savaskan,Bhattacharya, and VanWassenhove:Closed-Loop SupplyChainModels Management Science 50(2), pp.239-252, @2004

OriginalINFORMS 241

Originalof the (re)manufacturer when consumersact strategically.Whilewe specificallymodel the reversechannel design decisions, in the cited papers, such decisions areassumed exogenous to the model structure.

OriginalIn the supply chain management literature, Pasternack(1985),Emmons and Gilbert (1998),and Donohue (2000) determine optimal product return contracts for short life-cycle products.

OriginalThe returns considered in these studies occur at the end of the selling season due to demand uncertaintyand the retailer's overstocking of inventory. Related to this groupof work,Padmanabhanand Png (1997)explore how ordering flexibility from buy-back contracts affects the retail-level competition.

OriginalIn contrast, we considerused products,which arereturnedfromconsumersfor remanufacturing, and we discuss contract forms,whichwould jointlycoordinatethereverseand the forwardchannels.

OriginalRecentresearchalso shows a strong link between supply chain management and environmental improvement. Bierma and Waterstraat (2000) and Reiskinet al. (2000)discuss contractualmechanisms to reduce resourceuse.

OriginalCorbettand DeCroix (2001) examine shared-savingscontractsto overcomeincentive conflicts between a supplier and a buyer to reduce the use of indirect materials. This recent stream of work focuses on cost savings derived from reduction of consumption (ex ante), while we consider cost savings derived from product reuse (ex post).

OriginalIn the marketing literature, Stern et al (1996) describe the role and the function of each channelmemberin differentclosed-loopsupply chain structureswithout providing a quantitativebasis for comparing these different channel formats.

OriginalIn contrast,in this paper,we try to provide such a comparison between the rolesof the differentchannelparties. The quantitativemodels of channel design in marketing have only looked at forwarddistributionsystems (Jeulandand Shugan1983,McGuireand Staelin 1983,Coughlan1985).Whilethe model structurepresented in this paper is consistent with this stream of work, we expand these models to also include reverse product and financialflows from consumers to manufacturers.

OriginalLast, but not least, there is also growing research interest in decision models for used-product acquisition when there is quality uncertainty in the return flows. See Guide and Van Wassenhove (2001) for a detailed discussion of this issue.

OriginalIn this paper, we focus on the channel choice decision and assume homogenous quality of returned products. Next, we present our modeling assumptions and the three closed-loop supply chain models.

Original3. Model Assumptions and Notation

OriginalWe use the following notation throughout the paper: cmwill denote the unit cost of manufacturing a new product, and cr the unit cost of remanufacturinga returnedproductinto a new one, p is the retailprice of the product, w is the unit wholesale price, and b will denote the unit transferpriceof a returnedproduct fromthe retailer/thirdpartyto the manufacturer.

OriginalD(p) is the demand for the new productin the market as a function of product price, and II denotes the profit function for channel member j in supply chainmodel i. Superscripti will takevalues C, M, R, and 3P, which will denote the centrallycoordinated, manufacturercollecting, retailer collecting, and the third-partycollecting models, respectively.The subscript j will take values M, R, and 3P, which will denote the manufacturer,the retailer,and the third party,respectively.

OriginalThe primary goal of this paper is to understand the implicationsof differentclosed-loopsupply chain structureson incentivesto invest in used-productcollection and on supply chain profits.Hence, we consider the following scenarioand make the following modeling assumptions.

OriginalSuppose that the manufacturerhas incorporateda remanufacturingprocess for used products into her originalproductionsystem, so that she can manufacture a new product directly from raw materials,or remanufacture partorwhole of a returnedunit into a new product.

OriginalAsSUMPTION

Original1. Producing a new product by using a

Originalusedproduct is lesscostlythanmanufacturing a newone, i.e., cr < cm and cr is the same for all remanufactured products. This assumptionstatesthat savings from materials and assemblyof subsystemswithin the new product dominatethe additionalcosts of disassembly,inspection for reusability,and the cost of remanufacturing.2 Therefore,ceteris paribus, the manufacturerstrictly prefersa higherproductreturnrateto a lower product return rate from the market because, through remanufacturing, she can lower herproductioncosts.

OriginalThelastpartof Assumption1 caneasilybe relaxedby incorporatinga yield rateon returnedproductquality. Theyield ratemodels the uncertaintyin the reusability of used productsdue to differentusage patterns.3 ASSUMPTION 2.

OriginalWe characterize the reverse channel performanceby 7, the return rate of used productsfrom the customers. 7 denotesthefractionof currentgeneration productsremanufactured from returnedunits, i.e., 0 < 2Kodakincorporates considerations suchas partreusability, easeof disassembly,andrecoverability into theproductdesign processfor its single-usecameraline.

OriginalThisenablesthem to easily disassemble returnedcamerasand, thus, manufacturenew ones at lower unit costs by only replacingpartssuch as the lens and thebattery. 3Itcaneasilybe shownthattheuncertainty in thereturnedproduct qualityreducesthe incentivesto invest in used productcollection, becausethe benefitfromthe investmentwill be lower.

OriginalThis content downloaded from 142.12.73.66 on Mon, 22 Apr 2013 14:09:08 PM All use subject to JSTOR Terms and Conditions Savaskan,Bhattacharya, and VanWassenhove:Closed-Loop SupplyChainModels

Original242 Management

OriginalScience 50(2), pp.239-252, @2004

OriginalINFORMS

Originalr < 1. Wemodelr as afunctionof theproduct collection effort,whichis denoted by I, theinvestment in collection activities.Suchinvestments can beconsidered as promotionalexpenditures undertaken bythecollecting agent.

OriginalHence, one can think of r as the response of consumers who have an incentive/enthusiasm for the remanufacturingof their used products as a result of the promotional/advertisingactivitiesof the agent in the reversechannel.To characterizethe diminishing returnsto investment,we use the cost structure 7 = VI/CL, where CL is a scaling parameter. Similar forms of response functions have been widely used in the advertising response models of consumer retentionand product awareness(Lilienet al.

Original1992, Fruchterand Kalish 1997, Zhao 2000), and in salesforce effort response models in the marketing literature (Coughlan 1993). In the operations literature, Porteus (1986) and Fine and Porteus (1989) use similarinvestmentfunctionsto investigateopportunities for process improvement and lot sizing by investingin setupcostreductionandqualityimprovement.

OriginalThis paper investigatestradeoffsthat are similarto those in the above studies in a remanufacturing context. FromAssumptions 1 and 2, the average unit cost of manufacturing can be written as c = cm (1 - r) + c,7.

