Optimal Pricing and Return Policies for Perishable Commodities易腐商品的最优定价与退货策略

OptimalPricingandReturnPoliciesforPerishableCommodities

B.A.PasternackPresenter:GökhanMETAN1PasternackOutlineIntroductionModelImplicationsExamplesConclusion2Pasternack

IntroductionWhatthepaperisallabout?

Pricingpoliciesforamanufacturerthatproducesesgoodswithshortshelfordemandlife.PricingPolicy: Specifiesthepriceofthecommoditychargedfromtheretailers,perunitcreditforthereturnedgoods,andthepercentageofpurchasedgoodsallowedtobereturnedforthiscredit.3Pasternack

IntroductionQuestion:

Howwouldyousetthepriceoftheproductforyourretailers,andwhatreturnpolicywouldyouimpose?Howandwhatkindofdecisionsaremadetypically?Price: i-Costbasisdecisions ii-“Whatmarketwill bear”approachReturnPolicy: i-Fullcreditforall unsoldgoods. ii-Nocreditfor unsoldgoods.Nochannelcoordination!4Pasternack

IntroductionSetapricingpolicyPurchaseDecisionPrice,demand,productavailabilityCustomerSideProfitProfit5Pasternack

IntroductionAssumptionsaboutthemodel:iii-Anyretailerplaceonlyoneorderfromthemanufacturer.i-Singleitemisconsidered.ii-Itemhasshortshelfordemandlife.iv-Goodwillcostisincurredpartiallybytheretailerandpartiallybythemanufacturer.(wheninventoryisdepleated)v-Certainamountmaybereturnedtothemanufacturerforpartialcreditandtheremainingisdisposedofbytheretailerforitssalvagevalue.(wheninventoryremainsbeyondtheshelf/demandlife)6Pasternack

IntroductionAssumptionsaboutthemodel: Cont’dvi-Manufacturingcostperitemisindependentoftheproductionquantity.vii-Alltheretailerschargethesame(fix)pricefortheproduct.viii-Boththemanufacturerandtheretailersareprofitmaximizers.ix-Salvagevalueissameformanufacturerandtheretailers.x-Notransfermark-upsbetweenretailersandthemanufacturer.(amountpaidbytheretailer=amountreceivedbythemanufacturer)7Pasternack

IntroductionAssumptionsaboutthemodel: Cont’dxi-Demandattheretaillevelisstochastic.xii-Manufacturerhascontrolofthechannelandisfreetosetthepricingpolicy.Retailersdecidetocarrythecommodityornot.Objective:Todevelopapricingpolicythatoptimizestheexpectedprofitofboththemanufacturerandtheretailersaswellastoachievethechannelcoordination.8Pasternack

IntroductionMethodology:Singleperiodinventorymodel(newsboyproblem)isemployedintheanalyses.Interest:Notfindingtheoptimalorderingquantity!Whatpricingpolicyforthemanufacturerwillbeoptimal?9Pasternack

Model10Pasternack

ModelUnitsellingpricebytheretailerUnitpricepaidbytheretailertothemanufacturer.SalvagevalueperunitManufacturingcostperitemManufacturingcostperitem11Pasternack

ModelIntheanalyseswewillconsidertwocases:1)Wewillfirstassumesuchasystemthattheretailersbelongtomanufacturersown.Thatis,theyarecompanystores.2)Inthesecondcase,wewillconsiderindedendentretailers.Thatis,theretailersdeterminetheirorderquantity.Thiswillenableustodeterminetheoptimalpolicyforthesystemasawhole.Thiswillenableustodeterminetheoptimalpolicyforretailerswheretheyareindependent.12Pasternack

Model1stCASELetthecompanyproducesQ

unitsandsellsdirectlytothecustomersbyitsownretailersandEPT(Q)bethetotalexpectedprofit.TotalmanufacturingcostExpectedprofitwhendemandislessthantheproductionquantity.TotalProfitTotalSalvageValueforunsoldgoodsExpectedprofitwhendemandismorethantheproductionquantity.TotalProfitTotalgoodwillcostforlostdemands13Pasternack

