<%BANNER%>

Models for Assortment Planning under Product Returns

Permanent Link: http://ufdc.ufl.edu/UFE0024144/00001

Material Information

Title: Models for Assortment Planning under Product Returns
Physical Description: 1 online resource (127 p.)
Language: english
Creator: Grasas, Alexandre
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: assortment, consumer, inventory, nmnl, om, pricing, product, retailing, returns
Industrial and Systems Engineering -- Dissertations, Academic -- UF
Genre: Industrial and Systems Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: In the past decade, internet and flexible manufacturing have revolutionized some of the basic principles of retailing. Two such aspects relate to product assortment and return policies. With the aid of advanced production technology, companies continuously increase their product assortments to reach more customers and satisfy their specific needs better. Higher product variety, however, typically raises operational complexity and costs. In addition, these costs can even be more significant when product returns are considered. We integrated return policies into a multiproduct model, where assortment, inventory, and/or pricing decisions were made in an integrated manner. Our research agenda focused on an expected-profit-maximizing firm that offers a set of horizontally differentiated products. The firm accepts product returns that are in resalable condition. We characterized the firm's return policy by the money refunded to the customer in case of return. We have a demand model that is based on individual consumer behavior, conceptualized to fit a well established two-stage utility maximization framework (nested multinomial logit model). Consumers decide which product (if any) out of a given assortment to buy in the first stage, and then decide to keep or return the item in the second stage. Our study shows an interesting interaction between product assortment and return policy. We explored the implications of return policies on product assortment planning. We showed that the structure of the optimal assortment fundamentally changes depending on the amount refunded and/or operational mode (make-to-order versus make-to-stock). Surprisingly, there are situations where a retailer is better off by offering eccentric products (i.e., those that are least likely to be purchased by a typical consumer). We also explored return policies for customized products. We determined that customizing firms should aim for product returns that are neither a net cost nor a net benefit. This can be achieved by partial refunding when designing their consumer return policies. In addition, we were the first to investigate return policies in a multiperiod environment. Restricting return policies to a single period analysis only, as other authors do, may lead to wrong conclusions. We show, for example, that firms can reduce their price when they consider multiple periods. In this multiperiod setting, we found that a salvage-down-to level inventory policy is optimal.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Alexandre Grasas.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Akcali, Elif.
Local: Co-adviser: Alptekinoglu, Aydin.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2011-05-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0024144:00001

Permanent Link: http://ufdc.ufl.edu/UFE0024144/00001

Material Information

Title: Models for Assortment Planning under Product Returns
Physical Description: 1 online resource (127 p.)
Language: english
Creator: Grasas, Alexandre
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: assortment, consumer, inventory, nmnl, om, pricing, product, retailing, returns
Industrial and Systems Engineering -- Dissertations, Academic -- UF
Genre: Industrial and Systems Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: In the past decade, internet and flexible manufacturing have revolutionized some of the basic principles of retailing. Two such aspects relate to product assortment and return policies. With the aid of advanced production technology, companies continuously increase their product assortments to reach more customers and satisfy their specific needs better. Higher product variety, however, typically raises operational complexity and costs. In addition, these costs can even be more significant when product returns are considered. We integrated return policies into a multiproduct model, where assortment, inventory, and/or pricing decisions were made in an integrated manner. Our research agenda focused on an expected-profit-maximizing firm that offers a set of horizontally differentiated products. The firm accepts product returns that are in resalable condition. We characterized the firm's return policy by the money refunded to the customer in case of return. We have a demand model that is based on individual consumer behavior, conceptualized to fit a well established two-stage utility maximization framework (nested multinomial logit model). Consumers decide which product (if any) out of a given assortment to buy in the first stage, and then decide to keep or return the item in the second stage. Our study shows an interesting interaction between product assortment and return policy. We explored the implications of return policies on product assortment planning. We showed that the structure of the optimal assortment fundamentally changes depending on the amount refunded and/or operational mode (make-to-order versus make-to-stock). Surprisingly, there are situations where a retailer is better off by offering eccentric products (i.e., those that are least likely to be purchased by a typical consumer). We also explored return policies for customized products. We determined that customizing firms should aim for product returns that are neither a net cost nor a net benefit. This can be achieved by partial refunding when designing their consumer return policies. In addition, we were the first to investigate return policies in a multiperiod environment. Restricting return policies to a single period analysis only, as other authors do, may lead to wrong conclusions. We show, for example, that firms can reduce their price when they consider multiple periods. In this multiperiod setting, we found that a salvage-down-to level inventory policy is optimal.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Alexandre Grasas.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Akcali, Elif.
Local: Co-adviser: Alptekinoglu, Aydin.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2011-05-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0024144:00001


This item has the following downloads:


Full Text

PAGE 1

1

PAGE 2

2

PAGE 3

3

PAGE 4

Thisrepresentsthenaleofoneofthemostenrichingexperiencesinmylife,andIwouldliketothankallpeoplewhohelpedalongtheway.First,IamindebtedtoJaumeRibera,whosawinmepotentialtopursueanacademiccareerandencouragedmetostartthisjourney.Second,Iwishtoexpressmysinceregratitudetobothofmyadvisors,ElifAkalandAydnAlptekinolufortheirimmensehelpandguidance.Banaverdiinizdesteinkymetinibiliyor,herikinizedeokteekkrediyorum.IamthankfultotheothermembersofmySupervisoryCommittee,ProfessorsJosephGeunes,H.EdwinRomeijn,AsooJ.VakhariaandJaniceE.Carrillofortheirtimeandhelpfulcomments.IalsowouldliketoacknowledgethenancialsupportprovidedbytheNationalScienceFoundationunderGrantsNo.0522960and0536026.Gainesvillehasbeenmyhomeformorethanfouryears,andIhavehadtheopportunitytomeetwonderfulpeoplewithwhomIsharedmyupsanddownsduringthisadventure.Theyhavebeenmyfamilyacrossthepond.Ofallofthem,IwouldliketomentionVanessa,Ignasi,Caro,Guille,Laura,Martn,Jess,Gubjrt,rni,Gaia,MehmetandRichard.IalsothankallISEgradstudentsforallgatherings,BBQ'sandgoodmomentsinWeilHall.MythankfulnessalsogoestoallmysoccerbuddiesforkeepingmeinshapeandallowingmetowinallthoseGatorT-shirts.Next,Iwishtothankmyfamilyfortheirunconditionalloveandsupport(andtheirvisits):myparentsJoanandLaura,mybrothersEduandJoan,mybelovedsisterLaia,myparents-in-lawModestandChusandmybrother-in-lawDavid.Theywerealwaysunderstandingdespitedistanceandthetimewehavebeenabroad.Vullagrairalamevafamlialasevaestimaisuportincondicional(ilessevesvisites):elsmeusparesJoaniLaura,elsmeusgermansEduiJoan,lamevaestimadaLaia,elsmeussogresModestiChus,ielmeucunyatDavid.Hanestatsemprecomprensiusmalgratladistnciaieltempsquehemestatfora.

PAGE 5

5

PAGE 6

page ACKNOWLEDGMENTS ................................. 4 LISTOFTABLES ..................................... 9 LISTOFFIGURES .................................... 10 ABSTRACT ........................................ 12 CHAPTER 1INTRODUCTION .................................. 14 1.1BackgroundandMotivation .......................... 14 1.2Impact ...................................... 15 2LITERATUREREVIEW .............................. 16 2.1AssortmentPlanning .............................. 16 2.2ProductReturns ................................ 17 3ASSORTMENTPLANNINGUNDEREXOGENOUSPRICEANDREFUNDFRACTIONINASINGLEPERIODSETTING .................. 19 3.1Introduction ................................... 19 3.2LiteratureReview ................................ 22 3.3Model ...................................... 23 3.3.1ProductAssortmentandReturnPolicy ................ 24 3.3.2IndividualConsumerChoiceBehaviorandAggregateDemand ... 26 3.3.3SupplyProcessandtheTimingofEvents ............... 30 3.4StructureoftheOptimalAssortment ..................... 33 3.4.1TheMTOModelwithReturns ..................... 34 3.4.2TheMTSModelwithReturns ..................... 36 3.4.3TheMTOandMTSModelswithoutReturns ............. 38 3.4.4NumericalExample ........................... 38 3.5InsightsandDiscussion ............................. 39 3.5.1ProtLossfromIgnoringProductReturnsorAssumingtheWrongStructureforOptimalAssortment ................... 40 3.5.2DoesMoreLenientReturnPolicyMeanLessVariety? ........ 41 3.5.3ImpactofProductDierentiationonOptimalVarietyandProt .. 42 3.5.4EectofPost-purchaseHeterogeneityonOptimalProt ....... 44 3.5.5ImpactofDemandVariabilityonOptimalAssortment ........ 45 3.6ConcludingRemarks .............................. 45 6

PAGE 7

.................... 52 4.1Introduction ................................... 52 4.2EndogenousPrice ................................ 52 4.2.1VarietyversusPrice ........................... 52 4.2.2BehaviorofExpectedProtwithRespecttoPrice .......... 53 4.2.3OptimalPricewithRespecttoRefundFraction ........... 53 4.2.4OptimalPriceforMost-popularandMost-eccentricAssortments .. 54 4.3EndogenousRefundFraction .......................... 55 4.3.1BehaviorofExpectedProtwithRespecttoRefundFraction .... 55 4.3.2OptimalRefundwithRespecttoPrice ................ 56 4.3.3OptimalRefundFractionforMost-popularandMost-eccentricAssortments 57 4.4Multiple-PeriodProblem ............................ 58 5OPTIMALPRICEANDREFUNDFORAGIVENASSORTMENTINASINGLEPERIODSETTING ................................. 67 5.1Introduction ................................... 67 5.2LiteratureReview ................................ 70 5.3ModelDescription ............................... 72 5.3.1Firm ................................... 72 5.3.2DemandandReturnProcesses ..................... 74 5.4Analysis ..................................... 76 5.4.1SpecialCasewithNoReturnsAllowed ................ 78 5.4.2SpecialCasewithFullRefund ..................... 80 5.5Conclusion .................................... 82 6OPTIMALPRICE,REFUNDANDINVENTORYPOLICYFORAGIVENASSORTMENTINAMULTIPLEPERIODSETTING .............. 83 6.1Introduction ................................... 83 6.2OptimalInventoryPolicy ............................ 83 6.3OptimalPriceandRefund ........................... 86 6.4ExpectedReturnsHeuristicfortheOptimalPrice .............. 89 6.4.1HeuristicPerformance .......................... 91 6.4.2Multi-singlePeriodversusMultiplePeriod .............. 92 6.5ApproximateSolution ............................. 93 6.6Conclusion .................................... 94 7CONCLUSION .................................... 101 7.1Summary .................................... 101 7.2FutureResearch ................................. 102 APPENDIX:PROOFS ................................... 104 7

PAGE 8

....................................... 121 BIOGRAPHICALSKETCH ................................ 127 8

PAGE 9

Table page 3-1OptimalassortmentS,composedofproductsthatcorrespondtoshadedcells,fortheprobleminstanceinTable 3-2 withthresholdrefundfraction,(vl)=p=0:8 46 3-2BaseparametervaluesforthenumericalstudyinChapter 3 ........... 47 3-3Thepreferences(!values)forvesetsofproductswithdierentdegreesofdierentiation:I(identical),VS(verysimilar),S(similar),D(dierent),andVD(verydierent). 47 3-4OptimalassortmentS,composedofproductsthatcorrespondtoshadedcells,fortheprobleminstanceinTable 3-2 withdemandvariability=5 47 4-1BaseparametervaluesforthenumericalstudyinChapter 4 ........... 59 4-2OptimalassortmentS,composedofproductsthatcorrespondtoshadedcells,foramultipleperiodproblemwith3periods .................... 60 4-3OptimalassortmentS,composedofproductsthatcorrespondtoshadedcells,foramultipleperiodproblemwith10periods ................... 61 6-1BaseparametervaluesforstudyingtheExpectedReturnsHeuristic ....... 95 6-2Heuristicperformance ................................ 96 6-3ComparisonbetweenMulti-singlePeriodandMultiplePeriodProblems ..... 97 6-4Comparisonbetweenprices ............................. 99 9

PAGE 10

Figure page 3-1Protlossfromassumingthewrongstructure(foroptimalassortment)andfromignoringreturns .................................... 48 3-2Varietyversusreturnpolicy:Numberofproductsintheoptimalassortment(jSj)asrefundfraction()varies ......................... 48 3-3Numberofproductsintheoptimalassortment(jSj)atvedegreesofproductdierentiation(datagiveninTable 3-3 ) ....................... 49 3-4Percentincreaseinoptimalexpectedprot(withrespecttoscenarioI)atvedegreesofproductdierentiation(datagiveninTable 3-3 ) ............ 49 3-5Optimalexpectedprotversusrefundfraction()fordierentlevelsofpost-purchaseheterogeneity(2)underMTOenvironment .................... 50 3-6Optimalexpectedprotversusrefundfraction()fordierentlevelsofpost-purchaseheterogeneity(2)underMTSenvironment .................... 50 3-7Numberofproductsintheoptimalassortment(jSj)withdierentlevelsofaggregatedemandvariability() ................................ 51 4-1Varietyversusprice(MTO):Numberofproductsintheoptimalassortment(jSj)asprice(p)variesfordierentvaluesofrefundfraction() ............ 59 4-2Varietyversusprice(MTS):Numberofproductsintheoptimalassortment(jSj)asprice(p)variesfordierentvaluesofrefundfraction() ............ 60 4-3Protversusprice(MTO):Expectedprotasprice(p)variesfordierentrefundfractions(alpha)underoptimalassortment(S) .................. 61 4-4Protversusprice(MTS):Expectedprotasprice(p)variesfordierentrefundfractions(alpha)underoptimalassortment(S) .................. 62 4-5Priceversusrefund(MTO):Optimalprice(p)andrefund(p)fordierentvaluesofrefundfraction()underoptimalassortment(S) ........... 62 4-6Priceversusrefund(MTS):Optimalprice(p)andrefund(p)fordierentvaluesofrefundfraction()underoptimalassortment(S) ........... 63 4-7Optimalprice(p)withdierentassortmentstructuresforMTOcase ...... 63 4-8Optimalprice(p)withdierentassortmentstructuresforMTScase ...... 64 4-9Protversusrefundfraction(MTO):Expectedprotasrefundfraction()variesfordierentprices(p)underoptimalassortment(S) ............... 64 10

PAGE 11

............... 65 4-11Refundversusprice(MTO):Optimalrefundfraction()andrefund(p)fordierentprices(p)underoptimalassortment(S) ................. 65 4-12Refundversusprice(MTS):Optimalrefundfraction()andrefund(p)fordierentprices(p)underoptimalassortment(S) ................. 66 4-13Optimalrefundfraction()withdierentassortmentstructures ........ 66 6-1ExpectedprotfordierentpricesusingMonteCarlosimulationmethods ... 95 11

PAGE 12

Inthepastdecade,internetandexiblemanufacturinghaverevolutionizedsomeofthebasicprinciplesofretailing.Twosuchaspectsrelatetoproductassortmentandreturnpolicies.Withtheaidofadvancedproductiontechnology,companiescontinuouslyincreasetheirproductassortmentstoreachmorecustomersandsatisfytheirspecicneedsbetter.Higherproductvariety,however,typicallyraisesoperationalcomplexityandcosts.Inaddition,thesecostscanevenbemoresignicantwhenproductreturnsareconsidered. Weintegratedreturnpoliciesintoamultiproductmodel,whereassortment,inventory,and/orpricingdecisionsweremadeinanintegratedmanner.Ourresearchagendafocusedonanexpected-prot-maximizingrmthatoersasetofhorizontallydierentiatedproducts.Thermacceptsproductreturnsthatareinresalablecondition.Wecharacterizedtherm'sreturnpolicybythemoneyrefundedtothecustomerincaseofreturn.Wehaveademandmodelthatisbasedonindividualconsumerbehavior,conceptualizedtotawellestablishedtwo-stageutilitymaximizationframework(nestedmultinomiallogitmodel).Consumersdecidewhichproduct(ifany)outofagivenassortmenttobuyintherststage,andthendecidetokeeporreturntheiteminthesecondstage. Ourstudyshowsaninterestinginteractionbetweenproductassortmentandreturnpolicy.Weexploredtheimplicationsofreturnpoliciesonproductassortmentplanning.Weshowedthatthestructureoftheoptimalassortmentfundamentallychangesdepending 12