OriginalNote that when every consumer returns his or her used product (i.e., r = 1), c = cr. If the return rate of used products is zero, then all demand will be satisfied from manufactured units and, therefore, c = cm.If we denote unit cost savings from reuse by A (i.e., A = cmc,), the average unit cost is given by cmTA.

OriginalSimilar cost structures can also be found in the literature,which looks at process improvementdecisions and cost reductionincentives in supply chains(Guptaand Loulou1998,Gilbertand Cvsa2000).Thesimilarityin formulationis consistent because,in this paper,an increasein productremanufacturingwould also mean a reductionin the average unit cost of manufacturing.

OriginalASSUMPTION

Original3. There

Originalis a variable unitcostofcollectingandhandling a returned unit,whichis denoted byA. For remanufacturingto be economicallyviable,we assume that A < A, i.e., thefixed paymentper unit is less than the savings generatedper unitfrom remanufacturing.

OriginalOne can think of A as the fixed payment given to the consumer who returns a used product. Consider the reverse vending machines that collect used products (e.g., soft drink cans).

OriginalEach customer who returns a used product to these machines receives a fixed payment per unit, which is represented by the parameter A in our model. Note that A is exogenous to the model and does not affect the demand for the product.

OriginalThis would be the case for consumer products (i.e., cameras,cartridges)with low salvage value and no secondarymarkets(Swan 1972).In the case of durablegoods, one should also considerhow the secondarymarket/trade-invalue of a used product affectsthe consumer's decision to replacehis or her used product.Assumption 3 also implies that A does not increasewith the scale of operations.This is consistentwith supply chain structures,where the reverse channel has sufficient capacity so that the product returnrate is driven by the collection effort and by induced awarenessand participationof consumers in productremanufacturing.4 The total cost of collection C(r) can then be characterized as a function of the return rate of used

Originalproductsand is given by C(7)= I + ArD(p)= CLT2+ ATrD(p), where TD(p) is the total number of units returned from consumers and remanufacturedinto new products. Because we intend to compare the incentivesof collectingagentsacrossdifferentreverse channelstructures,we assumethe samecost structure forallclosed-loopsupply chainmodels.Intheconclusion section,we discuss otherfactorsthat may bring in collectioncost advantagesto some reversechannel structures.

OriginalAsSUMPTION

Original4. We consider a two-echelonsupply

Originalchainand modela bilateralmonopolybetweena single manufacturer and a single retailer.This enablesus to exploretheimplications of assigninga dualroleto aforwardchannelmember.

OriginalSpecifically, if the retailerundertakesthe collectioneffort,he not only determinesthe quantitydemanded in themarket bysettingtheretailprice of the product,but also by his collectioneffortlevel,he influences theaverage manufacturing costof theproduct.

OriginalEven thoughwe considera single manufacturer-retailer structure,the manufacturer can, infact, sell to different retailers if theretailers arenot in directcompetition. The manufacturer canalsomanufacture competing brands, but shedoesnotsellcompeting brands tothesameretailer and thebrands donotsharethesamemanufacturing process.5 Theretailer canalsocarrymanybrands, butforsimplicity, we consideronly one brand for whichhe takesdecisions independent oftheotherexistingbrands.

OriginalASSUMPTION

Original5. D(p) =

Original- - jSp, with 7 and P being positive parametersand 4 > Scm. We assume a downward sloping linear demand function. Lee and Staelin (1997) show that the vertical interaction between the channel members and the optimality of the channel strategies depend on 4 Forinstance,KodakandKmartengagein jointpromotionalactivities to increasethe awarenessof the single-usecamerarecycling programamongyoung consumers(DiscountStoreNews 1994).

Original5 Thisenablesus to decouplethe cross-brand elasticitiesin recommending a suitableclosed-loopsupply chain to the manufacturer in differentenvironments. This content downloaded from 142.12.73.66 on Mon, 22 Apr 2013 14:09:08 PM All use subject to JSTOR Terms and Conditions Savaskan,Bhattacharya, and VanWassenhove:Closed-Loop SupplyChainModels Management Science50(2),pp.

Original239-252,c2004 INFORMS 243 the convexity of the demand functions.Therefore,it should be pointed out that while the linear demand assumption is consistent with the literature(Bulow 1982,Weng 1995)and enables us to develop a firstcut analysis of the closed-loop supply chain decision of the manufacturer, the generalizabilityof the results to nonlineardemandfunctionsis a questionof future research.6 Thelastpartof Assumption5 is a condition for nonnegativedemand.

OriginalTo model the supply chain members' incentives under differentclosed-loop supply chain structures, we use the principal-agentframework (Laffontand Tirole1993)and make the following assumptionconcerningthe power structurein the supply chain.

OriginalASSUMPTION

Original6. In all our supplychainmodelswith

Originalremanufacturing, themanufacturer hassufficient channel powerover the retailerand the thirdparty to act as a Stackelberg leader. Thisassumptionstatesthatin determiningthe outcome of the game played between the manufacturer and the retailer,the manufactureruses her foresight abouttheretailer'sandthe thirdparty'sreactionfunctions in her decision making.

OriginalThe Stackelbergstructureforthe solutionof similargameshas been widely used in the supply chainliterature(Tayuret al.

Original1998).

OriginalAsSUMPTION7. Whileoptimizing theirobjective functions,all supplychainmembers haveaccessto the same information. This assumption enables us to control for inefficiencies and risk-sharingissues resultingfrom information asymmetry (Corbett and De Groote 2000).

OriginalSavaskanet al. (1999)examinethe closed-loopsupply chain performancewhen the manufacturerfaces an adverseselectionproblem.

OriginalASSUMPTION8.

OriginalTheclosed-loopsupply chain decisions areconsidered in a single-period setting. Weassumethe previousexistenceof the productin the market.Thoseproductssold in the previousperiods can be returned to the manufacturerfor reuse.

OriginalHence, the focus of analysis is on the averagesupply chainprofitsper period when similar products are introduced to the market repeatedly.7

Original4. Supply Chain Models

Originalwith Remanufacturing This section presents three decentralized supply chain models with remanufacturing, viz., the closed-loop Figure

Original1 Supply

OriginalChain Models with Remanufacturing iManufacturer IRetailer] (a)ModelC IManufacturerd Retailer[ (b)ModelM ManufacturerI Retailer (c)ModelR Manufacturer]- IThird Partyl Retailer (d)Model3P Forward Flow ReverseFlow supply chain with the manufacturercollecting used products (Model M, Figure lb), the closed-loop supply chain with the retailercollecting used products (Model R, Figure ic), and the closed-loop supply chain with third party collecting used products (Model 3P, Figure id).