ModelResultF(QT*)=(p+g2-c)/(p+g2-c3)14Pasternack

Model2ndCASELettheretailerordersQ

unitsandEPR(Q)betheretailer’sexpectedprofit.Retailer’stotalorderingcost15PasternackRQORDERDEMAND0Q(1-R)QxRetailer’srevenuefromitemssoldCreditobtainedforunsoldgoodsfromthemanufacturerTotalamountobtainedforunsoldgoodsfromtheirsalvagevalue

Model16PasternackORDERDEMAND0QRQ(1-R)QxRetailer’srevenuefromitemssoldCreditobtainedforunsoldgoodsfromthemanufacturer

Model17PasternackORDERDEMAND0QRQ(1-R)QxRetailer’srevenuefromitemssoldTotalgoodwillcostoftheretailer.

Model18Pasternack

Model00Notethat:Q*istheorderquantityofindependentretailerwhichsatisfiesequation(7).19Pasternack

ModelNow,theretailerordersQ*

unitsandEPM(Q*)bethemanufacturer’sexpectedprofit.ProfitobtainedbythesalesofQ*unitstotheretailer20PasternackRQ*ORDERDEMAND0Q*(1-R)Q*xTotalCreditpaidforreturnedunsoldgoodsminusthetotalsalvagevalueobtainedfromtheseitemsbythemanufacturer

Model21PasternackORDERDEMAND0Q*RQ*(1-R)Q*xTotalCreditpaidforreturnedunsoldgoodsminusthetotalsalvagevalueobtainedfromtheseitemsbythemanufacturer

Model22PasternackORDERDEMAND0Q*RQ*(1-R)Q*xTotalgoodwillcostofthemanufacturer(becauseoflostdemand)

Model23Pasternack

ModelNowwhatwehaveonhand?FromCase-1Analysis:Weknowthatthemanufacturerwantstomaximizethetotalchannelprofitandhencewants:QT*suchthatitsatisfiesF(QT*)=(p+g2-c)/(p+g2-c3)FromCase-2Analysis:Weknowthattheindependentretailerwantstomaximizeitsownprofitandhencewants:Q*suchthatitsatisfies:24Pasternack

ModelHenceset:Q*=QT*suchthatitsatisfiesF(Q*)=F(QT*)=(p+g2-c)/(p+g2-c3)25Pasternack

ModelThemanufacturerhasthecontrolovertheparametersc1(costofperunitorderfromthemanufacturer),c2(creditperunitpaidbythemanufacturertotheretailerforreturnedgoods)andR(percentageoftheorderquantity,Q,thatcanbereturnedtothemanufacturerforacreditofc2peritem).Results:Ifthemanufacturersetsthesethreeparametersinsuchawaythatthepreviousequationissatisfied,theindependentretailershouldorderthesamequantityfromthemanufactureraswouldthemanufacturerifoperatingacompanystore.Thisresultsinmaximumtotalprofitstotheretailerandmanufacturer,andthechannelissaidtobecoordinated.Observations:Asthereisnouniquesolutiontothepreviousequation,differentvaluesforthesetheredecisionvariablesresultindifferentdivisionsofexpectedprofitbetweenthemanufacturerandtheretailer.Therefore,themanufacturer’spricingandreturnpolicywillfunctionasarisksharingagreementbetweenmanufacturerandretailer.26Pasternack

ImplicationsTheorem1. Thepolicyofamanufacturerallowingunlimitedreturnsforfullcreditissystemsuboptimal.27Pasternack

ImplicationsTheorem2. Thepolicyofamanufacturerallowingnoreturnsissystemsuboptimal.Theorems1&2implythat“unlimitedreturnsforfullcredit”aswellas“noreturns”preventschannelcoordination.Theorem3. Apolicywhichallowsforunlimitedreturns(R=1)atpartialcredit(c2

<c1)willbesystemoptimalforappropriatelychosenvaluesofc1andc2.28Pasternack

ImplicationsIfc1andc2aresochosenandthemanufacturerallowsforunlimitedreturns,thenthetotalexpectedprofitfortheretailerandmanufacturerareasfollows:29Pasternack