PAGE 13

13

PAGE 14

RogersandTibben-Lembke 1998 ,pp.6).TheannualvalueofreturnedgoodsintheUnitedStatesisapproximately$100billion,andcompaniesspendmorethan$40billionannuallyontheirreverselogisticsprocessesforhandlinganddispositionofreturns( Blanchard 2005 Enright 2003 ). Returnpoliciesareusuallythoughtofasmicroandmoreoperational,whereasproductassortmentisusuallythoughtofasstrategicandmoremarketingrelated.Therefore,decisionsassociatedwitheachareoftenmadeseparately(see Stocketal. 2006 ,and OlavsonandFry 2006 ).Inourresearch,weintegratereturnpoliciesintoamultiproductmodel,whereassortment,inventory,and/orpricingdecisionsaremadeinanintegratedmanner;somethingthathasneverbeenexploredbeforeintheliterature.WeshowthatintegratingthesedecisionsOurresearchagendafocusesonan 14

PAGE 15

15

PAGE 16

Thetopicofthisdissertationmergestwostreamsofliteraturethathavebeentraditionallyseparate:assortmentplanningandproductreturns.InthisChapterweprovideageneraloverviewofthetwostreamsofliterature.InChapters 3 and 5 wediscussliteraturerelatedtoeachspecicprobleminmoredetail. Broniarczyketal. 1998 Hochetal. 1999 BoatwrightandNunes 2001 vanHerpenandPieters 2002 Borleetal. 2005 deVries-vanKetel 2006 Bergeretal. 2007 ).Thereisalsoanewlyburgeoningstreamofproductvarietyliteratureinoperationsmanagement(OM).Inaseminalpaper, vanRyzinandMahajan ( 1999 )introduceoperationalcosts(i.e.,inventorycosts)totheassortmentplanningproblem.Usingthemultinomiallogit(MNL)modelfortheconsumerchoiceprocess,theyshowthattheoptimalassortmenthasaverysimplestructure:itconsistsofsomenumberofmostpopularproducts.AsweproveanalyticallyinChapter 3 ,considerationofproductreturnscanreversethisintuitiveresult,alsoshowninvariousothercontexts( AydinandRyan 2000 HoppandXu 2005 MaddahandBish 2007 Li 2007 ).Later, Cachonetal. ( 2005 )introducetheconsumersearchtotheassortmentproblem.Intheirmodel,theconsumerscanopttoleavewithoutpurchasing,andsearchfortheproductelsewhere.Theauthorsndthat,whenthedierentproductswithinacategoryarelimited(e.g.,digitalcameras),thermexpandsitsassortmenttopreventthecustomerfrombalking. GaurandHonhon ( 2006 )alsostudytheassortmentplanningproblemwithinventorycosts,but,unliketheotherpaperscited,theyusealocationalchoicemodeltocharacterizethedemandprocess,andpointoutinterestingdierencesitmakes.Understaticsubstitution(thatis,costumersdonotsubstituteintheeventofastockout), GaurandHonhon ndthattheoptimalassortmentcontainsproductsthatareequallyspacedout 16

PAGE 17

MaddahandBish ( 2007 )extendtheworkof vanRyzinandMahajan ( 1999 )byendogenizingthepricingdecision;theyderivethestructureoftheoptimalassortmentwhenallproductshavethesameunitcostanddierentendogenousprices. Li ( 2007 )proposesanassortmentandinventoryjointoptimizationproblemwherethecostparametersfortheproductsareallowedtobedierent.Hedeterminestheoptimalstructureassumingthestoretraciscontinuous.Theoptimalassortmentincludessomenumberofproductswiththehighestprotrate(i.e.,expectedprotfromaproductifitweretoattract100%ofthestoretrac).Finally,thereaderisreferredto Kketal. ( 2006 )foracompletereviewoftheassortmentplanningliterature. GuideandvanWassenhove 2003 ,and Dekkeretal. 2004 ).Involvingunusedproducts, Pasternack ( 1985 ), EmmonsandGilbert ( 1998 ),and Tsayetal. ( 1999 )analyzereturnpoliciesoeredbymanufacturerstoretailers(sometimesalsoframedasbuy-backcontracts)forproductsthatremainunsoldattheendofasellingseason. Inourresearch,wefocusonconsumerproductreturns,thatis,thosereturnsoeredbyretailerstoconsumers,whereareturnedproductisusuallyinresalablecondition.InOM,arguingthatreturnsneedtobetakenintoaccountininventorymanagement,sincetheycanactasasupplementarysourcetosatisfydemand,theexistingresearchfocusesoncharacterizingtheoptimalorderingpolicyofaretailer( VlachosandDekker 17

PAGE 18

, Mostardetal. 2005 ,and MostardandTeunter 2006 ).Thesepapersassumeagivenconsumerreturnpolicy.Tothebestofourknowledge,onlythreepapersallowendogenousrefunddecisionsinaretailingcontext. MukhopadhyayandSetoputro ( 2005 )adoptadeterministiclineardemandmodelthatdependsonprice,refundandmodularity,wherethelasttwoaredecisionvariables. Yalabiketal. ( 2005 )integratelogisticsandmarketingdecisionsintothereturnsystem,and Su ( 2008 )endogenizespriceandorderquantityinadditiontorefund.Inthesetwopapers,demandisdrivenbyconsumervaluationoftheproduct. Inmarketingliterature,productreturnsresearchconcentratesontheinuenceofaretailer'sreturnpolicyonconsumers( Wood 2001 ).Forexample, Davisetal. ( 1995 ), Che ( 1996 ), Davisetal. ( 1998 )and Heimanetal. ( 2002 )studytheimplicationsoffullmoney-backguaranteesonconsumers'behavior.Otherstakerefundasdecisionvariable,andshowthebenetsofstricterreturnpolicies( Hessetal. 1996 MukhopadhyayandSetoputro 2004 Shulmanetal. 2007 ,and Shulmanetal. 2008 ). 18

PAGE 19

Stocketal. 2006 ,and OlavsonandFry 2006 ).Ourtheoreticalmodelcountersthisconventionalthinkingbyshowingthatoptimalassortmentdecisionsfundamentallychangeinthepresenceofreturns. Ifaconsumerdecidestoreturnaproductduetoqualityproblems(i.e.,asitisdamagedordoesnotwork),thentypicallytheretailerreturnsthisproducttothemanufacturerandiscompensatedforit.However,iftheconsumerdecidestoreturntheproductduetoalaterealizationofmistwithherpreferences(i.e.,theproductisnebuttheconsumersimplydoesnotwantitanymore,e.g.,agarmentnotfeelingright),thentheretailerhastohandlethereturn.Ourfocusinthisdissertationisthelattertypeofreturnsinvolvingaproductinresalablecondition. Financialimpactofreturnpoliciescanbequitelargeforaretailer.Overallcustomerreturnsareestimatedtobe6%ofsalesintheUnitedStates,andmayrunashighas15%formassmerchandisersandupto35%forcatalogande-commerceretailers( RogersandTibben-Lembke 1998 ,pp.6).TheannualvalueofreturnedgoodsintheUnitedStatesisapproximately$100billion,andcompaniesspendmorethan$40billionannuallyontheirreverselogisticsprocessesforhandlinganddispositionofreturns( Blanchard 2005 Enright 2003 ). Motivatedwiththequestionofwhetherretailersshouldconsiderreturnswhenmerchandising,inthischapterweexploretheinteractionsbetweenproductassortmentdecisionandreturnpolicyofaprice-takingretailerunderbothmake-to-order(MTO) 19

PAGE 20

Wehaveademandmodelthatisbasedonindividualconsumerbehavior,conceptualizedtotawellestablishedtwo-stageutilitymaximizationframework(nestedmultinomiallogitmodel).Consumersdecidewhichproduct(ifany)outofagivenassortmenttobuyintherststage,andthendecidetokeeporreturntheiteminthesecondstage.Onthesupplyside,theretailermakesanassortmentdecisionbychoosingasubsetofallpotentialproductoeringsthatfallwithinaparticularproductlineofhorizontallydierentiateditems.IntheMTScase,theretaileralsomakesaninventorydecisionforeachproductoered.Priceisexogenous(i.e.,dictatedbythemanufacturerthroughMSRP),andproductsdieronlyintermsoftheirattractiveness(denedpreciselyinx ).Wecallproductswithhigh(low)attractivenesspopular(eccentric),becausetheyaremore(less)likelytobepurchasedbyatypicalconsumer. Weexclusivelyfocusononeaspectofreturnpolicies:refundamount,whichweparameterizebyrefundfraction,thepercentageofpricerefundedintheeventofareturn.Likeprice,weassumerefundfractiontobeexogenous,possiblydrivenbyacategory20

PAGE 21

Weshowthatthestructureoftheoptimalassortment,whichmaximizestheretailer'sexpectedprot,criticallydependsontherefundfractionandwhethertheproductsaresuppliedonanMTOorMTSbasis.Morespecically,wehavetwomajorresults: conrmthis.Includingonlythemostpopularproductsinanassortmentagreeswithcommonintuition,previousresultsintheliterature( vanRyzinandMahajan 1999 AydinandRyan 2000 HoppandXu 2005 MaddahandBish 2007 Li 2007 ,and CachonandKk 2007 ),andsomeindustrypractice( Cargilleetal. 2005 ,and OlavsonandFry 2006 ).Asindicatedabove,weshowthatthepresenceofreturnscanreversethisintuitiveresult. Thebasicrationaleforincludinganeccentricproductintheoptimalassortmentistobenetfromtheprocessingandresaleofreturneditems.Thisbenetishigherforlowrefundfractions,andeccentricproductshaveahigherlikelihoodofbeingreturned.The vanRiperandNolan ( 2008 )formoreexamples. 21

PAGE 22

Inlightofouranalyticalresults(presentedinmoredetailinx )andnumericalobservations(reportedinx ),weconcludethat:retailersshouldnotonlycarefullyconsidertheirreturnpolicywhenmerchandising,theyshouldalsotaketheirbasicoperationalmode(MTOversusMTS)intoaccount. Shugan 1989 BayusandPutsis 1999 CachonandKk 2007 ,and AlptekinoluandCorbett 2008b );impactofproductvarietyonconsumerbehavior( Hochetal. 1999 Kimetal. 2002 ,and Borleetal. 2005 );andinteractionsbetweenproductvarietyandoperationalconsiderationssuchasinventoryandleadtime( vanRyzinandMahajan 1999 SmithandAgrawal 2000 AydinandRyan 2000 Cachonetal. 2005 HoppandXu 2005 GaurandHonhon 2006 Li 2007 MaddahandBish 2007 ,and AlptekinoluandCorbett 2008a ).Presenceofproductreturnsobviouslycomplicatesassortmentplanningfurther,yetithasnotbeenaddressedinthisliteraturesofar.Tothebestofourknowledge,ourworkistherstinposinganassortmentplanningproblemthatincorporatesreturns.Wedemonstrateaspecicsettingwhenreturnsmakeafundamentaldierenceforassortmentdecisions-beyondjustcomplicatingthem. Althoughoperational,tacticalandstrategicdecisionsassociatedwithusedproductreturnshavebeenwell-studiedintheclosed-loopsupplychainmanagementliterature(foranoverview,see GuideandvanWassenhove 2003 ,and Dekkeretal. 2004 ),researchonresalableproductreturnshasbeensomewhatlimited.Arguingthatreturnsneedto 22

PAGE 23

VlachosandDekker 2003 Mostardetal. 2005 ,and MostardandTeunter 2006 ). Guideetal. ( 2006 )notethevaluethatcanberecoveredfromreturnsistimesensitiveandfocusonidentifyingthepreferredreversesupplychainstructureforamanufacturer.Thisentirelineofworkexclusivelytreatssingleproductsystems.Therefore,byconsideringassortmentplanning,wetackleahostofissuesthathavebeenignoredbythecurrentliteratureonoperationsmanagementofreturns. Anotherlineofresearchthatiscloselyrelatedtoourworkpertainstoproductreturnpolicies.Whileastreamofresearchfocusesonreturnpoliciesbetweenamanufacturerandaretailer( Pasternack 1985 PadmanabhanandPng 1997 ,and EmmonsandGilbert 1998 ),anotherstreamconcentratesontheinuenceofaretailer'sreturnpolicyonconsumers( Wood 2001 Yalabiketal. 2005 ,and Shulmanetal. 2008 ).Ourworkissimilartosomeoftheworkinthelatterstreaminthatwehaveanexplicitmodelofconsumerchoice,andlimitattentiontoasingleaspectofreturnpolicies:refundamount.Thedierenceisthatweexplorehowreturnpolicyinteractswithproductassortment,anissuenoneofthesepapersaddress. 23

PAGE 24

AstandardassumptionintheliteraturewithregardtoassortmentdecisionsisthatthermincursaxedcostperproductincludedinS(see,forinstance, SmithandAgrawal ( 2000 )foradiscussionofwhatthisxedcostmayentailinretailing,p.55).Wedonotmakethisassumptionfortworeasons:parsimonyandaccent.Analyticallyspeaking,suchaxedcostcanbeeasilyincorporatedinourmodel,anditwouldnotnotablyinuenceanyofouranalyticalresultsormanagerialinsights.Therefore,wechoosetodropitforeaseofexposition.Secondly,xedcostitselfwouldbeareasontooerlessvariety.Sincewealreadyhavesuchareasoninthemodel,inventoryrisks(detailedbelow),wewishnottoconfoundtheeectofMTO/MTSenvironmentandtheassociatedproduction/inventorypoliciesonvarietyandreturns.Inotherwords,thecurrentmodelwithoutaxedcostforvarietygivesmoreprominencetoourresults,someofwhichmayotherwisebeperceivedasdrivenbyxedcosts. Assortmentdecision(S)consideredhereisforanarrowcategoryofproducts,whicharehorizontallydierentiatedalongatasteattributesuchascolororsomeothercomponentoffashion.AllproductsinNareassumedtohavethesameunitproductioncostc,thesameretailpricep,andthesamesalvagevaluev.Thereisonlyonedierenceamongtheproductsinquestion:theirattractiveness(a'sintroducedbelow).Followingstandardpractice,weassumethatv
PAGE 25

Furthermore,asdiscussedintheIntroduction,weassumeexogenousprices.Allowingpricestobedecisionvariableswouldbeclearlyuseful,butalsoanalyticallyverydicult(see MaddahandBish ( 2007 )foranattemptatendogenizingpriceinanMNL-choice-basedassortmentproblemthatalsoconsidersinventoriesbutomitsproductreturns).Yet,aspointedoutby vanRyzinandMahajan ( 1999 )inthecontextofacloselyrelatedmodel,therearerealisticcasesinwhicharetailer'spricingexibilityisquitelimited(p.1498).Welimitouranalysistosuchacase,astheyalsodo,withtheretailerexercisinglittleornocontroloverprices,e.g.,itsellstheproductlineinquestionatMSRP. Thetypesofreturnsweconsiderinvolveproductsreturnedinresalablecondition.Again,asdiscussedintheIntroduction,weassumeanexogenousreturnpolicy,andfocusononeaspectofit:percentageofpricerefundedbytheretailerwhenaconsumerreturnsaproduct.Letdenotetherefundfraction(01),whichmakestherefundamountperunitreturnp.WeassumethatthissinglerefundfractionappliestoallproductsinS,whichishowalmostallretailersoperateinpractice(especiallywithinagivennarrowproductcategory,asinourmodel).Theretailerincursareverselogisticscostlforeachunitofreturnedproducts.Thisgureincludessuchcostitemsassorting,repackaging,andrestocking. Finally,consistentwithcommonpracticeinretailing,weomitthepossibilityofproductexchange.Manyretailers,includingbackcountry.com(sportsgear),Lids.com(baseballcaps),SteveMadden(shoes),andbuydig.com(consumerelectronics),allowreturnsandaskconsumerstoplaceaneworderiftheywanttodoanexchangeevenforanotherproductinthesameproductline.Excludingexchangesfromconsiderationisnotwithoutlossofgenerality,ofcourse,becausethoseneworderswouldgotosubsequentperiods,whichwedonotmodel.Allowingexchangesisakintodynamicsubstitution, 25