OriginalAs a benchmarkcase, the Centrally Coordinated System(ModelC, Figurela) is analyzed to highlight inefficienciesresultingfrom decentralizationof decisionmaking,and is laterused for derivingthe channelcoordinatingpricingscheme.

OriginalWecomparethe models with respectto the wholesale price,the retailprice,the productreturnrate,and the total supply chain profits.The profitfunctionsof the supply chain membersare shown to be concave in the decision variables,so the first-orderconditions are used throughout to characterizethe optimality of the decision variables.8The single manufacturersingle retailerbilateralmonopoly model withoutproduct remanufacturing is well known in the literature (Jeulandand Shugan 1983)and has been extensively analyzed.Forcomparison,we will referto the results of this model in some partsof this paper.9

Original4.1. Model C-Centrally CoordinatedSystem

OriginalThe centrallycoordinatedsystem (ModelC) provides a benchmarkscenarioto compare the decentralized models with respect to the supply chain profits and the reverse channel performance.Because there is a single decision maker,the wholesale price w and the transferprice b are irrelevantto the formulation of the objectivefunction.

OriginalHence, the centralplanner optimizes Max c = (4 - pp)[p - c, + TA]- CLT2 - AT(4 - pp). p, T (1) 6We conjecture that the results of the model would hold for all demand patterns with nonpositive elasticities with respect to price.

Original7Kodak introduces new models of disposable cameras, which can incorporate components from previous generations. 8 For the clarity of the text, all proofs are provided in the appendix. 9The results of the bilateral monopoly model without remanufacturing are given in Appendix A. This content downloaded from 142.12.73.66 on Mon, 22 Apr 2013 14:09:08 PM All use subject to JSTOR Terms and Conditions Savaskan,Bhattacharya, and VanWassenhove:Closed-Loop SupplyChain Models

Original244 Management

OriginalScience 50(2), pp.239-252, @2004

OriginalINFORMS

OriginalThe simultaneoussolution of the first-orderconditions resultsin p*C =+Cm 1(A - A)2 m and 2p 2 4CL - P(AA)2 C - Cm)(Ah - A) 4CLP(AA)2 To ensure comparison of the interior point solutions to all four models, we impose the condition of alc(7)/r7 I=1< 0 on r (see Lemma1 in AppendixA).

OriginalFromthis conditionfollows Assumption9.

OriginalASSUMPTION

Original9. The parameterCLdefined in the collectioncostfunction is assumedto be sufficiently

Originallarge, suchthatr*c< 1. Morespecifically, 4CL> [(4 - 13cm) + Assumption 9 ensures that remanufacturing is sufficiently costly so that it is not economically viable to manufactureall units from used products(similar assumptions have been made in Gupta and Loulou 1998and Gilbertand Cvsa 2000).Note thatthe righthand side is the maximum savings contributionof remanufacturingif all the productswere remanufactured, i.e., 7*c= 1.

OriginalFromthebest-responsefunctions,it follows thatthe retailpricechargedis lower thantheretailpricein the centrallycoordinatedsystem withoutremanufacturing (see Table1 in Appendix A).

OriginalPartof the system profit gains from reduced unit variablecosts arepassed on to the customers as a lower retail price, which also enhances the demand of the product. The demand and total profits in the coordinateddistributionand collection system can be found by evaluating D(p) and 11c(p,r) at p*c and r.c.

OriginalTheresultsareshown in

OriginalTable1 in Appendix A.

Original4.2. Model M-Manufacturer Collecting

OriginalIn this model, the manufacturerundertakesthe used product collection effort, and decides on the wholesale price w and the productreturnrate,7.An example of this form of closed-loop supply chainstructure is Xerox'snetwork for printerand copy cartridgesin Europe and in the United States.

OriginalSpecifically,Xerox provides prepaid mailboxes so that the used cartridges canbe returnedto Xeroxat no expense to the customers. Becausethe manufactureris the Stackelbergleader, we begin by characterizing the best-responsefunction of the retailer.Fora given w, the retailer'sproblemis MaxpIM = (p - w)(4 - 0p).

OriginalBecause the objective function is concave in p, the retailer's first-order condition characterizes the unique best response, p*M= (4 + 3w)/(2f). The derived demand function of the retailer is given by D(w) = (4 - fw)/2.

OriginalThe manufacturer'sproblemcanbe stated as MaxII = - [wcm + TA]- CLT2 w, 2 - Ar (2) 2 Again,the objectivefunctionis jointlyconcavein w and r, and the manufacturer'sfirst-orderconditions characterizethe uniquebest response,

OriginalWM

Original_ + pcm (A - A)2(40-cm) w and 23 2[8CLP(A - A)2] *M (4-cm)(A - A) 8CL - p(AA)2 Optimal retailprice and equilibriumchannel profits can easily be found by substitution of w*M,r*M.The resultsarelisted in Table2 in Appendix A.

Original4.3. Model R-Retailer Collecting

OriginalIn this model, the retaileralso engages in the promotion and collection of used products in addition to distributingnew products. One characteristicof this channel format is that the ownership of used productsinitiallyrests with the retailerafterthe collection.

OriginalTo take the productsback, the manufacturer pays a transferprice b per product returned to her from the retailer.The transferprice, b is determined by the manufacturer.As an example of this closedloop supply chainstructure,Kodakcurrentlyengages retailersthat sell their products to participatein the collectionactivityof the disposed cameras.Similarly, forelectronicsproducts,such as television sets, home appliances,personal computers,retailersalso act as collection points when used products are returned to them at the moment of new sales.

OriginalIn this model, the retailerdecides the retailpricep, and the product returnrate r, throughhis collectioneffort. The retailer's problem is given by Maxp,iI = (4 - pp)[p - w] + br(4 - pp) - CLT2 - AT(4 - Pp).

OriginalBecause the objectivefunction is jointly concave in p and r, from the first-orderconditions, the best responses are p*R = (4 + p[w - (bA)r*])/(20) and 7*R= ((b - A)/(2CL))( -_pp*R).

OriginalGiven p*Rand r*R,the manufacturer optimizes Max

OriginalFI

Original= (4 - pp*R)[wcm + Ar*R]- br*R(4p*R). w (3) Fromthe concavityof the objectivefunction in w, it follows thatfor a given b, *R = + pcm (A - b)(bA)(4 - /cm) 2P 2[4CL - p(A - A)(bA)] This content downloaded from 142.12.73.66 on Mon, 22 Apr 2013 14:09:08 PM All use subject to JSTOR Terms and Conditions Savaskan, Bhattacharya, and Van Wassenhove: Closed-Loop Supply ChainModels Management Science 50(2), pp.239-252, c2004INFORMS 245 The optimalvalue of the wholesale pricecan then be used to compute the demand and the profitsfor the manufacturer.