ImplicationsIfthedemandforthecommodityfollowsanormaldistribution(x~N(μ,σ))thenthepreviousequationsbecome:OBSERVATIONS:c1chosenatitslowend(c1=c+ε)ManufacturermakesNOPROFITc1chosenatitshighend(c1=p–ε)RetailermakesNOPROFIT

30Pasternack

ImplicationsAsc2↑c1also↑31Pasternack

ImplicationsResults&Suggestions:Thepricingshouldbesetsothattheaverageretailestablishmentcapturesatleastsomeportionofthegainfromchannelcoordination.Ifitcanbedemonstratedtotheretailersthattheirprofitswillimproveasaresultofpricechanges,thentheyshouldbemorewillingtoacceptthenewpricingplan.Increasingtheretailers’profitsshouldresultinadditionaldistributionoutletsbeingopened,resultinginanincreaseinoveralldemand.REASON32Pasternack

ImplicationsResults&Suggestions:Adrawback!!!Multi-retailerEnvironmentManufacturersetsasingle(uniform)pricingpolicyforallretailersImpactsonretailerprofitabilitywillbedifferentApolicythatincreasesretailers’totalprofitdoesnotguaranteetoincreaseallindividualretailer’sprofit.Somemayfacedwithadecreaseintheirexpectedprofitduetothechannelcoordinatedpricingpolicy.Aneasybutnotfeasiblesolution:Adifferentandretailer-specificpricingpolicycanbedeterminedandsetforeachretailerandthisachievesthemanufacturer’sgoal.InfactitisnotdefendableundertheRobinson-PatmanAct(whichisanactaboutthecompetitionandpricingactionsinbusinessenvironment).33Pasternack

ImplicationsResults&Suggestions:AnotherissueGoodwillCostsHardtoQuantifyVaryamongdifferentretailersAuniformpricingpolicyforthoseretailercannotbesetFortunately,analysesshowthatwhenR=0theretailers’orderquantityisinsensitivetosmallchangesingoodwillcost.Apricingpolicyforanewproduct!Desirableenough$$$Ensurereasonablerateofreturn$$$$$$34Pasternack

ExamplesConsideraproductwith:Netretailpriceof$8.00 (p=8).Manufacturingcostof$3.00 (c=3)Salvagevalueof$1.00 (c3=1)Retailergoodwillcostis$3.00 (g=3)Manufacturergoodwillcostis$2.00 (g1=2)Totalgoodwillcostis$5.00 (g2=g+g1=5)g=3,g1=2,g2=5,p=8,c=3,c1=4,c3=1,R=0Supposethatmanufacturercharges$4.00(c1=4)peritemfromtheretailerandnotpermitreturnsforunsoldgoods(R=0).35Pasternackg=3,g1=2,g2=5,p=8,c=3,c1=4,c3=1,R=0

ExamplesAssumearetailer:Demand~N(200,50)andtheretailerisaprofitmaximizer.Q*=226 EPR(Q*)=$626.25 EPM(Q*)=$206.85(1)FromTheorem-2,thiscannotbeoptimal!Manufacturerdecidestoallowunlimitedreturnstoachievechannelcoordination.SetR=1.36Pasternack

Examplesg=3,g1=2,g2=5,p=8,c=3,c1=4,c3=1,R=1From

F(QT*)=(p+g2-c)/(p+g2-c3)c1=$4.28 c2=$2.936Q*=249 EPR(Q*)=$643.51 EPM(Q*)=$206.95(2)Ifallthegainisgiventotheretailerc1=$4.37 c2=$3.044Q*=249 EPR(Q*)=$626.86 EPM(Q*)=$223.61(3)Ifallthegainisgiventothemanufacturer37Pasternackc1=$4.32 c2=$2.984 EPR(Q*)=$636.11 EPM(Q*)=$214.35(4)BothManuf.&Retailerbenefitfromthestrategy

ExamplesNowsupposethisistheselectedpolicy...38Pasternack

ExamplesConsiderasecondretailer:Demand~N(200,10)andtheretailerisaprofitmaximizer.Beforechannelcoordination(c1=4,R=0)Q*=205 EPR(Q*)=$765.25 EPM(