PAGE 26

IntheN-MNLframework,consumerchoicecanbeviewedasasequentialprocessinwhichtheconsumerrstchoosesaproductinSortheoutsideoptionwithprobabilityPSi,wherei2S[f0g.Then,conditionalonthisrstchoice,theconsumerchoosestokeeporreturnthepurchasedproduct(ifany)withrespectiveprobabilitiesPkeepjiandPreturnjifori2S.Hencethejointprobabilityofchoosingi2Sandt2fkeep;returngisPSit=PSiPtji.Wenowdescribethistwo-stagechoiceprocessinmoredetail. i,andhasavarianceof22=6,whereisEuler'sconstant(0:5772)andisapositiveconstant.Gumbeldistributionisalsoknownasdouble-exponentialdistribution. 26

PAGE 27

Bytheprincipleofutilitymaximization,theprobabilitythatatypicalconsumerchoosesthereturnoptioninthesecondstageisthenPrfui;return>ui;keepg,whichyieldsthefollowingformula 1+expaip 2 Andersonetal. ( 1992 )foragenericproof):Ai=2lnexpai 2p Wemodeltheconsumer'spurchasedecisionalsobyutilitymaximization.Supposetheutilityofchoosingnesti2S[f0gisgivenby:Ui=Ai+"i,where"iareiidGumbel i1.See JohnsonandKotz ( 1970 )foraproof. 27

PAGE 28

Pj2S[f0gexpAj Insum,werepresentconsumers'choiceprocesswithatwo-stagerandomutilitymodel.Consumersareapriorihomogenous,butexpostheterogeneousontheirtastes,preferences,andoutsidefactorsthatmayshapetheirpre-andpost-purchasedecisions.Therandomtermscapturethisheterogeneity.Inparticular,"ireectconsumers'diversepreferencesforproductsandreturnpolicies,theirdiversecircumstancesinwhichtheyneedthisproduct,theirdiverseinformationstates,etc.Theyalsodierintheirpost-purchaseinclinations,assummedupini;keepandi;return.Heterogeneityatthisstagestemsfromhowdierentconsumersdealwithkeepandreturnoptionsgivenapurchasedecisionintherststage.Forinstance,amongtwoconsumerswhoareconsideringtokeepanapparelitem,theirspousesmaygivethemdierentfeedback.And,amongtwoconsumerswhoareconsideringtoreturnapairofhikingshoes,theirexperiencewiththeproductmaydierduetotheirdierentbackgrounds(orlackthereof)inhiking.Larger1and2meanhighervariancefortherandomtermsandthushigherheterogeneity.Forthe Andersonetal. ( 1992 )foraproof). 28

PAGE 29

McFadden 1978 ),whichisplausibleinourcontext.Consumers'pre-purchaseheterogeneityisgenerallyhigherthantheirpost-purchaseheterogeneity,becausepresumablythosewhobuythesameproductwillknowmoreaboutwhattheywant(ordonotwant)basedonrst-handexperiencewithagivenproduct,andwilldierlessfromeachotherduetothiscommonexperience. Wewillmakeasemanticdistinctionbetweenproductswithhighandlowvaluesofattractiveness.Thehighertheattractivenessofaproduct,thehighertheexpectedutilityofconsumingit(i.e.,buyingandkeepingit),andthushighertheprobabilityofpurchase.Inviewofutilitymaximizationbehaviordescribedabove,everyconsumerbuyswhattheyconsidertobethebestormost`attractive'product.So,themagnitudeofaidoesnotsomuchreecttheattractivenessofaproductinthecommonsenseoftheword,butratherdeterminesthelikelihoodofpurchaseforproducti.Wewillthusrefertoproductswithhighattractivenessvaluesaspopularproducts(inthesensethatatypicalconsumerismorelikelytobuythem);and,thosewithlowattractivenessvaluesaseccentricproducts(inthesensethatconsumerswithraretasteswillbuythem). WenowspecifyhowindividualconsumerchoicebehaviordescribedabovetranslatesintoaggregatedemandforeachproductinS.Letdenotetheaveragenumberofconsumersgoingthroughthischoiceprocess.Assumingthattheconsumers'productchoiceispurelygovernedbythesetS,andnotinuencedatallbythedetailsoftheretailer'sfulllmentprocess(e.g.,MTOversusMTS,inventorystatus,etc.),wemodelthedemandforproducti2SbyanormalrandomvariableDiwithmeanPSiandstandarddeviationPSi,where>0and0<1.(Thismodelofaggregatedemand,dubbedtheIndependentPopulationModel,hasbeenrstproposedby vanRyzinandMahajan ( 1999 ),andlaterusedby MaddahandBish ( 2007 ), Li ( 2007 )andothers.)Furthermore,wemodelthereturnsofproductibyanormalrandomvariableRiwithmeanPSi;returnandstandarddeviationPSi;return.Notethatthecoecientofvariation(denedasstandarddeviationdividedbymean)forDiandRiaredecreasing 29

PAGE 30

Theexpectedprotinthiscasecanbeexpressedasfollows: Thersttermwithinexpectationistherevenue,netofprocurementcosts.Thesecondtermisthenetcostofhandlingreturns:foreachunitofreturnedproduct,theretailerrefundsp,payslforreverselogisticsactivities,andeventuallysalvagesitforv(e.g.,sellsitinasecondarymarket,suchasaclearancestore).Weassumethatreturneditemscanonlybesalvaged(soldatasecondarymarketforareducedprice).Amoregeneralmodelofhandlingreturnswouldallowresaleofreturnedproductsinthestore(possiblyforfullprice),requiringamultiple-periodplanninghorizon. 30

PAGE 31

Intheeventofastock-out,theretailerplacesanemergencyorderataunitcostofe(v
PAGE 32

Giventhatthedemandforeachproducthasanormaldistribution,itiswell-knownthattheoptimalorderquantityforeachproductisgivenby:xj=PSj+z(PSj)forallj2S,wherez=1ec ev,and()isthecumulativedistributionfunctionofastandardnormalrandomvariable.Pluggingtheoptimalorderquantitiesbackintotheaboveprotexpression,weobtain: where()istheprobabilitydensityfunctionofastandardnormalrandomvariable. Asmentionedbefore,ourMTSmodelassumesbackloggingofexcessdemandthroughemergencyorders,whichisastandardassumptionintheinventorymanagementliteraturetogainanalyticaltractability( TagarasandVlachos 2001 ).Lostsalescase,whereconsumerswalkawaywhenfacedwithastock-out,ismuchmoredicult.Thekeydierenceisthatthenewsvendorcriticalfractile(z)wouldthendependonPSj,andthusbothonandS.Therefore,thiscompromiseiscrucialforustodevelopanalyticalresultsonhowproductassortmentandreturnpolicyinteract. 32

PAGE 33

Determiningtheoptimalrefundfractionisaninterestingprobleminitsownright.Itinevitablyrequiressimultaneousconsiderationofmultipleproductlines,whichisbeyondthescopeofourcurrentanalysis.EvenforasingleproductlineandagivenS,itisanalyticallyintractableinourmodelingframework.Fromapracticalstandpoint,however,optimizingisinsomesensetheeasyproblem.Because,refundfractionsinpracticeareusuallyroundnumbers;therefore,onecanalwayscomputetheexpectedprotfor=0%,1%,2%,:::,100%,tondthenear-optimalrefundfractionforagivenassortment(weindeeddemonstratethisinx ,whendevelopingmanagerialinsightsaboutoptimalrefundfractionbasedonanumericalstudy).Whatisdicultistondtheoptimalassortmentasthereare2ndierentpossibilities.Weprovidestructuralresultsinthenextsectionthatsignicantlyreducethesearchspaceforaccomplishingthistask. vanRyzinandMahajan 1999 ).Byassumption,A0=0and!0=1. Withoutlossofgenerality,wesortproductsinNindecreasingorderofpreference,i.e.,!1!2!n.Since!iisincreasinginAi,andAiisincreasinginai,thisorderingappliestoattractivenesslevelsaswell,i.e.,a1a2an.Thus,lower-indexedproductsaremorepopular,andhigher-indexedproductsaremoreeccentric. 33

PAGE 34

1 canbethoughtofasahypotheticalproductwithattractivenesslevelasuchthatitspreference!=exp(A=1)isequalto.Whencoincideswiththepreference!iofoneoftheproductsi2NnSpotentiallyconsideredforinclusionintheassortment,thenhMTO()representstheresultingprot,i.e.,hMTO(!i)=MTO(S[fig). StudyingthebehaviorofhMTO()allowsustoestablishalocaloptimalityresultonwhichproduct(ifany)shouldbeaddedtoanexistingassortmentS.Imagineatwo-stepprocedureforndingtheanswer:(1)ndtheadditionalproductithatyieldsthehighestprotMTO(S[fig),and(2)compareitwithMTO(S)todecideifishouldbeadded.Lemma 1 settlestherststep.Itessentiallysaysthat:forasucientlylenientreturnpolicywithrefundfraction(vl)=p,imustbethemostpopularoftheremainingproductsinNnS;whereas,forastrictreturnpolicywith<(vl)=p,imustbeeitherthemostpopularorthemosteccentricproductinNnS. 34

PAGE 35

2 saysthat,forproductitobeincludedinanexistingassortmentS,itsexpectedprotmarginmustbegreaterthanorequaltoboththeexpectedprotmarginofthecurrentsetSandthenewsetS[fig.Rulesofthumbsimilarinnaturetothisresulthavebeendocumentedinpractice( Cargilleetal. 2005 ,and OlavsonandFry 2006 ). Thesetwolemmas,regardingthelocaloptimalityofaddinganotherproduct(ifany)toanexistingassortment,providebuildingblocksforprovingthestructureoftheoptimalassortment.DeneAi=f1;:::;igandZj=fnj+1;:::;ngforallpositiveintegersiandjbetween1andn;anddeneA0=Z0=.Inwords,AiistheimostpopularproductsinN,andZjisthejmosteccentricproductsinN. (b)Forasucientlystrictreturnpolicywithreturnfraction<(vl)=p,theoptimalassortmentundertheMTOenvironmentiscomposedofsomenumberofmosteccentricproductsfromN,i.e.,S=Zkforsomek2f0;1;:::;ng. vanRyzinandMahajan 1999 AydinandRyan 2000 Hoppand 35

PAGE 36

2005 MaddahandBish 2007 Li 2007 ,and CachonandKk 2007 ).Sincehighrefundfractionsarecostly,theyinducetheretailertobemoreselectivewhendecidingonvariety,andthustooerproductswithlesschancesofbeingreturned,i.e.,thepopularproducts. However,iftherefundfractionislow,reectingastrictreturnpolicy,thenitisoptimaltocarryonlythemosteccentricproducts.Theintuitivereasonisthattheretailermakesmoremoneyfromanitemthatissoldandreturnedthananitemthatissoldandnotreturned.Intheformercase,netunitprotis(pcpl+v);whereasinthelattercase,itis(pc).Thisisakintotheserviceescapemodelof XieandGerstner ( 2007 ),inwhicharmprotsfromservicecancellations.Otherfactorsthatfavorpopularproducts,suchashigherprobabilityofpurchase,seemtobedominated.Notethat,byLemma 1 ,itcanbebesttoaddtoanexistingassortmentthemostpopular(remaining)product.Eventhoughthisistrueforincrementaladditionstoanassortment,Theorem 1 bestablishesmost-eccentricassortmentsasoptimalforstrictreturnpolicies. 36

PAGE 37

1 bisasubsetofthoseinTheorem 2 ;settingj=kleavesonlythoseassortmentswithsomenumberofmosteccentricproducts.Therefore,oneexamplewith0=j
PAGE 38

Clearly,ouranalyticalresultsintheMTScasearelimitedtothestrictreturnpolicycaseonly.Althoughweareunabletoprovethis,basedonextensivenumericalstudies(onlyasubsetofwhichispresentedinx )weconjecturethatthelenientreturnpolicycaserequirestheoptimalassortmenttoincludesomenumberofmostpopularproducts,justasintheMTOenvironment.TheintuitiongivenaboveforTheorem2alsosupportsourclaim,becauseforlenientreturnpoliciestheretailerndspopularproductsmoredesirableonbothcounts.Theynotonlyhavelessrelativedemandvariability,butalsoasmallerchanceofreturn. vanRyzinandMahajan ( 1999 )inanMTSmodelwithlostsalesandwithoutreturns.) Therefore,bycontrastingthisresultwithTheorems1and2,weconcludethatifretailersweretoignoreproductreturnswhenmerchandising,theymighteasilyruntheriskofcomposingsub-optimalassortments.Thisisespeciallytrueiftheyhaverelativelystrictreturnpolicies. 38

PAGE 39

3-1 displaystheoptimalassortmentoutofagivensetof10potentialproducts(sortedindecreasingorderofattractivenesslevels)fordierentvaluesofrefundfractionandforbothMTOandMTSmodels.Theoptimalassortmentineachoftheseinstancesiscomputedbycompleteenumeration.Notethatthethresholdrefundfractionthatseparatesstrictandlenientreturnpoliciesinthisexampleis(vl)=p=0:8. Asexpected,optimalvariety(jSj)islowerunderMTS.ThereasonisthathighervarietycostsmoreunderMTSduetooperationalrisksofover-andunder-stockingofproductsinanassortment. Thebaseparametervaluesusedthroughoutthissection,unlessotherwisenoted,aredisplayedinTable 3-2 .Thecorrespondingthresholdrefundfractionthatseparatesstrictreturnpolicies(<(vl)=p)fromlenientreturnpolicies((vl)=p)is 39

PAGE 40

3-1 3-2 3-5 3-6 ,and 3-7 .Alloftheobservationswemakeinthissectionappeartoberobust;equivalentexperimentswithdierentsetsofparametersyieldqualitativelysimilarresults. vanRyzinandMahajan ( 1999 )andothers(citedearlier).However,asweshowinTheorems 1 and 2 ,includingonlythemostpopularproductswouldbesub-optimalforrelativelystrictreturnpolicies.Inthissubsectionwequantifytheprotlosstheretailerwouldsuerbydoingso.Moreprecisely,wecomparethebestmost-popularassortmentwiththeoptimalassortment.Wealsoquantifytheprotlossfromignoringproductreturnswhenmakingtheproductassortmentdecision. Forvaluesofrefundfractionrangingfrom0to1with0:1increments,wecomputetheexpectedprotsfromtheoptimalassortment,fromthebestpossibleassortmentcomposedofmostpopularproductsonly(thisiswhatwecall`assumingthewrongstructure'),andfromthemostprotableassortmentwithproductreturnsignored(i.e.,withSoptimizedbysetting=,buttheresultingprotcalculated-aswiththeothertwoscenarios-from(S)foraxedvalue).Let,W,andIdenotetheseprots,respectively.Figure 3-1 plotsthepercentageprotlossthatresultsfromassumingthewrongstructure(W=),andfromignoringthereturns(I=)forbothoperationalmodes. Inthisparticularexample,thelossofprotfromassumingthewrongstructurecanbeupto12%(7%)intheMTS(MTO)environmentforstrictreturnpolicies.Thelossis0%forlenientreturnpolicies(whichisduetoTheorem 1 ainthecaseofMTO).Ignoringproductreturnscanbemuchmoreharmful(protlossesofupto23%arepossible), 40

PAGE 41

Thelessonfromamanagerialperspectiveisthataretailershouldbegenerallycarefulaboutassumingthatmost-popularassortmentsarealwaysthemostprotable.Forrelativelystrictreturnpolicies,thiscommonsensicalassumptioncanbequitemisleading,andmoresoforMTS-duetoinventoryrisk-thanforMTO.Also,notverysurprisingly,ignoringproductreturnswhenmakingassortmentdecisionscanresultinalossofopportunityofmakingsubstantiallymoreprots(thequestionofhowsubstantialcanonlybeaddressedwithrealdata,ofcourse). 3-2 thecardinalityoftheoptimalassortmentjSjasafunctionof(rangingfrom0to1with0:01increments).Clearly,forsucientlyhighandsucientlylowvalues,higherrefundfractionleadstolessvariety.Yetthereisalsoarangeofvaluesforwhichthevarietyisincreasingin;thatis,morelenientreturnpoliciesresultinmorevariety. 41