OriginalThemanufacturer's profitsaregivenby (4o - pcm)2/(8p) 1 - P(A - A)(b - A)/(4CL) Note that because the manufacturer'sproblem is concave in w for a given b, this enables us to find the value of b,which maximizesthe optimalvalue of the manufacturer'sprofit function.'1Thus, we make the following observation." OBSERVATION 1.

OriginalBecausethe manufacturer's profits areincreasingwith respectto b, the transferpricebis set equal to its upperbound of A, i.e., b= A. Surprisingly, in the R Model,we find thatthe manufacturerdoes not extractany of the direct savings fromremanufacturing, but prefersto pass them on to the retailer.Therearetwo main driving forcesto this seemingly counterintuitiveresult.

OriginalWhenthe retailerundertakesthe used-productcollection activity,a unit increasein demand increases his profits in two distinct ways. First,an additional unit of demand contributesthe margin (i.e., p - w) fromthe purchaseof the new product.Second,it partially contributesthe salvage value (i.e., bA) of a used product.

OriginalIn other words, in the R Model, the retailerhas a highermarginalprofitabilityfroma unit increasein demand than the cases when the manufactureror the third party are the collecting agents.

OriginalHence, for a given level of 7, passing on all the savings to the retailerresultsin increasedpayoffs for the retailer (i.e., (A - A)r > (b - A)r), and this acts as an incentiveto reducethe retailpriceof the productand increasedemand,which resultsin increasedprofits.A second-degreeeffectof increasingdemandalso actsto set 7.

OriginalA largermarketsize makesused-productcollection more profitablefor the retailer(i.e., scale effect) and,hence,the retailerhas anincentiveto increasehis investmentin used-productcollection,andincrease7.

OriginalThe manufacturerprefers to transfercost savings directlyto the retailerfor the following reasons.Even though she does not internalizethe unit cost savings from remanufacturingdirectly, her profits increase because of an increasein the product demand.

OriginalNote that if the manufacturer had retainedpartof the unit cost savings (i.e., r(A - b) > 0), because of double marginalizationin the channel,a partof these savings would be internalizedin the retailer'sprofitmargin laterwhen the retailerset the productprice.As a consequence, the demand and the investment in usedproductcollectionwould be lower.

OriginalThe analysis of the R Model shows that the way the cost savings from remanufacturingare shared between supply chainmembershas importantimplications for pricing decisions in the forward supply chain,both for the manufacturerand the retailer.

Original4.4. Model 3P-Third-Party Collecting

OriginalIt is also not unusual to see the used-productcollection activitycontractedby the manufacturer to a third party,who is engaged only in the collection of the used productsfromthe market.TheInternethasbeen an essential enabler for such third-partymanaged product return channels (Hickey 2001).

OriginalIn these closed-loop supply chains, the third party acts as a brokerbetween the customerand the manufacturer. In the 3P Model, for a given transferprice b of a used product,the thirdpartymaximizeshis profitsto determine the investment in used-productcollection and, hence, decides the value of 7.

OriginalAs in Model M, the retailerengages only in the distributionof the product.The retailersolves for p*3P as a function of the wholesalepricesetby the manufacturer. Thethird party assumes the collection activity and maximizes MaxT IIP = br( - 3p*3P) - CLT2 - Ar() - Pp*3P).From the concavityof the objectivefunctionin r, the optimal value of the productreturnrate r*3Pis given by ((b - A)/(2CL))(0 - pp*3P).

OriginalGiven p*3P and T*3P, the manufacturer solves MaxII = (4 - pp*3P)[w - cm+ (A - b)7*3P]. (4) w b 4 From the first-orderconditions, the manufacturer sets the wholesale priceof the productto w*3P= O+f3cm 4)-pcI - P(b-A)(A-b)/(4CL) 1 2p/ 23 1-p(b-A)(A-b)/(4CL) fromwhich the optimalretailpriceandprofitsforthe three parties are calculated.These results are tabulated in Table2 in Appendix A.

OriginalSubstitutingthe value of w*3P backin 3,P the manufacturer'sprofitsaregiven by (4 - cm/)2/(83) 1 - P(A - b)(bA)/(4CL) We make the following observation regarding the optimal b value in the 3P Model.

OriginalOBSERVATION 2.

OriginalThemanufacturer'sprofitfunction is maximizedwhen b= (A+ A)/2. Note that in the 3P Model, the incentive of the third party to invest in the used-product collection effortis directlydrivenby b,the transferprice.Hence, the manufacturerfaces the following tradeoff.If she 'oSeePetruzziandDada(1999),Whitin(1955),andZabel(1970)for a similaruse of the methodology. nNote thatto ensureconcavityof the retailer'sobjectivefunction, b< A should be satisfied.See Lemma1 in AppendixA. Alternatively,one canalso show thatin equilibrium, when b> A,retailer's profitsbecomenegative.

OriginalThis content downloaded from 142.12.73.66 on Mon, 22 Apr 2013 14:09:08 PM All use subject to JSTOR Terms and Conditions Savaskan,Bhattacharya, and VanWassenhove:Closed-Loop SupplyChain Models

Original246 Management

OriginalScience50(2),pp. 239-252,c2004 INFORMS assigns a large value to b, she observes a high level of investmentby the thirdpartyin used-productcollection, but at the same time, her net savings from remanufacturing diminish, (i.e., Ab decreases)and, therefore,her profitsdecreaseas b approachesA.

OriginalWe find that the direct and indirect effects of b on the manufacturer'sprofits balance when b = (A+ A)/2, i.e., when both parties equally share the gains from remanufacturing.

OriginalFrom Observations 1 and 2, it is important to note that the transferprice b has completely different implicationsfor the supply chainprofitsin the R and the 3P Models. In the R Model, through b, the unit cost savings from remanufacturingare directly reflectedin the final demand of the product (i.e., the retailersets a lower price for the product),whereas in the 3P Model, b is a direct cost (i.e., a reduction in unit cost savings) for the manufacturerand the supply chain.

OriginalHence, the choice of the manufacturerconcerningwith whom and how she shares the cost savings from product remanufacturinghas importantconsequencesfor forwardchannelpricing decisions.

OriginalIn the following section,we comparethe threesupply chain models with respectto the retailprice, the product return rate, and the profits of the channel members.

Original5. Comparison of the Three

OriginalClosed-Loop Supply Chain Models Based on the results summarizedin Tables1 and 2, some interestingobservationscanbe madeon theperformance of decentralizedclosed-loop supply chain structures.

OriginalPROPOSITION

Original1. Theoptimalproductreturnratesare

Originalrelatedas r*c > TR > 7*M> rT3P Note that while the total savings from remanufacturing in the third-party model are given by (bA)7D(p(w)), the total savings are given by (AA)rD(p(w)) in the manufacturer collecting model.

OriginalFromObservation2, we see thatthe marginal benefit of investing in increasing7 in the 3P Model is less than the marginal gains in the M Model (i.e., (b*3P - A) < (A - A)). Hence, the third party invests less in used-product collection compared to the manufacturer in the manufacturer collecting system.

OriginalIn addition, the manufacturer can strategically set w in a way that would make used-product collection more profitable resulting in a second-degree effect on 7. Comparing the closed-loop supply chain models where the manufacturer versus the retailer collects, from Observation 1, we see that while both the manufacturer and the retailer face the same marginal gains from investing in increasing 7 (i.e., b*R - A = AA), the retailercanimpactthe marketsize by choosingp, whereas the manufacturercan influencethe demand only by strategicallychoosingthe wholesale price, w.

OriginalTheMModelhas a lowerproductreturnratethanthe R Model,becauseof double marginalization,the unit cost savings from remanufacturingis only partially reflectedin the finalpriceof the product.

OriginalThe centrally coordinated system leads to the highest investment level in used-productcollection, because the decisions are fully coordinated in the channel. The implications of Proposition 1 form the basis of an interestingfinding of the paper, vis-a-vis, the closer an agent is to the market,the more efficientis the collectionof used productsforallpartiesinvolved in the channel.The effective loss of efficiencyin the decentralizedsystemis mitigated,in part,by the ability to act more closely at influencingthe underlying demand.

OriginalPROPOSITION

Original2. The retailprices in the coordinated

Originalchannel andthethree casesin thedecentralized channel are relatedas follows: p*c < p*R< p*M < p*P. Consequently, D*c > D*R> D* > D*3P. The investment in collecting used products from the marketbenefits only the third party directly in the 3P system, and thereis only a second-ordereffect on the retail price in the form of a lower wholesale price offeredby the manufacturerto the retailer.

OriginalThe effect on the retail price is more direct in the M Model,as the manufacturer sets a lower wholesale price to increasedemand, and therebyincreasesher savings throughproductremanufacturing.

OriginalThereduction in retailpricein the RModelis the largestamong the decentralizedchannels,as the retailercan directly reflect the unit cost savings in the final demand through his pricing decision.

OriginalThe price in the coordinated channelis lower than all three decentralized channels, because the gains in efficiency from the coordinationeffortcan be effectivelysharedwith the marketto increaseboth demand and profits.

OriginalPROPOSITION

Original3. Themanufacturer's

Originalandretailer's profits in the decentralizedchannel are related as follows: l>I > * > HIl and [IR > [iM > Hi*3P. The total profits in the coordinatedchannel with recoveryalways dominate the total profits in the decentralizedchannel with recovery.Specifically,1*c > IRI> I; > H3P The implication of Proposition 3 and this section is that the ranking of the different closed-loop supply chain structures (in terms of benefits to the manufacturer and retailer) mirrors the benefits to nonsupply chain members as well.

OriginalThe benefits to society, in terms of an increased used-product return rate (greater reuse of products) as well as an increased This content downloaded from 142.12.73.66 on Mon, 22 Apr 2013 14:09:08 PM All use subject to JSTOR Terms and Conditions Savaskan,Bhattacharya, and VanWassenhove:Closed-Loop SupplyChainModels Management Science 50(2), pp.239-252, c2004INFORMS 247 ability to buy the product (greater demand), complement the increased profits for the manufacturer and retailerin the coordinatedsystem and R Model.

OriginalMcCartney(1999)and our own observationsin the industry empiricallycorroboratethe findings of the model. Whenthe manufacturer owns the distribution channel,as in the coordinatedcase, the manufacturer undertakesthe used-productcollectioneffortherself, as in the case of Xerox(XeroxCorporation2001).

OriginalIn the next section, we show that the manufacturercan furtherimprove the profitsin the R Model by coordinatingthe forward and the reverse channel decisionsvia a single two-parttariff.Tohighlight incentive issues, we consider an environmentwhere all cost parametersare common knowledge to the channelmembers(i.e.,no adverse selectionproblem) and the used-productcollectioneffortis fully observable (i.e.,no moralhazardproblem).

Original6. Improvements on the R Model

OriginalUnderthe assumptionof completeinformationabout cost and demand data and full observabilityof the retailer'scost when he undertakesthe used-product collectioneffort,we show that the manufacturercan offer a wholesale price to the retailerto induce him to choose an effort level that maximizes total channel profits.The details of the proof are presented in AppendixC.Proposition4 statesone formof the optimal contractthat the manufactureroffersthe retailer.

OriginalThe optimal coordinatingwholesale price is linear in the unit cost of manufacturing,Cmand 7. w(7) stands for a wholesale pricing scheme contingenton the returnrateof used productsfromthe market,and F is a fixedpaymentmadeby the retailerto the manufacturerthatdistributesthe efficiencygains.HI*c is the total profits in the coordinated channel, and IIHis the retailer'sprofitsin the decentralizedchannelwith the retailercollecting.

OriginalPROPOSITION 4.

OriginalThe form of the optimal contract, W*(7) = (w*(7), F*), which ensures that the retailer undertakesthe coordinated collectioneffort level and chargesthe optimalcoordinated retailpriceis given by w*(7) = c. - (A - b)r, 0 < T < 1,andF*= H*cfl2.

OriginalAs stated in the above proposition, to ensure that the retailer's profit-maximizing product return rate is, indeed, equal to the coordinated channel product return rate, the manufacturer offers a wholesale pricing scheme contingent on the product return rate characterized by the term (A - b)7.

OriginalSpecifically, the manufacturer puts the retailer in a position where he directly internalizes the cost consequence of his used-product collection effort. Besides ensuring the coordinated channel product return rate, the contract also provides a means for making the retail price of the product equal to the coordinated channel price level, thereby overcoming inefficienciesbecause of double marginalization.The optimal contractmakes thetransferpricebunnecessary,as themanufacturer's profitsarethe same for any b< A.

OriginalOur findings are consistent with the extant literature in marketingand economics, which shows that if the manufacturertransfersthe productsat the realized unit cost of production, coordinated channel retail price and profit levels can be attained in the decentralized setting.