PAGE 42

WeobserveinFigure 3-2 ,thatstartingat=0,thereisrstadecreaseandthenanincreaseinthenumberofproductsinSasapproachesto(vl)=p.Attheextremes,whenisclosetoeither0or(vl)=p,theexpectedprotmarginintheMTOcase(Mj)approaches(pc)forallj,makingallproductsalmostequallyprotable.(Because,wheniscloseto0,Preturnjj'0;and,wheniscloseto(vl)=p,p+lv'0.)Asaconsequence,wecanexpecthighervarietyaroundtheseboundstocapturemoredemandwithoutmuchcannibalization.Forvaluesinbetween,themarginsbecomeunequal,leadingtomorecannibalizationconcernsandthuslessvariety.ForMTS,weobservebasedonournumericalexperimentsthatasimilarpatternholds(except,changesinvarietyareusuallylesssteep,andjSjpeaksearlier). Themanagerialtakeawayfromthisexperimentisthefactthatmorelenientreturnpoliciesmaysometimescallfordeeperassortmentswithhighervariety.Thishappensespeciallywhentherefundfractionisatneitherextreme(0%or100%),butjustbelowacertainthreshold((vl)=p).Therefore,forproductcategorieswithgoodsecondarymarkets(vp)andlowreverselogisticscosts(l),i.e.,whenthisthresholdiscloseto1,thisobservationislikelytobemoresalient. Toinvestigatethiseect,werstconsideraproblemwhereall10potentialproductsinsetNhaveidenticalattractivenesslevels.Fortwospecicvalues,0:5and1,we 42

PAGE 43

3-3 showsthepreferences(!'s)thatcorrespondtovesetsofproductsconsideredinthisexperiment.WemaintaintherestoftheparametervaluesasinTable 3-2 1 and 2 .Inlargerassortmentsthecannibalizationhasamorenegativeimpactbecauseitlessensthedemandforthemostprotableproducts. Figure 3-3 plotsthenumberofproductsintheoptimalassortment,jSj,for=0:5and=1underMTOandMTSenvironments.Othervaluesofyieldsimilarcurves.Thedescent(ifany)intheMTScaseisusuallynotassteepasinMTO. 3-4 ).Sincedierentiationincreasesthedierencesinmargins,theretailercanchoosethemostprotableproducts,asdiscussedabove,toincreaseitsoverallprot.Withregardtothemagnitudeofthisincrease,werstnotethattheimpactinMTSisalwaysmoresignicantthanitisinMTO.InMTS,thepossibilityofchoosingamongmoredierentiatedproducts,allowsthe 43

PAGE 44

Fromamanagerialpointofview,aretailermovingfromanMTOtoanMTSenvironmentshouldseekhigherproductdierentiationinitsconsiderationset(N),becauseitwillmattermore.Thateortisevenmoreworthwhilewhentheretailer'sreturnpolicyismorelenient. Shulmanetal. ( 2008 )).Inotherwords,theymaybeabletodirectlyinuencepost-purchaseheterogeneity(characterizedby2inourmodel)bytheiractions.Onequestionofpracticalinterestisthenwhetherretailersshouldalwayspreferreducingit. InN-MNL,itcanbeshownthatonlytheratio[of1=2]canbeidentiedfromthedata( Ben-AkivaandLerman 1985 ,p.287).Therefore,itiscommontonormalize1to1.Thisnormalizationgivesusanaturalrangefor2;inthisexperimentweset1=1andvary2inthe(0;1)interval.Morespecically,Figures 3-5 and 3-6 plottheoptimalexpectedprotforgivenvaluesofrefundfraction,andfordierentlevelsofpost-purchaseheterogeneity(2=0:25,0:50,0:90),underMTOandMTS,respectively. WelearnfromFigures 3-5 and 3-6 thatlowerpost-purchaseheterogeneityyieldshigherprotwhenreturnpoliciesarelenient.Therationaleisquitetransparent:sincegivinghigherrefundsismorecostlyfortheretailer,itwilltrytominimizereturnsbyreducingthepost-purchaseheterogeneity.Nonetheless,forstrictreturnpolicies,theeectisopposite.Sincetheretailercanobtainadditionalprotfromreturns,aspointedoutin 44

PAGE 45

3.4.1 ,higherheterogeneityinthekeep/returndecisionincreasestheprobabilityofreturn,andthereforeitbenetstheretailer. Themanagerialinsightfromthisexperimentisclear:itispossiblethathigherpost-purchaseheterogeneitycanbebenecialforaretailer.Thereasonablepresumptionthathigherheterogeneityaboutconsumers'keep/returndecisionswillleadtolowerprotsiswrongforstrictreturnpolicies. vanRyzinandMahajan 1999 ),isparameterizedbyand,whereisanindicatorofdemandvariability.Obviously,inaMTOcontext,demandvariabilitydoesnotchangetheoptimalassortmentbecauseallproductsareorderedafterdemandisrealized.IntheMTScase,however,highervariabilitywillhaveanimpactsincethereexistsinventoryriskforoverstockingandunderstocking.UsingthebasecaseexampleinTable 3-2 ,wecomputetheoptimalassortmentfordierentvaluesofandvaryingfrom0to1in0.01increments.AsseeninFigure 3-7 ,highervariabilityleadstonarrowerassortments. Itisquiteintuitivethatinahighlyvariablemarketwhereinventoryrelatedcostsaremorerelevant,thermreducesitsassortment.Ifwetakeacloserlooktothecompositionoftheoptimalassortmentwhendemandvariabilityishigh,i.e.,=5(seeTable 3-4 ),weobservethatthermismoreinclinedtooerjustthemostpopularproductbecauseithaslowerrelativedemandvariability,andthereforelessinventoryrisk. 45

PAGE 46

Ouranalyticalandnumericalresultsamplyillustratethatassortmentandrefundfractioncanexhibitinteractionsthatarenoteasilypredictable.Therefore,endogenizingthereturnpolicydecisionanalyticallywouldbeaworthwhileextensionofourwork.Anequallyimportantdirectionwouldbetoendogenizethepricingdecision. Table3-1. OptimalassortmentS,composedofproductsthatcorrespondtoshadedcells,fortheprobleminstanceinTable 3-2 withthresholdrefundfraction,(vl)=p=0:8 i 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 MTO 1 2 3 4 5 6 7 8 9 10 MTS 1 2 3 4 5 6 7 8 9 10 46

PAGE 47

BaseparametervaluesforthenumericalstudyinChapter 3 Parameter Value Product,i ai 1 4.00p 2 3.72e 3 3.44c 4 3.17v 5 2.89l 6 2.611 7 2.332 8 2.06 9 1.78 10 1.50 Table3-3. Thepreferences(!values)forvesetsofproductswithdierentdegreesofdierentiation:I(identical),VS(verysimilar),S(similar),D(dierent),andVD(verydierent). IVSSDVD Table3-4. OptimalassortmentS,composedofproductsthatcorrespondtoshadedcells,fortheprobleminstanceinTable 3-2 withdemandvariability=5 i 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 MTS 1 2 3 4 5 6 7 8 9 10 47

PAGE 48

Protlossfromassumingthewrongstructure(foroptimalassortment)andfromignoringreturns Figure3-2. Varietyversusreturnpolicy:Numberofproductsintheoptimalassortment(jSj)asrefundfraction()varies 48

PAGE 49

Numberofproductsintheoptimalassortment(jSj)atvedegreesofproductdierentiation(datagiveninTable 3-3 ) Figure3-4. Percentincreaseinoptimalexpectedprot(withrespecttoscenarioI)atvedegreesofproductdierentiation(datagiveninTable 3-3 ) 49

PAGE 50

Optimalexpectedprotversusrefundfraction()fordierentlevelsofpost-purchaseheterogeneity(2)underMTOenvironment Figure3-6. Optimalexpectedprotversusrefundfraction()fordierentlevelsofpost-purchaseheterogeneity(2)underMTSenvironment 50

PAGE 51

Numberofproductsintheoptimalassortment(jSj)withdierentlevelsofaggregatedemandvariability() 51

PAGE 52

3 ,wewereabletodeterminethestructureoftheoptimalassortmentforagivenpriceandrefundfractioninasingleperiodsetting.Themainpurposeofthischapteristodemonstrate(bynumericalexperimentation)thattheanalyticalresultsofthepreviouschapterarerobusttothefollowingextensions:(1)endogenousprice,(2)endogenousrefundfraction,and(3)multipleperiods.Thatis,interestingaspectsofourresultsregardingwhenaretailershouldcarryeccentricproductssurvivetheseextensions,which-wehavegoodreasonstobelieve-areanalyticallyintractable. Unlesswestateotherwise,inallexperimentsweuseasetofbaseparametervaluesdisplayedinTable 4-1 4-1 and 4-2 ).For=0:5,andallpriceswithintherangeconsidered(from2to3),weareinthestrictreturnpolicyregion,i.e.,<(vl)=p.Aspriceincreases,theunitcostofreturns(p+lv)approachesto0,andthatmakesallproductsmoresimilarintermsoftheirprotability.Theretailerthenoptstooerfullassortmenttocapturemoredemand.For=0:8,theeectisoppositeandmoreinteresting,especiallyintheMTOcase.Increasingpriceincreasestheprobabilityofreturn.Sinceweareinthelenientreturnpolicyregion((vl)=p)forallpricepointsexceptp=2,andtheunitcostofreturns 52

PAGE 53

AlptekinoluandCorbett 2008b ),butinmonopolyenvironmentspriceandvarietyareusuallypositivelyrelated(infact,wedonotknowofacounterexampletothisrule,besidetheonecausedbyproductreturnsinthiswork).ForMTS,thenumberofproductsintheoptimalassortmentisalmostconstant. Fordierentvaluesofrefundfraction,Figures 4-3 and 4-4 plottheexpectedprotaspricevariesfrom2to6inMTOandMTScases,respectively.Foreverydatapointshowninthecharts,theassortmentisoptimized.Weobservethattheexpectedprotisunimodalfortheseprobleminstances.Infact,wehavenotseenanyprobleminstancetothecontrary.Notealsofromthegraphsthattheoptimalpriceincreasesasrefundfractiondecreases.Weexaminethisinmoredetailinthenextsubsection. 4-5 and 4-6 ,forMTOandMTS,respectively,showhowoptimalpricechangesasrefundfraction()variesbetween0and1byincrementsof0:1.Adashedlineseparatesthestrictreturnpolicyregion(p
PAGE 54

Theoptimalpriceincreasesveryslightlyforstrictreturnpolicies,andthensuddenlydropsforlenientreturnpoliciesasrefundfractionapproachesto1.Thisisbecausetheretailertriestoreducetheprobabilityofreturnbyloweringtheprice.Withalenientpolicy,theretailerwouldratherchargelessandobtainanalsalethansalvageaproductforalowerrevenue.Itissurprisingthatoptimalpricewoulddropforincreasinglymorelenientreturnpolicies(higher).Evenfromtheperspectiveofabsoluterefundamount,theconsumerenjoysamorefavorablereturnpolicyasincreases,becausepalsokeepsincreasing,albeitatadiminishingrate.TheoptimalpricefortheMTScaseisalwayshigherthanthatoftheMTOcase,althoughthedierenceisminimalasitcanbeobservedinthegraphs. 3.4.1 and 3.4.2 .Weconsidertheassortmentsthatincludeimostpopular(eccentric)products,Ai(Zi)fori=1;:::;10,andcomparehowtheoptimalpricechangesaswekeepaddingthenextmostpopular(eccentric)producttotheassortment.Intuitively,asweaddmoreproducts,theassortmentimprovesinthesensethatacustomerismorelikelytobuyaproduct.Wedubthisthebroaderassortmenteect.Doesitalwaysleadtohigherpricesinconsequence?Theanswerisnotalways. Startingfromanassortmentwiththemosteccentricproduct,aswekeepaddingproductsthermisabletochargeahigherprice(seeFigures 4-7 and 4-8 )fortworeasons.First,addedproductshavehigherexpectedutility,andtheassortmentbecomesbetteringeneral.Second,cannibalizationofdemandtothesemorepopularproductsreducesprobabilityofreturn,alsoallowingthermtoincreasetheprice.Thisexplainswhy`Most-eccentricassortment'curvesareincreasing.Forhighervaluesof(i.e.,=1inthe 54

PAGE 55

4-9 and 4-10 plottheexpectedprotforseveralvaluesfrom0to1(with0:05increments)atthreedierentpricepoints.Foreverydatapointweoptimizetheassortment,thereforedierentdatapointsmaycorrespondtodierentproductassortments.ForbothMTOandMTScases,atp=2theoptimalrefundfractionis=0:55;atp=2:25,=0:5;andatp=2:5,=0:45.So,forthethreepricepointsconsideredinthisexperiment,theoptimalrefundfractionislowerforhigherprices. 55

PAGE 56

4.2.3 3 forthebasemodel,whereastheoptimizationoverisdonenumericallybylinesearch.Forallprobleminstancesthatwehaveseen,weobservethattheexpectedprotisgenerallyunimodalin,whichmakesthelinesearcheasy. Doeshigherpriceimplyhigherrefundfraction?Theanswerisnotnecessarily.AsseeninFigures 4-11 and 4-12 ,theoptimalrefundfractionrepresentedbysquaredots,rstdecreasesandthenincreasesinprice.Theintuitionisthefollowing.Startingfromalowprice,anincreaseinpriceraisestheprobabilityofreturn,forcingtheretailertoreducetodiscouragereturns.Forlowvaluesofp,theexpectedprotmarginperunitsales,pc(p+lv)Preturnji,ismoresensitivetoreturnssince(pc)issmallrelativetothecostofreturnsterm.Aswekeepincreasingprice,(pc)increasesandreturnsbecomelessrelevantfortheprotmargin.Sincetheretailerisextractingenoughprotfrom(pc),itcanaordincreasingtomakeitsvaluepropositionmoreattractive.Notethatadashedlineseparatesthestrictreturnpolicyregion(p
PAGE 57

4-13 .Notethatwhentheretailerkeepsaddingthenextmostpopularproducttoitsassortment,theoptimalrefundfractiondecreases(see`Most-popularassortment'curvesinthegraph).Asproductswithlowerexpectedutilityareadded(i.e.,higherlikelihoodofbeingreturned),itisdesirablefortheretailertomakeitsrefundpolicystrictertodissuadeconsumersfromreturning. Inthecaseofeccentricproducts(see`Most-eccentricassortment'curvesinthegraph),however,thereisrstadecreaseandthenanincreaseintheevolutionof.Thedecreaseisduetothedemandexpansioneect,andtheincreaseduetoapopularityeect.Whentheretaileronlyoersthemosteccentricproduct(productn),itcanexpectarelativelylowdemand.Addingasecond(orathird)productincreasesthetotaldemandconsiderably,allowingtheretailertodecreasetherefundfractionasitfeelslesspressuretooerbetterrefundstoattractmoredemand.Atsomepoint,whenadditionalproductsyieldonlysmallgainsindemand(i.e.,demandexpansioneectbecomesmuchlessrelevant),startsgoingup,becausemoreandmoreconsumersswitchtorelativelymorepopularproductswithinS,whicharelesslikelytobereturned.Duetothispopularityeect,inturn,theretailerisabletoaordhigherrefundfractionvaluesthatmaketheassortmentmoredesirableoverall.Finally,notethatFigure 4-13 exhibitsverysimilarcurvesfortheMTOandMTSmodels.Thatis,foragivenassortment,theeectofoperationalmodeonappearstobealmostnegligible. 57

PAGE 58

4-1 ,wecomputetheoptimalassortmentfordierentvaluesofaswedidinChapter 3 .Weuseaninventorycostof0:05perperiodforthereturnskeptinstock.Inordertocomputetheexpectedprotformultipleperiods,weuseMonteCarlosimulationmethods.Theprocedureisasfollows:foreveryproductintheassortmentwegeneraterandomdemandandreturnstringsofsizeT,thelengthoftheplanninghorizon.Withknowndemandsandreturns,weeasilycomputetheactualprot.Wethenestimatetheexpectedprotbyaveragingtheprotsatasucientlylargesampleofrealizations,1;000inourcase( RobertandCasella 1999 ,p.208).BytheLawofLargeNumbers,thisestimationconvergeswithprobability1totheexpectedprotasthesamplesizegoestoinnity.Foreverypossibleassortment(i.e.,2101=1023),wecomputetheapproximateexpectedprot,andchoosetheonethatyieldsthemaximum. Weobservethattheassortmentsthatyieldmaximumexpectedprothavethesamestructuresfoundtobeoptimalinthesingleperiodsetting(seeChapter 3 ).Tables 4-2 and 4-3 showtheoptimalassortmentforMTOandMTScasesforthemultipleperiodproblemwithT=3andT=10,respectively. Aninterestingquestionthatarisesinamultiple-periodcontextiswhethertheretailerincludesmoreproductsasthelengthoftheplanninghorizonTincreases.Tables 4-2 and 4-3 suggestthat,thelongerplanninghorizon(andmultiplere-sellingopportunitiesitbrings)changesneitherthestructureoftheassortmentnorthecompositioninanysignicantfashion. 58

PAGE 59

BaseparametervaluesforthenumericalstudyinChapter 4 ParameterValueProduct,iai Figure4-1. Varietyversusprice(MTO):Numberofproductsintheoptimalassortment(jSj)asprice(p)variesfordierentvaluesofrefundfraction() 59

PAGE 60

OptimalassortmentS,composedofproductsthatcorrespondtoshadedcells,foramultipleperiodproblemwith3periods i 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 MTO 1 2 3 4 5 6 7 8 9 10 MTS 1 2 3 4 5 6 7 8 9 10 Figure4-2. Varietyversusprice(MTS):Numberofproductsintheoptimalassortment(jSj)asprice(p)variesfordierentvaluesofrefundfraction() 60

PAGE 61

OptimalassortmentS,composedofproductsthatcorrespondtoshadedcells,foramultipleperiodproblemwith10periods i 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 MTO 1 2 3 4 5 6 7 8 9 10 MTS 1 2 3 4 5 6 7 8 9 10 Figure4-3. Protversusprice(MTO):Expectedprotasprice(p)variesfordierentrefundfractions(alpha)underoptimalassortment(S) 61

PAGE 62

Protversusprice(MTS):Expectedprotasprice(p)variesfordierentrefundfractions(alpha)underoptimalassortment(S) Figure4-5. Priceversusrefund(MTO):Optimalprice(p)andrefund(p)fordierentvaluesofrefundfraction()underoptimalassortment(S) 62

PAGE 63

Priceversusrefund(MTS):Optimalprice(p)andrefund(p)fordierentvaluesofrefundfraction()underoptimalassortment(S) Figure4-7. Optimalprice(p)withdierentassortmentstructuresforMTOcase 63

PAGE 64

Optimalprice(p)withdierentassortmentstructuresforMTScase Figure4-9. Protversusrefundfraction(MTO):Expectedprotasrefundfraction()variesfordierentprices(p)underoptimalassortment(S) 64

PAGE 65

Protversusrefundfraction(MTS):Expectedprotasrefundfraction()variesfordierentprices(p)underoptimalassortment(S) Figure4-11. Refundversusprice(MTO):Optimalrefundfraction()andrefund(p)fordierentprices(p)underoptimalassortment(S) 65

PAGE 66

Refundversusprice(MTS):Optimalrefundfraction()andrefund(p)fordierentprices(p)underoptimalassortment(S) Figure4-13. Optimalrefundfraction()withdierentassortmentstructures 66

PAGE 67

Johnson 2002 ),establishingdirectchannelstoidentifyconsumerpreferences.Today,manufacturersareabletoelicitrst-handinformationaboutindividualconsumers'tasteswithoutcostlyintermediarysalesagents.Anincreasingnumberofcompaniesfromamyriadofindustriesareusingonlinechannelstooercustomizedgoodstotheirconsumers( Berman ( 2002 )and AlptekinoluandCorbett ( 2008b )citesomespecicexamples).AccordingtoTheStateofRetailingOnline2007report Sellingcustomizedproductsmakesinventorymanagementintheforwardsupplychaineasier,becauseproductionoccursafterdemandrealizes(i.e.,make-to-order).Customizingcompaniesenjoytheadvantagesofreduceddemanduncertaintyandproduct 67

PAGE 68

GuptaandBenjaafar 2004 ).However,whenconsumerproductreturns,ahabitthataverages7%ofonlinesalesintheU.S. Stocketal. 2006 ).Inaddition,customizationaggravatesfurtherthealreadycostlyreturnhandlingoperations,sinceitleadstocountlessproductvariantsthatmay,intheextreme,tsingleindividualsonly,makingafutureresaleimpossible.Despitetheseeminglytroublesomecombinationofcustomizationandreturns,somecustomizers,inpursuitofmarketshareordrivenbycompetition,arewillingtoacceptreturnsaswell.Afterall,allowingreturnscanenhancetheshoppingexperienceandboostcustomersatisfaction.Asamatteroffact,nineoutoftendirectshoppers(i.e.,onlineandcatalogshoppers)indicatedaconvenientreturnpolicyasdeterminanttoshoponline,accordingtoa2007surveycommissionedbyreturnsmanagementprovider,Newgistics,Inc.( Campanelli 2007 ). Consumerreturnpoliciesvaryacrossindustriesandretailers,bothwithregardtomoneyrefundedandconditionsforreturn(e.g.,graceperiod,opened/unopenedpackage).Wealsoobservemoresignicantdierencesinreturnpoliciesbetweenbrick-and-mortarandonlineretailers.Whilelenientreturnpolicies(e.g.,100%money-backguarantees)arecommonfortheformer,thesamecannotbesaidforthelatter.Onlineretailersingeneral,andcustomizersinparticular,havestricterreturnpoliciesintheformofnonrefundablechargesforshippingandhandlingcostsorrestockingfees( Hessetal. 1996 ). Hessetal. ( 1996 )ndthatroughly90%ofthecatalogretailerssurveyedhadnonrefundableshippingcharges.Forexample,Lands'EndandYankeeCandleallowreturnsforafullrefundofthesellingpriceminusshippingcosts.CustomizationmasterDelldoesnotrefundshippingcostseither,andmaychargeupto15%ofthepurchasepriceinrestockingfees.Yetanotherexample,Robb&Stuckyimposesapickupfeeandanonrefundableshippingand

PAGE 69

Thepresenceofproductreturns,then,raisesinterestingquestionsforcustomizingrms.Shouldthesecompaniesacceptproductreturns?Ifso,whatistheoptimalreturnpolicy?Howwouldtheirpricescompareunderdierentreturnpolicies?Pricesandreturnpoliciesaredeterminantfactorsinanonlinepurchaseofcustomizedproducts.Tothisend,weconsiderasinglerm,acustomizingmanufacturerwhohasonlineretailingpresenceontheinternet,andoersatypeofproductthatcanbecustomizedintoawide(nite)varietyofendproducts,whichwecallproductvariants.Weareparticularlyinterestedincustomizedproductswithvariantsthatmayeachbeofinteresttomultiplecustomers,i.e.,customizationisaccomplishedoveranitesetofoptionsasintheexamplesmentionedabove.Inourworkwedonotconsidercustomizationviapersonalizedfeaturessuchasmonogramming,embroideringorengraving.Suitablecustomizationexamplesforourstudywouldinvolvechoiceofcolor(apparel,electronics,furniture),styleanddesign(hats,apparel),frameandfabric(furniture),andscent(candles),tonameafew. Thecustomizingrmacceptsproductreturns,whichweassumeareinas-good-as-newcondition.Wecharacterizetherm'sreturnpolicybythemoneyrefundedtothecustomerincaseofreturn(asin Hessetal. 1996 Yalabiketal. 2005 ,and Shulmanetal. 2008 ).Thepurchaseofacustomizedproductisclearlyatwo-stagedecisionprocess,wherethecustomerchoosesaproductvariantrstand,uponreceipt,shedecidestokeepitorreturnit( Wood 2001 ).AsinChapter 3 ,wemodelpurchaseandsubsequentkeep/returndecisionswithanestedmultinomiallogitmodel.Inthismodel,consumerswithheterogeneoustastesseektomaximizetheirexpectedutilitybyeitherchoosingafeasibleproductvariantoranoutsideoption(i.e.,notbuyingfromtherm).Therefore, 69

PAGE 70

Inthischapter,weaddresstheproblemofproductreturnsforcustomizedproductsinasingleperiodsetting.WestudythemultiperiodsettinginChapter 6 .Theformerisappropriateincontextswherethereisasinglesellingseason(e.g.,Christmas,merchandiseforspecialevents).Moreover,itwilllaythegroundworkforthestudyofthelatter,suitableforotherproductsforwhichmultiplesellingperiodsexist(e.g.,classicclothing).Inasingleperiodcontext,allreturnscanbesalvagedattheendoftheseason(e.g.,soldinasecondarymarket).However,whentherearemultipleperiods,thedispositiondecisionisnotasstraightforward.Returnscaneitherbesalvaged,orbestockedforfutureperiods.Therefore,thepresenceofreturnsgivesrisetoamake-to-order(MTO)environmentwhereinventorypolicymayplayacriticalrole.InChapter 6 ,wealsotacklethisinventoryproblem,andshowtheoptimalityofasalvage-down-topolicy.Wecharacterizeaclosedformexpressionforthethresholdinventorylevelbeyondwhichallreturnsshouldbesalvaged.Weshowthebenetsofemployingsuchinventorypolicyforcustomizingrms. Davisetal. 1995 )behind,anumberofpapersinbothmarketingandoperationsmanagementexplorestricterreturnpoliciesoeredbyretailers.Fromapurelymarketingperspective,severalauthorsndthatpartialrefundsareoptimalunderavastnumberofdierentscenarios. Hessetal. ( 1996 ),forexample,showthatnonrefundablechargesareoptimalindirectmarketing,andsupporttheirndingswithempiricaldata. MukhopadhyayandSetoputro ( 2004 )and Shulmanetal. ( 2007 )optimizepriceandrefundinasinglermandaduopolyscenarios,respectively. MatthewsandPersico ( 2005 )introduceproductinformationacquisitionby 70

PAGE 71

Shulmanetal. ( 2008 )extendthislastworktotwoproductswhereanexchangeisalsopossible. Intheoperationsmanagementliterature,business-to-businessreturnpolicieshavebeenstudied( EmmonsandGilbert 1998 ).Butcurrentliteratureonconsumerreturnpoliciesissomewhatscarce.Tothebestofourknowledge,onlythreepapersallowendogenousrefunddecisionsinaretailingcontext. MukhopadhyayandSetoputro ( 2005 )adoptadeterministiclineardemandmodelthatdependsonprice,refundandmodularity,wherethelasttwoaredecisionvariables. Yalabiketal. ( 2005 )useademandmodelwithtwoconsumertypesthatareeitheramatchoramismatch.Theyintegratelogisticsandmarketingdecisionsintothereturnsystem,andconcludethatoptimalrefundsarenotunique.Ontheotherhand, Su ( 2008 )considersallcustomersexpostheterogeneous.Heendogenizespriceandorderquantityinadditiontorefund,andndsthatpartialrefundsareoptimal.Inourmodel,asin Yalabiketal. ( 2005 )and Su ( 2008 ),demandisdrivenbyconsumervaluationoftheproduct,andweconsiderallcustomersexpostheterogeneousasin Su ( 2008 ).Incontrasttothesethreepapers,ourdemandmodelentailsproductchoiceandanoutsideoption.Wearethersttostudyconsumerreturnpoliciesinamultipleperiodsettingwithmultipleproducts. Ourworkalsodrawsfromthreeotherliteraturestreams:customization,assortmentplanning,andpricingandinventorycoordination.Productcustomizationhasbeengatheringgrowinginterestinthepastdecade.Strategic( Pine 1993 MurthiandSarkar 2003 ),inventory-andproduction-related(see SwaminathanandTayur ( 2003 )forareview),andcompetitiveissuesinvolvingpriceandproductmix( Dewanetal. 2003 SyamandKumar 2006 AlptekinoluandCorbett 2008b )havebeenaddressedtodate.Forareviewofassortmentplanningliterature,thereaderisreferredto Kketal. ( 2006 ).Ininventorytheory, Chanetal. ( 2004 )and YanoandGilbert ( 2005 )providecomprehensivereviewsofmodelsthatjointlyoptimizepricingandinventorydecisions.Inventorymodelswithdisposalorsalvagingoptionarealsorelatedtoourwork.Intheformer,discarding 71

PAGE 72

Simpson 1978 Inderfurth 1997 ),whereasitisprotable( Lovejoy 1990 PetruzziandMonahan 2003 )inthelatter. Ourworkmergesdierentresearchtopicsthathavebeentraditionallyseparateinthepast.Wecontributetothereturnsliteraturewithamodelthatincludesaninventorystrategystemmingfromourmultiperiodapproach,andastochasticdemandmodelwithmultiple(customized)products. 5.3.1Firm AndersonanddePalma 1992 vanRyzinandMahajan 1999 ).Underthissetting,itisreasonabletoassumethatallproductvariantshavealsoidenticalsalespricep,unitproductioncostc,andsalvagevaluev.Thisisconsistentwithinstitutionalpractice;forexample,Lands'Endchargesthesamepriceforcustomizedpantsregardlessoftheoptionschosen( SyamandKumar 2006 ). Theretaileracceptsproductreturnswhichweassumetobeinperfectlyresalablecondition.Theretailerrefundsb,withbp,andincursareverselogisticscostl(e.g.,sorting,testing).Thus,thedierence(pb)wouldbetheretailer'snonrefundablecharge 72

PAGE 73

Davisetal. ( 1998 )foradiscussionofwhatthiscostmayentail). InthisChapterweconsiderasingleperiodproblemalthoughwesetupthemodelforamultipleperiodcontext,analyzedinChapter 6 .Weassumethatreturnsarriveattheendofeveryperiod.Thisisareasonableassumptionwhenreturnsareaccumulatedandprocessedtoverifytheirconditionattheendoftheperiod.Thecustomizersalvagesallreturnsattheendoftheperiodcollectingaper-unitrevenueofv,whereisaper-perioddiscountfactor(0<1).Asin Hessetal. ( 1996 ),weassumethatreturnsareeconomicallyecient,i.e.,v>l.Inasingleperiodcontext,thecustomizersalvagesallreturns.Inamultipleperiodcontext(Chapter 6 ),however,thecustomizermaychoosetokeepaportionofthereturnsinstock,andsatisfysomeofthefuturedemandfromthisstock.Althoughproductsaremadetoorder,thepresenceofreturnsforcesthermtoadoptaninventorystrategy.Specically,thermemploysasalvage-down-toinventorycontrolpolicy(whichisshowntobeoptimalin 6.2 ).Thatis,atthebeginningofeveryperiod,iftheamountofinventoryforaparticularproductexceedsacertainthreshold,salvage-down-tolevel,thenthermsalvagesthereturnsinexcessofthisthreshold,collectingaper-unitsalvagerevenuev.Thermincursaninventoryholdingcosthforeachproductunitremainingininventory.Notethatsettingthisthresholdtozerowouldmeanthermsalvagesallreturns,andkeepsnonishedgoodsinventory. Weassumethattheinitialinventoryiszeroforallproductvariants,andthermoperatesforalongtimesothataninnitenumberofperiods,indexedbyt,isacceptable.Demand,returnsandallparametersareconsideredstationaryintime.Revenuesandcostsarediscountedfromperiodtoperiodby,aswementionedearlier.Thisparametercapturesthetimevalueofmoney.Weletxitandyitbetheunitsofproductvariantiinstockatthebeginningofperiodtbeforeandafterthesalvagedecision,respectively. 73