OriginalThe fixed payment, F can be seen as a franchisee fee paid by the retailerto the manufacturertohavetherightsnotonlytoselltheproduct in themarket, butalsoto collecttheusedunits.It is interestingto note that by using a singlecontractual agreement(i.e., a simple two-parttariff,linear in 7), the manufacturercan coordinatethe decisions in the closed-loopsupply chain.Simpleformsof contractual agreements for channel coordinationalso make the R Model more attractivefor the manufacturercompared to a third-partysystem, for which one would need to design separate contractualagreements for the retailerand for the third party (Savaskanet al.

Original1999).

Original7. Contributions, Limitations, and

OriginalFutureResearch Designing effective remanufacturing systems has importantramificationsfor firms, regulatorybodies, and the market.The first contributionof this paper has been to identify the appropriateclosed-loop supply chain structurefor OEMs.We show that firms can design closed-loopsupply chainsto enhancetheir profits and marketdemand, and in conjunction,can increase the used-product return rate.

OriginalCoordination mechanismsaresuggested to betterachievethe above aims by providing suitableincentives in the form of simple two-parttariffs(aper unit wholesalepricelinear in productreturnrate coupled with a franchisee fee) to align the objectives of the members in the closed-loop supply chain.

OriginalIn the earlyphase of this research,we have made a numberof assumptionsthatmustbe relaxedin future research to develop a more comprehensive understanding of remanufacturing systems.

OriginalWe assume that, for the agent who implements the used-product collection effort, an infrastructure for the logistics of getting products back from customers and delivering them to the OEM already exists independently.

OriginalBased on the model analysis and insights, we conjecture that a high cost of establishing such a network would make it even more appropriate for a forward distribution channel member (e.g., the retailer) to undertake the used-product collection effort, as such networks are already in place in typical systems for forward distribution activities.

OriginalThis paper considered only a single agent undertaking the collection This content downloaded from 142.12.73.66 on Mon, 22 Apr 2013 14:09:08 PM All use subject to JSTOR Terms and Conditions Savaskan,Bhattacharya, and VanWassenhove:Closed-Loop SupplyChainModels

Original248 Management

OriginalScience50(2),pp. 239-252,c 2004INFORMS process. If there are multiple agents (e.g., retailers) undertaking the collection process in separate markets (such as geographically dispersed markets), the results of the model are not affected.

OriginalSavaskan and Van Wassenhove (2001) study the impact of product collection on retail competition. The location of the agents vis-a-vis the consumers and proximity to the market was not considered in this research.

OriginalIf the used-product collection is done through a fixed-price delivery system (such as prepaid envelopes in the regular mail), then the results of the model are not affected.

OriginalWe also did not model the multiperiod game, an extension of this study could find the impact of possible nonstationary material flows on the channel choice decision. We also assume that the firm has designed the product platform for reuse so that older products can be easily incorporated partially or wholly into the new product (Xerox Corporation 2001).

OriginalAn extension of this study should consider product platform design issues to make products easier to remanufacture. This research also assumed that all the products that are collected are usable for remanufacturing into new products.

OriginalFuture research should investigate the effect of the degree of product durability in the remanufacturing process. We assume that the marginal cost of collecting a used unit is independent of the scale of the operations.

OriginalThis is consistent with supply chain structures where there is already an existing reverse logistics network in place with sufficient capacity. There are two interesting avenues of research concerning costs of the collection effort.

OriginalFirst, one can examine the choice of closed-loop supply chain when the marginal cost of collection increases with the scale of operations.12 Second, one can also investigate capacity investment decisions in the closed-loop supply chain.

OriginalThird, we assumed that the cost of collecting a used unit is the same for all the agents of collection. An extension of this research could consider the case of unequal costs of collection because of economies of scale (we conjecture that this would favor third-party collection), proximity to the consumer (this would favor retailer collection), and other possible reasons.

OriginalThe modeling framework in this paper can easily be extended to address such related questions. In summary, this paper makes a contribution to the literature on distribution channel design by drawing attention to closed-loop supply chains, and developing a model of the tradeoffs underlying such systems.

OriginalOur recommendation is that firms make a conscious choice of supply chain, as different closed-loop supply chains may be appropriate in different environments, depending on the cost structures of the agents of collection.

OriginalSection 5, which summarizes the results of the model, provides some guidance in this regard. A combined design of the closed-loop supply chain can not only provide the firm with much-needed flexibility to reduce logistics costs for forward and reverse activities, but also enable it to signal continued concern and action on environmental issues.

OriginalAppendix A

OriginalLEMMA1.

OriginalIf thecondition of dHC(7)/d lT=1 < 0 is satisfied, thenr*,, f*RI *M, and T.c areall between 0 and1.

OriginalPROOF.

OriginalConsiderModelC-Centrally Coordinated

OriginalModel.

OriginalFor HIcto be concave in p and 7, Hc should satisfy conditions (i) 2HIC/aT2 < 0, (ii) d2FIC/d2p< 0, and (iii) (a2nC/ap2)(a2InC/lt2) > (a2IC/dpar)2. Notethat(i) holds since a2IiC/a72= -2CL and CL > 0. Likewise, (ii) holds since a2HC/lp2= -23 <0 and p> 0. To have an interior point solution for 7*c (i.e., 7*C < 1), we impose aC/la71,I= < 0. This condition can be written as 4CL> (0 - pcm)- (A - A) + 1(A - A)2.

OriginalFor condition (iii) to hold, we need (-2CL)(-21) > 32(A - A)2 #=4CL> p(AA)2,which follows fromthe previouscondition.Note that from condition (iii) and A > A, 7*c> 0 follows automatically(see Table1).

OriginalConsiderModelM--Manufacturer Collecting

OriginalModel.

OriginalHlMis concave in p since 2-M /d2 = -20 < 0 and > 0. n' is concavein w and 7 since a2H1M/w2 = -P < 0, d32M /~r2 = -2CL <0 and (d2IM/aw2)(d2nM/ r2) = 238CL > (p32/4)(AA)2= (d212M /dWr)2. Note thatthelastinequality holds from the condition (dIH(C)/rT,=j1 < 0) of Model C, and it ensuresT*M > 0 (see Table2).

OriginalFromTables1 and 2, we have 7*M= (0 - PCm)(A - A) (8CL - P(A - A)2)-1 < T*C,hence, 7*M < 1. Table

Original1 Comparison

Originalof Coordinated Supply Chain Models withor Without Remanufacturing Channel Decentralized Coordinated decision supply supply Coordinated supply and chain without chain without chain with profitsremanufacturing remanufacturing remanufacturing 3(o3Cm)2 (43pcm)2 (0gCm)2/(43) T 16P/ 4 [1- /(A - A)2/(4CL)]2 3 +3 pcm +3 pcm, b +pcm ( - pcm)(A - A)2

OriginalS4P 2 2/3 2(4CP3(A

Original- A)2)

OriginalSN/A N/A

Original( - Cm)(A - A) * +/3cm N/A N/A 2/3 ( c)2 N/A N/A * ( - pCM)2 S16Cm)2 N/A N/A 16/3 12 One way to model this aspect is to assume a total cost function, which is convex (e.g., quadratic)in the numberof returned products.