PAGE 74

Fromasupplystandpoint,thermcustomizeseveryproductafterdemandisrealizedataunitcostc(withc>vfortheproblemtobewellposed).Withinthismake-to-orderscenariothen,theorderingdecisionbecomestrivialsincethereisnoneedtoplanordersaheadintime.Weassumethatleadtimesarenotanissueinthemodel,andcustomersarewillingtowaitfortheircustomizedproduct.Weassumethatproductscanbecustomizedanddeliveredtothecustomerwithinthesameperiod.Consideringpositivedeterministicleadtimeslargerthanaperiodisunlikelytochangeanythingstructurallyaslongasweassumethatproductionofanorderstartsrightafterdemandisrealized. Thecustomizer,whoseekstomaximizeitsexpectedprot,needstomakethreedecisions:(1)sellingprice,p,(2)refund,b,and(3)inventorypolicycharacterizedbythenumberofproductssalvagedpriortoeverysellingperiod,(xityit).Forthesingleperiodproblemtheinventorydecisionistrivialandallproductreturnswillbesalvagedatthebeginningofnextperiod. 3 ,theproductchoiceprocess,aswellasthesubsequentreturnbehavioraremodeledusingthenestedmultinomiallogit(N-MNL)model( Ben-Akiva 1973 ).Thatis,intherststageoftheN-MNL,theconsumerchoosestheproductvariantthatmaximizesherutility(ifany)withprobabilityq,sameforallvariantsbecausetheirawasassumedtobethesame.Withprobabilityq0,shechoosestheoutsideoptionandtherefore,doesnotpurchaseacustomizedproductfromtherm.Obviously,q0+nq=1.Inthesecondstagethen,giventhataproductvarianthasbeenpurchased,thecostumerdecideswhethertokeepitorreturnitwithprobabilitiesqkeepji

PAGE 75

1+expa+kb 2 2+expbk 2p

PAGE 76

1 1+exp~u0 1+exp~u0 Ross 2003 ,p.296)withratesnqandq0,respectively.Bythesameargument,everypurchasewillresultinareturnwithprobabilityqr,andnoreturn(ornalsale)withprobability(1qr).Therefore,purchasesreturnedandkeptarealsoindependentPoissonprocesses,withratesnqqrandnq(1qr),respectively.WedenoteDtandRtthetotaldemandandtotalreturnsinperiodt,respectively.Poissonprocessesareusedextensivelyinstochasticinventoryliteraturewithproductreturns( deBritoandDekker 2003 ). 76

PAGE 77

whereDrepresentsthe(random)demandforeachproductvariant,andRrepresentsits(random)returns.Theretailer,foreachunitdemanded,obtainsanetmargin(pc),andforeachunitreturned,incursacost(b+l)minusthediscountedsalvagevaluev.Theretaileraimstomaximizetheexpectedvalueof( 5 )forallproductvariantswhich,afterpluggingE[D]=qandE[R]=qqr,resultsin(p;b)=nE[(p;b)]=nq[pc(b+lv)qr] ItwillbeconvenientforexpositionofouranalysistodenoteMtheexpectedprotmarginperunitsalesofaproductvariant,thatis,M=pc(b+lv)qr.Then,=nqM.Wearetheninterestedinndingthepricepandrefundbthatmaximizetheexpectedprotin( 5 ).Theresultsareshowninthefollowingtheorem: 5 )aregivenbyp=nexp~u(p)~u0 2+expvlk 2ip.

PAGE 78

3 providesanimplicitexpressionfortheoptimalpricethatcanbeeasilycomputedusingasimplesearch.Theoptimalrefundisensuredtobestrictlybetweenzeroandp,sincev>landvl
PAGE 79

Maximizingtheexpectedprotaboveyieldstheoptimalpricegiveninthefollowingtheorem: 5 )isuniquelygivenbytheimplicitexpressionpNR=nexp~uNR(pNR)~u0 4 isakintotheoneforpartialrefundsinTheorem 3 ,theonlydierenceisinthepre-purchaseexpectedutility~uNR.Infact,bycomparingsuchutilitiesforbothcases,weareabletoestablishthefollowingproposition: Davisetal. 1995 TsayandAgrawal 2000 ).Proposition 2 isalsoconsistentwiththeresultby MukhopadhyayandSetoputro ( 2004 )wheredemandandreturnsarecharacterizedbyalinearmodel. Next,wecomparetheoptimalexpectedprotbetweenthereturnsandnoreturnscasesinthefollowingproposition.

PAGE 80

3 impliesthatcustomizingrmsarealwaysbetterobyacceptingreturns(undertheconditionsofourmodel).Wehavetobecautiouswiththisndingthough.WehaveseeninTheorem 3 thattheoptimalrefundistightlyrelatedtothesalvagevalueandthelogisticscostofthereturn.Asthedegreeofcustomizationincreases,thesalvagevalueofapotentialreturnmightdecreaseconsiderably(e.g.,theextremecaseofmonogrammeditemswithalmostzerosalvagevalue).Also,forsomerms,productreturnscanbeverycostly,incurringalargel.Combined,lowsalvagevalueandhighlogisticscostcouldgiverisetoaverylowoptimalrefund.Forsuchcases,althoughthermwouldbenetmorefroma(low)partialrefund,itmaygoforthenorefundalternativeinstead. Themainmanagerialinsightforsuchrmswouldbetosearchforprotablesecondarysaleschannels(e.g.,outletretailstores)toincreasev,anddevelopecientreverselogisticsprocessestodecreasel.Eectivereturnsbothalleviatetheconsumers'purchaserisk,andincreasesalesallowingtheretailertogenerateextraprotasseeninProposition 3 Davisetal. 1995 ).Nevertheless,inonlineretailing,andforcustomizedproductsspecically,suchgenerouspoliciesareunusual.Infact,itcanbeshownasaconsequenceofTheorem 3 ,thatfullrefundisneveroptimal(asin MukhopadhyayandSetoputro 2004 ,and Su 2008 ).Inthissection,giventhatrefundb=p,weareinterestedinndingtheoptimalprice.First,wederiveaveryintuitiveupperboundfortheoptimalprice.WeusethesubscriptFR(fullrefund)throughoutthissection.Forfullrefund,theexpectedprotmarginperunitsalesofproductisMFR=pFRc(pFR+lv)qr.Wecanthenwrite 80

PAGE 81

5 isasfollows:araiseinthepriceincreasestheprobabilityofnopurchasing,whichdrivestheexpectedprotdown(reectedontherightsidetermabove).Intheabsenceofthisloss,wewouldsetthepricesuchthattheexpectedmarginMFRwasmaximized(i.e.,settingtheleftsidetermto0).Consideringbotheects,theoptimalityexpressiontradesothedecreaseintotalsalesversusthedecreaseinexpectedprotmarginperunitsales. NotethatfromTheorem 5 ,eitherwhen(pFR+lv)orqrareclosetozero,theoptimalityconditiontendstowardthatofthegeneralcase(seeTheorem 3 'sproof). 81

PAGE 82

82

PAGE 83

5 ,wewereinterestedinndingtheoptimalpriceandrefundforacustomizingrminasingleperiodsetting.Theinventorydecisionwastrivialinthatcasesinceallreturnsweresalvagedattheendoftheperiod.However,thepresenceofinventoryduetoreturnscomplicatesthecharacterizationoftheoptimalpriceandrefundconsiderablyinamultiperiodsetting(aswewilldemonstratelater).Thermmustrstchooseapriceandrefundatthebeginningofthesellinghorizon(staticdecision),andthendecidetheinventorystatusdynamically.Weanalyzetheinventoryproblemrst;ourinnitehorizonstationaryapproachyieldsastructuralresultontheoptimalinventorypolicy,andaneasy-to-computesolution.Later,weanalyzetheoptimalpriceandrefund.WeusethesamenotationasinChapter 5 where[a]+=maxf0;ag.Recallthattheinventoryanalysisconsistsofdecidinghowmanyunitstosalvageeveryperiod,thatis,xtyt.Thesequenceofeventsineachperiod,whichcorrespondstotheorderoftermsin( 6 ),isasfollows.(i)Thesalvagedecisionismadeandarevenueofv(xtyt)isobtained.(ii)Theinventoryholdingcosthytisincurredfortheitemsstocked.(iii)DemandDtisrealizedanditscorrespondingrevenuepDtiscollected.(iv)Demandisthensatisedwithon-handinventory(ifany),andwith 83

PAGE 84

Thepresentvalueoftheexpectedprotofallproductvariantsoverinniteperiodsisthen:1=n1Xt=1t1E[t(xt)] wherethesuccessiveperiod'sinitialinventorylevelsarerelatedbyxt+1=[ytDt]++Rtandytarethedecisionvariables.Ourinnitehorizoninventoryproblemcanbeformulatedasmax1=max(n1Xt=1t1Ev(xtyt)hyt+pDtc[Dtyt]+(b+l)Rt)subjectto0ytxtt=1;2;::: HeymanandSobel ( 1984 ,p.65),wersttransform( 6 )intoamucheasierproblem. 6 )isequivalenttomaxn1Xt=1t1E[pDt(b+lv)Rt]n1Xt=1t1E[G(yt)]subjectto0ytxtt=1;2;::: 6 )isequivalenttominimizingitslastterm.Thekeyofthisresult,asin HeymanandSobel ( 1984 ),isbeingabletocollectalltermsinvolvingyt,evaluatetheirexpectations,andobtainexpressions,namelyG(), 84

PAGE 85

5 below,suchminimizationcanbeeasilycomputedeachperiod(asasingleperiodproblem)suppressingtemporaldependence.Thistypeofpolicyiscalledmyopicpolicy,anditturnsouttobeoptimalinourcase(see HeymanandSobel ( 1984 )foradiscussionofotheroptimalmyopicinventorypolicies). cv 5 isalwaysbetween0and1.Notethatthiscriticalfractilehasafamiliarnewsvendorinterpretation.Thenumeratorrepresentsthecostofhavingoneunitlessinstocktosatisfydemand(i.e.,underagecost),thatis,theunitproductioncostincurred(c)minuswhatthermsavesonholding(h),minustherevenueobtainedbysalvaging(v),whichisnegativebecauseitisarevenue.Thecostofhavingoneextraunitinstock(i.e.,overagecost)istheholdingcost(h)plusthedierencebetweenthecurrentandthesubsequent(i.e.,discounted)salvagevalues(vv).Addingthecostofunderageandoverageprovidestheexpressioninthedenominator.Lemma 5 setsthebasisfortheoptimalinventorypolicydetailedbelow. 6 ).Ithastheformyt=8>><>>:xtifxtssifxt>s

PAGE 86

6 statesthatiftheinventoryatthebeginningofperiodtisbelowthesalvage-down-tolevels,wesalvagenothing(i.e.,xtyt=0),andconversely,iftheinventoryisaboves,wesalvage(xts)unitstobringitdowntos.Thisresultisverygeneralandindependentofthedemanddistribution.Therefore,itcouldbeappliedtonumeroussituationswherethereexistsaowofreturnedproducts.Itcanbeshownthatsuchsalvage-down-toinventorypolicyisalsooptimalforanitehorizonproblem.Inthatcase,optimalsalvage-down-tolevelsaredecreasingovertime,andaclosedformexpressioncanbeobtainedonlyforthelasttwoperiods. 6.2 ,thermdecidespriceandrefundatthebeginningofthesellinghorizoninordertomaximizethepresentvalueoftheexpectedprot,whichisgivenby1(p;b)=n1Xt=1t1E[pDt(b+lv)Rt]n1Xt=1t1E(v+h)yt+cE[D1yt]+vE[ytD1]+) Unfortunately,thevaluesofytforeveryperiodareunknownapriori,whichcomplicatestheanalysisextremely.Thetruncatedexpectationsinthesecondsummationtermin( 6 )impedeusfromndingananalyticalsolutionfortheoptimalprice.Togiveasenseoftheanalyticalchallengewefacehere, KarlinandCarr ( 1962 )studythejointoptimizationofinventoryandpriceforasingleproductwithnoreturns.Theircaseiseasierinthesensethatinventorypositioncanbesettotheoptimalorder-up-tolevelforeveryperiod.Inourcase,however,ifinitialinventoryisbelowtheoptimalsalvage-down-tolevel,wecannotincreaseit.Hence,theinventorypositionisarandomvariableaswell.Despitetheintractabilityoftheexpectedprotundertheoptimalinventorypolicy,weareabletoestablishlowerandupperboundsfor1,thatwillallowustoderivetheoptimalrefund 86

PAGE 87

6 ),wewouldsetthebeginninginventoryineachperiodtoyt=sinordertomaximizeprot.Tomakethispossible,weassumethatthermwouldbeobtainingadditionalunits,i.e.,[sxt]+,whenevernecessaryatnocost.Obviouslythisisnotfeasible,but,forcomputationalpurposes,thisidealscenarioprovidesanupperboundfortheoptimalexpectedprot. Lemma 6 providestwonaturalboundsfortheexpectedprotthatwillbehelpfulindelimitingtheoptimalprice.Notethatthelowerboundisnothingelsethaninnitediscountedsingleperiodproblems,i.e., cv,and()isthecumulativedistributionfunctionofastandardnormalrandomvariable.Pluggingtheexpressionforsin( 6 )weobtain where()istheprobabilitydensityfunctionofastandardnormalrandomvariable. 87

PAGE 88

2p 88

PAGE 89

6 ,wecanwritetheexpectedprotundertheoptimalinventorypolicyasaconvexcombinationofthelowerandupperbound,i.e.,1= 1,with01.Beingabletodosoandafterhavingfoundtheoptimalpriceforthesebounds(Lemma 7 ),theanalysisoftheexpectedprotleadsustotheTheorembelow: 5 ,isparticularlyrelevantwhenkeepinginventoryisrelativelycheap,orthecustomizerdoesnotbenetfromprotablesecondarymarkets.Whatismoresurprisingisthatcustomersmayalsobenetfromthismultiperiodscenario.Goingfromasingleperiodsettingtoamultipleperiodsettingcomplicatestheinventorymanagementoftherm.Havingtodealwithrandominventoryloadsfromperiodtoperiodmayincreasetherm'soveralloperationalcosts.Weshow,however,thataneectivesalvage-down-topolicymayallowthermtopasssomeofthesavingstoitscustomersbyloweringpriceasshowninTheorem 7 b,whereoptimalpisshowntobelowerthanp 5 ,weoptimizedpriceandrefundforthesingleperiodcase.Forthemultiperiodcase,wecouldonlyoptimizetherefundandprovidelowerandupperbounds 89

PAGE 90

FromTheorem 7 ,weknowthattheoptimalpricewillbeoftheform:p=nexp~u(p)~u0 2p Theonlymissingpiecewhichcannotbecomputedanalyticallyis.Numerically,wecanresorttoMonteCarlosimulationmethodstogeneratestringsofrandomdemandsandrandomreturnsforeverygivenpriceaswedidin 4.4 .Withknowndemandsandreturns,wecaneasilycomputetheactualprotthen.Averagingtheprotsofasucientlylargesampleofrealizations,wecanestimatetheexpectedprot( RobertandCasella 1999 ,p.208).BytheLawofLargeNumbers,thisestimationwouldconvergewithprobability1totheexpectedprot1asthesamplesizegoestoinnity.Therefore,forevery,wecanestimatetheexpectedprotandchoosethatmaximizesit.Althoughwemayhavetogenerateseveralsamplesofdemandandreturnsformanydierentprices,thismethodologywouldbeeectiveespeciallywhenthepricerange(i.e.,dierenceofpricebounds)isrelativelylow. Toavoidthepossiblylargecomputationalburdenofhavingtosearchfor,weproposeaheuristictoestimateit.LetHbethatestimation,andpHitscorrespondingprice.Thelowerandupperboundexpressionsfortheoptimalexpectedprotareobtainedbyassumingthattheinventorylevelineveryperiodis0ands,respectively.Inreality,theinventorylevelwillnotnecessarilybeateitherofthesebounds,andwilltakeavalueinbetween.Sinceinitialinventoryisdirectlyrelatedwithreturnsfromthepreviousperiod,ourheuristicusestheexpectedreturns,E[Rt],asapproximationoftheinitial 90

PAGE 91

1. Initialize:0=0:5.Setj=0. 2. Computepricepjwithjusingequation( 6 ). 3. Determinesalvagelevel,sj,andexpectedreturns,E[R]j,forpj. 4. Computej+1=1minnE[R]j 5. Ifj6=j+1,gotoStep2withj!j+1.Otherwise,gotoStep6. 6. SetH=jandpH=pj. Inthenextsubsectionweevaluatetheperformanceofourheuristicforseveralprobleminstances. 6-1 ),andmodifyoneoftheparameterswhilekeepingtherestconstant.Foreverysetofparameters,wethencomputethenearoptimalsolutionusingMonteCarlosimulation,andtheheuristicsolution.UsingthefactthattheoptimalpriceisbetweentheboundsprovidedbyTheorem 7 ,anear 91

PAGE 92

6-1 illustratestheexpectedprotforpricesbetweenthetwoboundsprovidedbyTheorem 7 usingtheparametersinTable 6-1 .Theexpectedprotseemstobeconcaveinprice,soobtaininganearoptimalpriceisrelativelyeasyusingsimulationmethods. Wethereforecomparethenearoptimalpricewiththepriceprovidedbyourheuristic.Inallourexperiments,therelativedierencebetweenthenearoptimalpriceandtheheuristicprice,computedas(jppHj)=(p)waslessthan2%.Table 6-2 displaystheresultsfromatypicalsubsetofourexperiments.Therstandsecondcolumnsspecifytheparametermodiedanditscorrespondingvalue(therestoftheparametersaregiveninTable 6-1 ). Asobservedinthelastcolumnofthetable,allpricesprovidedbyourheuristicareveryclosetothenearoptimalsolution.Weconcludethatourheuristicworksverywell. 6.3 thatthecompanycanobtainadditionalprotbykeepingsomeofthereturnsininventoryaccordingtoasalvage-down-toinventorypolicytosatisfyfuturedemand.But,howmuchextraprotcanbeobtained?Next,wecomparetheexpectedprotobtainedbysalvagingallreturnsandkeepingnoinventorytotheexpectedprotofthemultipleperiodproblemwithanoptimalsalvage-down-topolicy.Table 6-3 showsoptimalprices,p 92

PAGE 93

Thepercentagedierencecanbesignicantforsomeextremecases(inexcessof40%).Obviously,forprobleminstanceswithhigherprobabilityofreturn,thebenetsofamultiperiodapproacharemorerelevantsincethermcangainfromtheresaleofareturnedproduct.Note,forexample,theprobleminstancewitha=1wherethereisa44.79%dierencebetweenthetwocases.Theproduct'slowattractivenessleadstoahighprobabilityofreturnwhosenegativeconsequencesarerelievedbythepossibilityofaresaleinamultipleperiodproblem.Onthecontrary,theexamplewith2=0:1hasalmostnodierencebetweenthemulti-singleperiodandmultipleperiodproblemsbecausethelowpost-purchaseheterogeneity2makestheprobabilityofreturnnegligible. 6.3 .InthisSectionweprovideanapproximateanalyticalsolutiontotheoptimalpriceinthemultiperiodproblem,andshownumericallyitsusualproximitywithtonearoptimalsolutionobtainedbyMonteCarlosimulation.Theapproximationoftheexpectedprot,denotede1,isobtainedasfollows.Wetakethepresentvalueofexpectedprotgivenbyequation( 6 ),andsubstituteE[Rt]foryt,(E[D1]E[Rt])forE[D1yt]+,and0forE[ytD1]+.Inotherwords,wesupposethattheinitialinventoryisalwaysequaltotheexpectedreturnsfrompreviousperiod.Afterpluggingtheoptimalrefundb=vlandcomputingtheexpectedvalues,theresultingequationisgivenby:e1(~p;b)=nq 93

PAGE 94

6-4 thepricingresultsforboththeapproximateandexactobjectivefunctionsforthesamesetofexperiments.Lastcolumndisplaystherelativedierencebetweentheprices,computedas(jp~pj)=(p).Thedierencesinallcasesarerathersmall,sotheapproximationoftheexpectedprotprovidesnear-optimalpriceforthemultipleperiodproblem. 5 toamulti-periodsetting,whereweinvestigateoptimalprice,refundandinventorydecisionsforagivenproductassortment.Weanalyzetheinventoryproblemrstusinganinnitehorizonstationaryapproach.Weshowthatasalvage-down-tolevelinventorypolicyisoptimal.Thatis,insteadofsalvagingallreturns(e.g.,bysellingtheminasecondarymarket),asinthesingleperiodsetting,thermdecidestokeepsomeofthemuptoasalvageleveltosatisfyfuturedemand.Second,weaddressthepriceandrefundoptimization. Asinthesingleperiodsetting,wealsondthatthermshouldsetitsrefundsuchthatreturnsarecostlessfortherm.Althoughpriceoptimizationisanalyticallyintractable,wecanestablishupperandlowerboundsontheoptimalprice,andweprovideaheuristicandanapproximateanalysisthatperformwell.Ouranalysisprovidesaninterestingresult.Onecanintuitivelyexpectthatacustomizingrmbeingabletoextractsomeadditionalvaluefromareturnedproductbysellingitinthenextperiodwouldrefundahigherfractionofthesellingprice,whichcanbecomputedasrefunddividedbyprice.Thisisindeedtrueinourcase.Butsurprisingly,thehigherfractionisnotdue 94

PAGE 95

Table6-1. BaseparametervaluesforstudyingtheExpectedReturnsHeuristic ParameterValue Figure6-1. ExpectedprotfordierentpricesusingMonteCarlosimulationmethods 95

PAGE 96

Heuristicperformance.Basecaseinboldface ParameterValuebp 96

PAGE 97

6-2 .(continuedfrompreviouspage) ParameterValuebp Table6-3. ComparisonbetweenMulti-singlePeriodandMultiplePeriodProblems.Basecaseinboldface ParameterValuep 97

PAGE 98

6-3 .(continuedfrompreviouspage) ParameterValuep 98

PAGE 99

Comparisonbetweenprices.Basecaseinboldface ParameterValuep~pDierence(%) 99

PAGE 100

6-4 .(continuedfrompreviouspage) ParameterValuep~pDierence(%) 100

PAGE 101

InChapter 3 ,motivatedbywhetherretailersshouldconsiderproductreturnswhentheycomposetheirproductassortments,weanalyzetheretailer'sassortmentdecisionundertwobasicoperationalmodes,make-to-order(MTO)andmake-to-stock(MTS).Weshowthatthestructureoftheoptimalassortmentstronglydependsonboththereturnpolicy,whichweparameterizebyrefundfraction(percentageofpricerefundeduponreturn),andthesupplymode(MTOvs.MTS).Forrelativelystrictreturnpolicieswithasucientlylowrefundfraction,itisoptimalfortheretailertooermosteccentricproductsintheMTOmode,andamixofmostpopularandmosteccentricproductsintheMTSmode.Forrelativelylenientreturnpolicies,ontheotherhand,conventionalthinkingapplies:theretailerselectsmostpopularproducts.Therefore,whenmerchandisingaspartoftheirproductstrategy,retailersshouldnotonlycarefullyconsidertheirreturnpolicy,butalsotaketheirbasicoperationalmode(MTOversusMTS)intoaccount. InChapter 4 ,westudythreeextensionsofourpreviousbasemodeltoincorporate:(1)endogenousprice,(2)endogenousrefundfraction,and(3)multipleperiods.We 101

PAGE 102

InChapters 5 and 6 ,wefocusonthecharacterizationoftheoptimalpricing,consumerreturn,andinventorypoliciesofacustomizingrmunderagivenproductassortment.Weanalyzetheprobleminsingle-andmultiple-periodsettings,andweconcludethatretailersshouldaimforcostlessreturnswhendesigningtheirconsumerreturnpolicies.Inasingleperiodcontext,weshowthatoeringpartialrefundsisoptimal.Thermisalsoabletoincreaseitssellingpricewhileoeringpartialrefunds.Thiscanbeseenasaservicepremiumsincereturnsreducecustomers'riskinthepurchasedecision.Inamultipleperiodsetting,weprovethatasalvage-down-toinventorypolicyisoptimal,whichenablesthermtoincreaseitsexpectedprotcomparedtotheoneobtainedinmultiplesingleperiods.Wealsodeveloppracticallyimplementableheuristicstodeterminetheoptimalpriceandrefundintheanalyticallyintractablemultiple-periodsetting. 5 and 6 weconcentratedoncustomizedproductsthataremadetoorderafterdemandisrealized.Anaturalextensionistoconsiderproductsthathavetobeorderedorproducedinadvance.Make-to-stockproductsnotonlycomplicatetheinventorypolicy,butalsothereturnpolicyanalysissincereturnswouldnowdependonsalesratherthanondemand. Inthecontextofonlineversusbrick-and-mortarretailers,thereexistsamyriadofpotentialproblemsrelatedtotheseareasthatareworthexploring.Thepopularityofonlineshoppingwithaproliferationofonlineretailersovertheseyearshasredenedretailingindustry.Aneverincreasingnumberofconsumersconsidertheonlinechannelastheirrstshoppingoption.Thecoexistenceoftraditionalretailingande-tailingbringsupveryintriguingresearchquestions.Amongthose,questionsrelatedtoproductassortmentandreturnpoliciesareveryinteresting.Thesetwocomponentstogetherwithpricearethemaindriversofretailerchoiceamongconsumers.Twopossibleresearchdirections 102

PAGE 103

Furthermore,inonlineretailing,thevirtualnatureofstoresgivesretailersadditionalpossibilitiesasfarastheirinventorymanagementisconcerned.Forexample,drop-shipping,whereasupplierstocksgoodsanddeliversthemdirectlytocostumers,isaverycommonpracticeintheindustry.Researchontheinventorymanagementofsuchsupplychainshasbeenconductedrecentlywiththeobjectiveofdeterminingtheappropriatechannelstructureunderdierentmarketcircumstances.However,presenceofproductreturnsinthisinventorysettinghasnotbeenaddressedintheliterature.Considerationofproductreturnsaddsinterestingreverseowstothesupplychainthatmanagerscannotignore.Onlineretailershaveseveraloptionstohandleproductreturns:keepthemtosatisfyfurtherdemand,sendthembacktothesupplier(ordrop-shipper),salvagetheminsecondarymarkets(e.g.,outletstores),oroutsourcetheirmanagementcompletelytospecializedcompanies.Howdoestheretailer'sinventorystrategychangewhenproductreturnsaretakenintoaccount?Whatarethebestchannelstructuresunderdierentcircumstances?Besidesaddinganotherdimension(andmoregenerality)tosupplychainswithdrop-shippingoperations,webelieveproductreturnscouldrevealinterestingimplications,whichmakesthisproblemveryappealingtoinvestigate. 103

PAGE 104

[ThroughouttheappendixwewillusetheshorthandnotationPrjiforPreturnji.]ProofofLemma 1 p,andquasiconvexwhen
PAGE 105

A )impliesthatthersttermisalwayslessthanthesecondterm,andtheirsumisthereforepositive.Hence,wecanconcludethatintheinterval[b;1),h0MTO()ispositive,orhMTO()isincreasingwhenvl p. Ontheotherhand,forhMTO(b) Furthermore,wehavepreviouslyshownthathMTO()isquasiconcavewhenvl p.BythedenitionofquasiconcavityhMTO(L+(1)H)minfhMTO(L);hMTO(H)g;2[0;1] A )or( A ).Hence,whenvl p,weconcludethathMTO()isnon-decreasingfor
PAGE 106

1+Pk2S!kh1+Pk2S[fig!kiMiXj2S24!jh1+Pk2S[fig!ki!j1+Pk2S!k 1+Pk2S!kh1+Pk2S[fig!ki35(MjMi) A )byh1+Pk2S[fig!ki,wealsoobtain:h1PS[figiiMiXj2SPS[figjMjMiXj2S[figPS[figjMj=MTO(S[fig) 1 ProofofPart(a) 106

PAGE 107

1 ,producticanbereplacedwithproductna+1withoutdecreasingtheprot.Proceedingrecursivelywithsuchprot-improvingreplacements,na=kwillintheendbesatised,whichimpliesthatS=Ak. Theproofisbyconstruction.Theclaimholdstriviallyfork=n1.TakeanysubsetSofNwithcardinalityk2f1;:::;n2g.Letna=maxfijAiS,i2f0;1;:::;kggbethenumberofmostpopularproductsofNthatbelongtoS;andnz=maxfjjZjS,j2f0;1;:::;kggbethenumberofmosteccentricproductsofNthatbelongtoS.Clearlyna+nzcannotbestrictlylargerthank.Ifna+nz
PAGE 108

AssumethattheoptimalassortmentisS=Akforsomek2f1;:::;n1g,andset=1withoutlossofgenerality.Wewillshowthataddingthenextmostpopularproductisalwaysprot-improving,i.e.,MTO(Ak+1)>MTO(Ak),whichisacontradiction.Usingequation( 3 )andtheprotmarginnotation,thenewprotafteraddingproductk+1isasfollows:MTO(Ak+1)=Xj2Ak+1PAk+1jMj=Xj2AkPAk+1jMj+PAk+1k+1Mk+1=Xj2AkPAk+1jMj+24Xj2Ak[f0gPAkjPAk+1j35Mk+1 TheproofisduetoLemma 2 .AssumethattheoptimalassortmentisS=Ai[Zjwithi>0,j>0,andi+j
PAGE 109

2 athat:Mk
PAGE 110

1 barenolongervalidfortheMTScase.Themainreasonisthattheexpectedprotmarginperunitsales(denedbelow)nowdependsontheassortmentS(whereas,intheMTOcase,MjisindependentofS):fMj(S)=pc(p+lv)Prjj(ev)(z)(PSj)1ProofofProposition 1 1 athat,forlenientreturnpolicieswithvl p,theoptimalassortmentiscomposedofsomenumberofmostpopularproducts,i.e.,S=Akforsomek2f0;1;:::;ng.Furthermore,accordingtoLemma 2 ,thermisbetterobyaddingproduct(i+1)toanexistingassortmentSNthatincludestheimostpopularproducts,i.e.S=Ai,ifandonlyifthefollowinginequalityholds: Itiseasytoverifythat,asincreases,theexpectedprotmarginMjdecreasesandpreference!jincreasesforallj.Therefore,ifMi+1decreasesatleastasfastasMjforallj2S,theleft-hand-sidewillberelativelysmallercomparedtotheright-hand-side,asweincrease.Thisisequivalenttosaythatintheregionwherevl p,amorelenientreturnpolicy(higher)leadstolowervarietysincetheincentivetoaddaproducttoanyexistingassortmentwillbelower,i.e.,inequality( A )willbelesslikelytobesatised.Forthistobetrue,itissucientthat@Mi+1 2Prjj(1Prjj). 110

PAGE 111

3 11(1qr) 11 11(1qr) 11=0 Tosatisfybothconditions,clearly,(1qr) 11(1qr) 1+1+(1qr)

PAGE 112

A ),thesecondderivativeatbisnegative@2(p;b) 1+1nqqr(1qr) A )mustbesatisedatoptimality,q0(pc)=1.Substitutingtheprobabilityofnotbuying,weobtaintheimplicitexpressionfortheoptimalprice,p=hnexp~u(p)~u0 2+expvlk 2ip.Notethatsince~udecreasesinp,thesolutiontotheequalityisunique.Finally,wecheckthesecondderivativeofwithrespecttoptoshowthatpisamaximum:@2(p;b) 11nqq0 1+1 1=1.ProofofTheorem 4 1(pNRc)+1 112

PAGE 113

1q0+1<0 2 2+expbk 2p>2lnexpa 2p=ap=~uNR(p) 2>0.TheresultfollowsfromtheoptimalpriceexpressionsinTheorems 3 and 4 .ProofofProposition 3 1=1forboththepartialrefundcaseandthenoreturnscase.Let'susethesuperscriptPRandNR,respectively,todistinguishbetweenprobabilitiesinbothcases.WemusthaveqPR0(pc)=qNR0(pNRc)=1.ByProposition 2 ,weknowthat(pc)>(pNRc).ThenqPR0nqNR.SinceexpectedprotmarginMandprobabilityofpurchasenqarehigherforthepartialrefundcase,theresultfollowsdirectly.ProofofLemma 4 Thetermoutsidethebrackets,nq(1qr),isalwaysnonnegativeandcanbeleftasidefortheanalysis.DenoteLTandRTtheleftandtherightterms,respectively,inbracketsin 113

PAGE 114

A ):LT=1qr @pFR=qr(1qr) WenextshowthatpFRmaximizesMFRandisunique.ThederivativeofMFRis@MFR 5 4 ,settingtherstderivativeoftheexpectedprot( A )to0,weobtain:1qr 114