OriginalThis content downloaded from 142.12.73.66 on Mon, 22 Apr 2013 14:09:08 PM All use subject to JSTOR Terms and Conditions Savaskan,Bhattacharya, and VanWassenhove:Closed-Loop SupplyChainModels Management Science50(2),pp.

Original239-252,c2004 INFORMS 249 Table

Original2 Comparison

OriginalofDecentralized Supply Chain Models with Remanufacturing Channel decision andprofits RModel MModel 3PModel (3/4)(4pcm)2/(4p) ((4) - Pcm)2/(4p))[3/4 - p(AA)2/(16CL)] (() - (m,)2/(4p))[3/4P(AA)2/(64CL)] [1P(AA)2/(4CL)] [1P(AA)2/(8CL)]2 [1P(AA)2/(16CL)]2 [3CL - P(AA)2]0 + PCLCm 3)+ Cm ( - cm)(A - A)2 34+ pcm (4 - lCm)(A - A)2 P[4CL - P(AA)2] 4p 4[8CL - P(AA)2] 4P 4[16CL - P(AA)2] (0pcm)(A - A) ( m)(A - A) ( -Cm)(A -A) 8CL - 2P(A - A)2 8CL - P(AA)2 [16CL - P(A - A)2] * + 3Cm + 3Cm (AA)2( - p3Cm] 4) + 3Cm (0 - 3Cm)(A - A)2 2p 21 2[8CL - P(AA)2] 2p 2[16CL - 1(AA)2] ( m - pcm) /(8g) ( - lCm)2/(8p) ( - Pcm)l2 (8) [1p(AA)2/(4CL)] [1- (AA)2/(8CL)] [1- (AA)2/(16C)] ( p - /C,)2 m )2 - pCm,)2/(16) 16p[1p(AA)2/(4CL)] 163[1 - p(AA)2/(8CL)]2 [1P(A - A)2/(16CL)]2

OriginalI, N/A N/A (( - pCm)2/(16P))P(A -

OriginalA)2/(16CL)

Original[1p(AA)2/(16CL)]2 Consider Model R--Retailer CollectingModel. 11R is strictlyconcave in p and 7 since 821R/dp2 - -2/3 < 0, d2fR/d2 = -2CL < 0 and (2H-R/p2)(a2H-R/ar2) = 4PCL> p2(b - A)2 =- (d2H-R/dwdr)2.

OriginalNote that when the condition (dlIC(r)/dr=7I7 < 0) of Model C and b < A hold, the last inequalityis satisfied.FromTable2, we see that *R= (4 - Cm)(A - A)/(2[4CL - P(A - A) -(AA)]) = ,*c/2.

OriginalBecause 0 < r*c < 1, we get 0 < 7*R< 1. For Model 3P, Third-PartyCollectingModel, the concavity and the interiorpoint conditionscan be easily shown in a similarmanner. O

OriginalAppendix B

OriginalPROOF

OriginalOFOBSERVATION1.

OriginalFor the R system, the proof of Observation1 can be given as follows. First,we show that the manufacturer's profitfunctionis concavein w for a given b. This allows us to optimize the manufacturer's problem first over w for a given b and then examine the effectof b.

OriginalNote thatin the R system, for a given w and b, the retailersolves the followingproblem: Max(p - w)(4 - op) + br(o - pp) - CLT2 - Ar(T - pP). The optimalp and 7 values arelisted in the text in s4.3.

OriginalThemanufacturer takesintoaccountthereactionfunctionof the retailerand solves the following optimizationproblem. Max[w - Cm + (A - b)7*(w, b)]D(p*(w, b)). w,b Aftersubstitutingt*(w,b) and p*(w,b), the problemof the manufacturer is given by: w,b 4CL -3(b - A)2 2CL(bA)(A - b)( (4C, - P(b - A)2)2 Toshow thatthe manufacturer's profitsareconcavein w for a given b,we examinethe sign of d2r /l/dw2.

OriginalIt follows that 2 2CL 4CLP2(b - A)(Ab) dW2 4CLP(b - A)2 (4CLP(b - A)2)2 To show d2l-R/Iw2 < 0 for a given b, one needs to show mIW \'IC jV~LU IC l~~bL LV that 4CL82(bA)(A - b) 4CLQ (4CLP(b - A)2)2 4CLP(b - A)2 or, equivalently, P(b - A)(A - b) < 4CLP(b - A)2, which reduces to P(b - A)(A - A) < 4CL.Because 4CL> P(A - A)2 holds from the interiorpoint restrictionon 7* in Model C (Lemma 1) and b < A, it follows that P3(b - A)(A - A) < 4CL holds.

OriginalHence,IH'lis concavein w for a given b. In the second partof the proof,we examinethe effectof b on the profits of the manufacturer. Hence, the proof of Observation1 for the R system follows from the fact that j-H/9b and OHd4/ab > 0. To show these statements,note that / (4pCm)2 A-A db 32CL (1 - P3(A - A)(b - A)/(4CL))2' which is always positive.Fromthe value of HIR, aftersome simplification, arR (~ - 3Cm)2 A -b db 32CL (1 - P3(A - A)(b - A)/(4CL))3' which is always nonnegative from the assumption that A > b and P(b - A)(A - A)/(4CL) < P(A - A)2/(4CL) < 1, which follows fromour Assumption9.

OriginalO

OriginalPROOF

OriginalOFOBSERVATION.

OriginalWe follow a similar procedure for the proof of the optimal b value in the 3P system. First, we show that the manufacturer'sprofitsare concavein w fora given bandthen,we optimizeoverb.Inthe3Psystem, This content downloaded from 142.12.73.66 on Mon, 22 Apr 2013 14:09:08 PM All use subject to JSTOR Terms and Conditions Savaskan,Bhattacharya, and VanWassenhove:Closed-Loop SupplyChainModels

Original250 Management

OriginalScience 50(2), pp.239-252, c 2004

OriginalINFORMS

Originalthe retailerand the third party solve the following problems, respectively, for p*(w) and r*(b): Maxp(pw)(0 - pp) and Max,br(4 - pp) - CL72Ar(0 - op). The manufacturertakes into accountthe reactionfunctions of the retailerand the thirdparty and solves the following optimizationproblemfor w*: Max[4 - 1p*(w)][w - Cm + (A - b)7*(b)] Max0-pow [ Cm (Ab)(bA)( - pw) w 2 To show that the manufacturer'sprofitis concave in w for a given b, we examine the sign of d2H3PM/w2.

OriginalNote that d21/3MP/W2 = -[1 - 3P(b - A)(A - b)/(4CL)]. By rearranging the terms, it follows that the concavitycondition d2H-3P/,w2 < 0 reduces to 4CL> p(b - A)(Ab). Fromthe interior point restrictionon 7*in Model C (Lemma 1), this holds true.

OriginalBecause P3(bA)(A - b) is equivalent to P(b - A)(A - A) - P(b - A)2, which is less than P(A - A)2, the concavity condition 4CL> ,P(b - A)(A - b) also holds for a given b. Next, we solve forthe optimalbvalue,which maximizes the manufacturer's profits.Note thatthe optimizationof r13P~( - o Cm)2/(80) M 1- (A - b)(bA)/(4CL) w.r.t.b is equivalentto the minimizationof the expression 1 - P(A - b)(bA)/(4CL), and this expression is minimized when 3(Ab)(bA) is maximized.

OriginalIt can easily be shown that b*= (A+ A)/2.

OriginalPROOF

OriginalOFPROPOSITION

Original1. The proof of Proposition 1 can

Originalbe trivially observed from the values of 7*(the product returnrate)for the C,R, M, and 3P channelsin Table2.

OriginalPROOFOF PROPOSITION2.

OriginalWedivide the proofinto three parts: (i) To prove p*C< p*R,we have to show that +-pcCm (0--pCm)(A - A)2 [3CL-(A-A)2]b+/CLCm 2/3 2(4CL - /(A - A)2) 3P[4CL - (AA)2] Aftersimplification,this reducesto showing that 0 + pcm (4 + Pcm)[4CL - P(A - A)2]+ 2CL (4 - 3Cm) 2 2-----4CL -/3(A - A)2] 2P 2P[4C,- P(AA)2] or 0 > [Cm, which is true by Assumption 4 (nonnegative demand).

Original(ii) Toprove p*R< p*M, we have to show that [3CLP(A - A)2]4)+ ICLCm P[4CLP(A - A)2] 34 + pcm (4 - pcm)(AA)2 43 4[8CLP(A - A)2] (4 - pcm)(AA)2 4[8C,- P(AA)2] < {(34 + Pcm)[4CLP(A - A)2] - [3CLP(A - A)2]44 - 4P8CLCm - {4P[4CL - P(A - A)2]}-1.

OriginalOn simplification,this reducesto showing that (4 - pcm)(A - A)2 (0 - PCm)(A - A)2 4[8CLP(A - A)2] 4[4CLP(A - A)2 ' which follows fromsimple algebra. (iii) Toshow thatp*M < p*3P, we have to show 34)+ pcm (4 - pcm)(AA)2 4/ 4[8CLP(A - A)2] 34) + Cm (4 - PCm)(AA)2 4/ 4[16CL - P(AA)2]' which follows from simple algebra.Becausethe ordering for the retailprice p*holds, the orderingfor the demands of the channelsfollows trivially.

OriginalO

OriginalPROOF

OriginalOFPROPOSITION

Original3. The proof of Proposition 3 follows fromsimplealgebra.InTable2, HR > IIM and IlH*>

OriginalH` areobvious,as aretheresultsof II*R>

OriginalIIIM

Originaland HM > HI3". Because

OriginalRHI

Original> HM and

OriginalHIR

Original> M, it triviallyfollows that n*R> I1MM. To show that i*M> H*3P, we have to show (4 -pCm)2 3 P(A - A)2 ( - Cm)2 3 P(A - A)2 4P 4 16CL 40 14 64C p(A - A)2 2 P( - A)2 8CL 16CL which follows fromsimple algebra.Theproofof i*c > IR is analogous.

OriginalAppendix C

OriginalFollowingthe theoryof incentivecontracts(see Laffontand Tirole1993),we take a principal-agentapproach,with the manufacturer as the principal.Theroleof the manufacturer as the principalis consistentwith the spirit of the earlier sectionsof this paper,which give the manufacturer the role of theleaderin theStackelberg game.Themanufacturer can influence the retailer'schoice of the collectioneffort level by specifying a contract of the type W(7)= [w(7), F]. Here, w(7) stands for a wholesale pricingscheme contingenton the returnrateof used productsfromthe market,and F is a fixedpaymentmadeby theretailerto the manufacturer that distributesthe efficiency gains.

OriginalThus, the manufacturer's problemis formulatedas Max Hl = (w(r) - (Cm - AT))D(p) - brD(p) + F (5) W(T),T" subjectto r = argmax{IHl(W(r), b)) (6) p=argmax{IHR(W(r), b)} (7) p where HI is the retailer's profit level realized in the decentralized channel structure,and I (W(r), b) = [p - w(7)]D(p) + brD(p) - C(7) - F is the profit function of the retailerunder the contractW(r).

OriginalThe first two constraints are the incentive compatibility constraints for 7 and p, This content downloaded from 142.12.73.66 on Mon, 22 Apr 2013 14:09:08 PM All use subject to JSTOR Terms and Conditions Savaskan,Bhattacharya, and VanWassenhove:Closed-Loop SupplyChain Models Management Science 50(2), pp.239-252, @2004

OriginalINFORMS 251

Originalrespectively,which ensure that p and 7 are maximizersof the retailer'sprofitfunction,while the last constraintis the individualrationalityconstraintof the manufacturer, which ensuresthatthe retaileracceptsthe contract.

OriginalWhen the retailerretainsprivate informationabout the cost of his collectioneffort(i.e.,the adverseselectionproblem),orwhen thecollectioneffortlevel of theretailercannot be fullyobserved,orthereis noise in the returnrateof used products(i.e.,the moralhazardproblem),the optimalcontractis updatedto incorporatethe informationconstraints.

OriginalIn Savaskanet al. (1999),it is shown thatthe adverseselection problemin the closed-loop supply chain can be overcomeby using a menuof contracts,whichwould inducethe retailerto revealthe true cost of his collectioneffortto the manufacturer.However, to achieve this, the manufacturer leaves some rentwith the retailer,which leads to an inefficientlevel of productreturnrateand lower supply chain profits.If the manufacturer facesmoralhazardissues in the closed-loopsupply chain,and if the retaileris riskneutral, one can easily show thatthe full informationoutcomecan be obtainedby using the linearcontractoutlined as above (Holmstrom1979, 1982).When the retaileris risk averse, the optimalcontractis adjustedby takingintoconsideration the riskaversionof the retailerand the informationon the productreturnrate.