PAGE 115

A ),respectively.ThesecondderivativeofFRevaluatedattheoptimalpricepFRis@2FR(pFR) @pFR=qr @pFR=q0(1qr) 4 ).Thiscompletestheproof.ProofofProposition 4 HeymanandSobel ( 1984 ).Thepresentvalueoftheexpectedprotprovidedin( 6 )canbewrittenas1=nv(x1y1)hy1+pD1c[D1y1]+(b+l)R1+n1Xt=2t1v(xtyt)hyt+pDtc[Dtyt]+(b+l)Rt 115

PAGE 116

A )weobtain1=nvx1+n1Xt=1t1(v+h)yt+pDtc[Dtyt]+(b+lv)Rt+v[ytDt]+=n1Xt=1t1fpDt(b+lv)Rtgn1Xt=1t1(v+h)yt+c[Dtyt]+v[ytDt]+ 6 )canthenbereformulatedasmaximizen1Xt=1t1E[pDt(b+lv)Rt]n1Xt=1t1E[G(yt)]subjectto0ytxtt=1;2;:::ProofofLemma 5

PAGE 117

Theminimizersisgoingtobethesmallestintegersuchthattherstforwarddierenceisnon-negative,thatis,F(s)cvh cv.ProofofTheorem 6 5 andtheconstraintytxt.ProofofLemma 6 6 ),andfortheupperboundwesubstituteyt=sin( 6 ).SincesminimizesG(yt)(Lemma 5 ),theresultfollows.ThesecondpartoftheLemmaisalsotrivial.ProofofProposition 5 7 ProofofPart(a) 3 'sproof. 3 'sproof,andwejustsketchitforcompleteness.Let 117

PAGE 118

11(1qr) 11+(cv)(z)q0 b M 1+1(cv)(z)q0 (1)2nqq0q2r(cv)(z) 2(1)21p 11=(cv)(z)q0 Similarlyfortheoptimalprice,therstorderconditiondeterminesthatq0h 2p 2p M 1+1(cv)(z)q0 2(1)21p 11byrstordercondition.Thus, 5 .ProofofTheorem 7 ProofofPart(a) 3 'sproof.Werstwritetheexpectedprotunderoptimalinventorypolicyasaconvexcombinationofthe 118

PAGE 119

1=nq 11(1qr) 11+(1)(cv)(z)q0 1.Thesecondderivativeof1withrespecttobatoptimalityis@21(p;b) 1+1(1)(cv)(z)q0 (1)2nqq0q2r(1)(cv)(z) 2(1)21p 11=(1)(cv)(z)q0 2p 2p 1+1(1)(cv)(z)q0 2(1)21p

PAGE 120

11byrstordercondition.Thus,pisamaximum,andsince01, 6 1[~pc+(cvh)qr]+1 120

PAGE 121

Alptekinolu,A.,C.J.Corbett.2008a.Leadtime-varietytradeoinproductdierentiation.Workingpaper,SMU,Dallas,TX. Alptekinolu,A.,C.J.Corbett.2008b.Masscustomizationvs.massproduction:Varietyandpricecompetition.ManufacturingServiceOper.Management10(2)204. Anderson,S.P.,A.dePalma.1992.Multiproductrms:Anestedlogitapproach.J.Indust.Econom.40(3)261. Anderson,S.P.,A.dePalma,J.F.Thisse.1992.DiscreteChoiceTheoryofProductDierentiation.MITPress,Cambridge,MA. Aydin,G.,J.K.Ryan.2000.Productlineselectionandpricingunderthemultinomiallogitchoicemodel.Workingpaper,PurdueUniversity,WestLafayette,IN. Bayus,B.L.,W.P.Putsis.1999.Productproliferation:Anempiricalanalysisofproductlinedeterminantsandmarketoutcomes.MarketingSci.18(2)137. Ben-Akiva,M.1973.Structureofpassengertraveldemandmodels.Ph.D.thesis,DepartmentofCivilEngineering,MIT,Cambridge,MA. Ben-Akiva,M.,S.R.Lerman.1985.DiscreteChoiceAnalysis:TheoryandApplicationtoTravelDemand.MITPress,Cambridge,MA. Berger,J.,M.Draganska,I.Simonson.2007.Theinuenceofproductvarietyonbrandperceptionandchoice.MarketingSci.26(4)460. Berman,B.2002.Shouldyourrmadoptamasscustomizationstrategy?BusinessHorizons45(4)51. Blanchard,D.2005.Movingforwardinreverse.LogisticsToday46(7)7. Boatwright,P.,J.C.Nunes.2001.Reducingassortment:Anattribute-basedapproach.J.Marketing65(3)50. Borle,S.,P.Boatwright,J.B.Kadane,J.C.Nunes,G.Shmueli.2005.Theeectofproductassortmentchangesoncustomerretention.MarketingSci.24(4)616. Broniarczyk,S.M.,W.D.Hoyer,L.McAlister.1998.Consumers'perceptionsoftheassortmentoeredinagrocerycategory:Theimpactofitemreduction.J.MarketingRes.35(2)166. Cachon,G.P.,A.G.Kk.2007.Categorymanagementandcoordinationinretailassortmentplanninginthepresenceofbasketshoppingconsumers.ManagementSci.53(6)934. Cachon,G.P.,C.Terwiesch,Y.Xu.2005.Retailassortmentplanninginthepresenceofconsumersearch.ManufacturingServiceOper.Management7(4)330. 121

PAGE 122

Cargille,B.,C.Fry,A.Raphel.2005.Managingproductlinecomplexity.OR/MSToday32(3)34. Chan,L.M.A.,Z.J.Shen,D.Simchi-Levi,J.L.Swann.2004.Coordinationofpricingandinventorydecisions:Asurveyandclassication.D.Simchi-Levi,D.Wu,Z.J.Shen,eds.,HandbookofQuantitativeSupplyChainAnalysis:ModelingintheE-BusinessEra.KluwerAcademicPublishers. Che,Y-K.1996.Customerreturnpoliciesforexperiencegoods.J.Indust.Econom.44(1)17. Davis,S.,E.Gerstner,M.Hagerty.1995.Moneybackguaranteesinretailing:Matchingproductstoconsumertastes.J.Retailing71(1)7. Davis,S.,M.Hagerty,E.Gerstner.1998.Returnpoliciesandtheoptimallevelofhassle.J.Econom.Bus.50(5)445. deBrito,M.P.,R.Dekker.2003.Modellingproductreturnsininventorycontrol-exploringthevalidityofgeneralassumptions.Internat.J.ProductionEconom.81-82225. deVries-vanKetel,E.2006.Howassortmentvarietyaectsassortmentattractiveness:Aconsumerperspective.Ph.D.thesis,RSMErasmusUniversity,ErasmusResearchInstituteofManagement.http://hdl.handle.net/1765/7193. Dekker,R.,M.Fleischmann,K.Inderfurth,L.N.vanWassenhove.2004.ReverseLogistics:QuantitativeModelsforClosed-LoopSupplyChains.Springer-Verlag,NewYork. Dewan,R.,B.Jing,A.Seidmann.2003.Productcustomizationandpricecompetitionontheinternet.ManagementSci.49(8)1055. Emmons,H.,S.M.Gilbert.1998.Theroleofreturnspoliciesinpricingandinventorydecisionsforcataloguegoods.ManagementSci.44(2)276. Enright,T.2003.Post-holidaylogistics.tracWORLD(Jan03)20. Gaur,V.,D.Honhon.2006.Productvarietyandinventorydecisionsunderalocationalconsumerchoicemodel.ManagementSci.52(10)1528. Guide,V.D.R.,Jr.,G.C.Souza,L.N.vanWassenhove,J.D.Blackburn.2006.Timevalueofcommercialproductreturns.ManagementSci.52(8)1200. Guide,V.D.R.,Jr.,L.N.vanWassenhove.2003.BusinessAspectsofClosed-LoopSupplyChains.CarnegieMellonUnivPress. 122

PAGE 123

Heiman,A.,B.McWilliams,J.Zhao,D.Zilberman.2002.Valuationandmanagementofmoney-backguaranteeoptions.J.Retailing78(3)193. Hess,J.D.,W.Chu,E.Gerstner.1996.Controllingproductreturnsindirectmarketing.MarketingLett.7(4)307. Heyman,D.,M.Sobel.1984.StochasticModelsinOperationsResearch,vol.2.McGraw-Hill,NewYork. Hoch,S.J.,E.T.Bradlow,B.Wansink.1999.Thevarietyofanassortment.MarketingSci.18(4)527. Hopp,W.J.,X.Xu.2005.Productlineselectionandpricingwithmodularityindesign.ManufacturingServiceOper.Management7(3)172. Inderfurth,K.1997.Simpleoptimalreplenishmentanddisposalpoliciesforaproductrecoverysystemwithleadtimes.ORSpektrum19(2)111. Johnson,L.K.2002.NewviewsondigitalCRM.MITSloanManagementRev.44(1)10. Johnson,N.L.,S.Kotz.1970.ContinuousUnivariateDistributions.JohnWiley&Sons. Karlin,S.,C.R.Carr.1962.Pricesandoptimalinventorypolicy.K.J.Arrow,S.Karlin,H.Scarf,eds.,StudiesinAppliedProbabilityandManagementScience.StanfordUniversityPress,Stanford,CA. Kekre,S.,K.Srinivasan.1990.Broaderproductline:Anecessitytoachievesuccess?ManagementSci.36(10)1216. Kim,J.,G.M.Allenby,P.E.Rossi.2002.Modelingconsumerdemandforvariety.MarketingSci.21(3)229. Kk,A.G.,M.L.Fisher,R.Vaidyanathan.2006.Assortmentplanning:Reviewofliteratureandindustrypractice.KluwerAcademicPublishers. Kotha,S.1995.Masscustomization:Implementingtheemergingparadigmforcompetitiveadvantage.StrategicManagementJournal1621. Li,Z.2007.Asingle-periodassortmentoptimizationmodel.ProductionOper.Manage-ment16(3)369. Lovejoy,W.S.1990.Myopicpoliciesforsomeinventorymodelswithuncertaindemanddistributions.ManagementSci.36(6)724. Maddah,B.,E.K.Bish.2007.Jointpricing,assortment,andinventorydecisionsforaretailer'sproductline.NavalRes.Logistics54(3)315. 123

PAGE 124

Matthews,S.A.,N.G.Persico.2005.Informationacquisitionandtheexcessrefundpuzzle.Workingpaper,UniversityofPennsylvania,Philadelphia,PA. McFadden,D.1978.ModellingtheChoiceofResidentialLocation.North-HollandPublishingCompany,Amsterdam. Mostard,J.,R.deKoster,R.Teunter.2005.Thedistribution-freenewsboyproblemwithresalablereturns.Internat.J.ProductionEconom.97(3)329. Mostard,J.,R.Teunter.2006.Thenewsboyproblemwithresalablereturns:asingleperiodmodelandcasestudy.Eur.J.Oper.Res.169(1)81. Mukhopadhyay,S.K.,R.Setoputro.2004.Reverselogisticsine-business:optimalpriceandreturnpolicy.Internat.J.PhysicalDistribution&LogisticsManagement34(1)70. Mukhopadhyay,S.K.,R.Setoputro.2005.Optimalreturnpolicyandmodulardesignforbuild-to-orderproducts.JournalofOperationsManagement23(5)496. Murthi,B.P.S.,S.Sarkar.2003.Theroleofthemanagementsciencesinresearchonpersonalization.ManagementSci.49(10)1344. Olavson,T.,C.Fry.2006.Understandingthedynamicsofvalue-drivenvarietymanagement.MITSloanManagementRev.48(1)63. Padmanabhan,V.,I.P.L.Png.1997.Manufacturer'sreturnspoliciesandretailcompetition.MarketingSci.16(1)81. Pasternack,B.A.1985.Optimalpricingandreturnpoliciesforperishablecommodities.MarketingSci.4(2)166. Petruzzi,N.C.,G.E.Monahan.2003.Managingfashiongoodsinventories:dynamicrecourseforretailerswithoutletstores.IIETrans.35(11)1033. Pine,B.J.1993.MassCustomization:TheNewFrontierinBusinessCompetition.HarvardBusinessSchoolPress,Boston,MA. Robert,C.P.,G.Casella.1999.MonteCarloStatisticalMethods.Springer-Verlag,NewYork. Rogers,D.S.,R.S.Tibben-Lembke.1998.Goingbackwards:Reverselogisticstrendsandpractices.UniversityofNevadareport,CenterforLogisticsManagement.ReverseLogisticsExecutiveCouncil.URL Ross,S.M.2003.IntroductiontoProbabilityModels.8thed.AcademicPress,SanDiego,CA. Shugan,S.M.1989.Productassortmentinatriopoly.ManagementSci.35(3)304. 124

PAGE 125

Shulman,J.D.,A.T.Coughlan,R.C.Savaskan.2008.Optimalrestockingfeesandinformationprovisioninanintegrateddemand-supplymodelofproductreturns.Workingpaper,UniversityofWashington,Seattle,WA. Simpson,VincentP.1978.Optimumsolutionstructureforarepairableinventoryproblem.Oper.Res.26(2)270. Smith,S.,N.Agrawal.2000.Managementofmulti-itemretailinventorysystemswithdemandsubstitution.Oper.Res.48(1)50. Stock,J.,T.Speh,H.Shear.2006.Managingproductreturnsforcompetitiveadvantage.MITSloanManagementRev.48(1)57. Su,X.2008.Consumerreturnspoliciesandsupplychainperformance.Workingpaper,HaasSchoolofBusiness,UniversityofCalifornia,Berkeley,CA. Swaminathan,J.M.,S.R.Tayur.2003.Modelsforsupplychainsine-business.Manage-mentSci.49(10)1387. Syam,N.B.,N.Kumar.2006.Oncustomizedgoods,standardgoods,andcompetition.MarketingSci.25(5)525. Tagaras,G.,D.Vlachos.2001.Aperiodicreviewinventorysystemwithemergencyreplenishments.ManagementSci.47(3)415. Tsay,A.A.,N.Agrawal.2000.Channeldynamicsunderpriceandservicecompetition.ManufacturingServiceOper.Management2(4)372. Tsay,A.A.,S.Nahmias,N.Agrawal.1999.Modelingsupplychaincontracts:Areview.KluwerAcademicPublishers. vanHerpen,E.,R.Pieters.2002.Thevarietyofanassortment:Anextensiontotheattribute-basedapproach.MarketingSci.21(3)331. vanRiper,T.,K.Nolan.2008.Thetoughestholidayreturns.Forbes(Jan14,2008).URL vanRyzin,G.,S.Mahajan.1999.Ontherelationshipbetweeninventorycostsandvarietybenetsinretailassortments.ManagementSci.45(11)1496. Vlachos,D.,R.Dekker.2003.Returnhandlingoptionsandorderquantitiesforsingleperiodproducts.Eur.J.Oper.Res.151(1)38. Wood,S.L.2001.Remotepurchaseenvironments:Theinuenceofreturnpolicyleniencyontwo-statedecisionprocesses.J.MarketingRes.38(2)157. 125

PAGE 126

Yalabik,B.,N.C.Petruzzi,D.Chhajed.2005.Anintegratedproductreturnsmodelwithlogisticsandmarketingcoordination.Eur.J.Oper.Res.161(1)162. Yano,C.,S.Gilbert.2005.Coordinatedpricingandproduction/procurementdecisions:Areview.A.K.Chakravarty,J.Eliashberg,eds.,ManagingBusinessInterfaces:MarketingandEngineeringIssuesintheSupplyChainandInternetDomains.Springer. 126

PAGE 127

AlexGrasaswasborninBarcelona,Spain.HereceivedhisB.S.fromtheIndustrialEngineeringdepartmentattheTechnicalUniversityofCatalonia(UPC)inSpain(2001).HeworkedforthreeyearsasresearchassistantintheOperationsManagementdepartmentattheIESEBusinessSchoolinSpain.Afterthat,hemovedtoGainesville,FL,topursuehisdoctoratedegreeinindustrialandsystemsengineeringattheUniversityofFlorida.Hisresearchinterestsincluderetailoperations,supplychainmanagementandoperations/marketinginterface.Heiscurrentlyworkingontheinteractionsbetweenproductassortmentandreturnpolicyofaretailer.Heexpectstocontinuehiscareerinacademia. 127