study on quality decision making and coordination in dual

ScientificJournalofEconomicsandManagementResearchVolume3Issue3,2021

ISSN:2688‐9323

StudyonQualityDecision‐makingandCoordinationinDual‐channelWhenConsideringShowroomingEffect

RuitianYan*

SchoolofEconomicsandManagement,XidianUniversity,Xi'an,710000,China

*18735201753@163.com

Abstract

IntheDual‐channelsupplychain,consumersgenerallychoosetheconsumptionmodeoffirstexperiencingofflineandthenpurchasingonline.Thisconsumptionpatternleadstothe increased demand for retailers with their offline services is divided bymanufacturers’ online direct sales channels, which reduces the retailer’s serviceenthusiasmand intensifies theconflictbetweenchannels.To investigate thischannelconflictproblem, thispaper adopt thedifferential game theory to study theoptimaldynamicqualitydecisionsofsupplychainmembersundertheshowroomingeffect.TheoptimalstrategiesforcentralizedDecision‐makinganddecentralizedDecision‐makingarerespectivelysolved,andthemanufacturer’sservicequalitycostsharingcontractfortheretailer isdesigned.Throughthiscontract,thePareto improvementofthesupplychainsystem inthecaseofdecentralizedDecision‐makingcanberealized.Theresultshows that in thecaseofdecentralizedDecision‐making, themanufacturer’sproductqualitydecisionwillnotbeaffectedbyconsumers’showroomingbehavior.Theretailer’sservicequalityandcorporategoodwillwilldeclinewiththe increaseofshowroomingeffect,whichwillreducetheoverallprofitofthesupplychain.Byestablishingacontractforthesharingofservicecostbetweenthemanufacturerandretailer,thispaperalsohassomeconclusion:thenegativeimpactoftheshowroomingonretailercanbealleviated,the enthusiasm of retailer to provide service is increasing, corporate goodwill isimproved, and Pareto improvement of supply chain profits is achieved underdecentralizedDecision‐making.

Keywords

Showrooming; Dual‐channel Supply Chain; Quality Decision; Differential Game; CostSharingContract.

1. Introduction

WiththerapiddevelopmentoftheInternet,manymanufacturingcompanieshaveestablishedonlinedirectsaleschannels,formingaDual‐channelsupplychainwiththeoriginalofflinesaleschannels, such as NIKE, Uniqlo, and Bonobos. In this Dual‐channel model, consumersmaytransfer to the manufacturer’s online channel to purchase after experiencing the productperformanceinthephysicalstore.Atthistime,theretailer’sservicehasashowroomingeffectonthedemandofonlinechannel[1,2].Inthesalesprocessofclothing,shoes,furniture,books,sportinggoodsandelectronicproducts, it isvery likely to induceconsumers’ showroomingbehavior[3‐5]. When the sales of offline channels are divided by online channels, it willinevitablyaffectretailers’serviceenthusiasm,bringresistancefromdownstreamretailers,andexacerbate channel conflicts. For example, Levis finally closed its online store under theresistanceoftraditionalretailers;DaphneannouncedonAugust25,2020thatitwillcompletelywithdrawfromthephysicalretailbusiness.Inaddition,withtheexpansionofsaleschannels,theconsumermarketcontinuestoexpand, leadingtotheemergenceofmanyhomogeneous

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products.Besidesthepricefactor,consumersalsoconsiderthequalityoftheproducts.Qualityincludesthequalityattributesoftheproductitself,aswellastheserviceattributesthatcanonlybemeasuredbyperception[6].Thequalitydecisioninthisarticleincludesproductqualitydecision and service quality decision. Product quality decision mainly refers to themanufacturer’simprovementofproductappearanceandpackaging,productqualityinspection,establishmentof productmanagementmechanism.The servicequalitymainly refers to theservice paid by retailers to provide consumerswith relevant product information. Existingstudieshaveshown thatmanufacturingcompanieshave increased theirprofits through theoperationalstrategyofqualityimprovement.Inadditiontoadvertising,qualityisanimportantfactoraffectingconsumerbrandfavorability.Improvingproductqualityandservicequalitycanhelpestablishandimprovecorporategoodwill[7],andgoodwillwillhaveacertainimpactonproductsales.Manufacturersandretailersmustconsiderthisimpactongoodwillwhenmakingqualitydecisions.Therefore,howtoachieveawin‐winsituationbymakingqualitydecisionsandcoordinatingstrategyforsupplychainparticipantsarequestionsworthstudying.Takingintoaccountthecommonconsumer’sshowroomingbehaviorintheDual‐channelsupplychain,weintendtostudythefollowingquestions1.What’s the influence of showrooming effect on manufacturer and retailer? Does theshowroomingeffectcrackdownretailer’sactivenessinservicequalityinvestment?2.Doesthecost‐sharingcontractreducethenegativeeffectofshowroomingeffectonretailer’sactiveness in service quality investment? Which condition would be more effective inmotivatingretailertoincreaseinvestment?

2. LiteratureReview

Theresearchismainlyrelatedtofollowingtopics:showroomingeffect,Dual‐channelsupplychaincoordinationandqualityresearchinDual‐channel.

2.1. ShowroomingEffectResearch on the phenomenon of showrooming generally believes that consumers’showroomingbehaviorswillcausedamagetophysicalstoresandthesupplychain.Basaketal.[5]usedgametheorytostudythepricedecisionsofaphysicalretailerandanonlineretailerunderthephenomenonofshowrooming.Theresultshowedthattheshowroomingeffectwouldleadtoanoveralldecreaseinretailprices,whichisbeneficialfromaconsumer’spointofview.Withtheincreaseoftheshowroomingcoefficient,theprofitsofthetraditionalretailerandtheonline retailer will decrease. The showrooming phenomenon is not only detrimental totraditional retailers, but also detrimental to online retailers. Jing et al. [8] found that theshowrooming behavior would intensify channel competition and proposed five short‐termstrategies to counter the showrooming effect. But these strategies will reduce consumerdemandtosomeextent.Somescholarsalsoanalyzedtheadvantagesthatshowroomingmaybringtosupplychainmembersfromapositiveperspective.Kokhoetal.[9]usedaqualitativemethodtostudythepotentialopportunitiesthattheshowroomingphenomenonmaybringtoretailersbasedontheperspectiveofconsumershoppingexperience.Theresearchshowsthatretailerspayattentiontoconsumers’shoppingexperienceandmakedecisions,whichcanturnthe threat posed by the showrooming phenomenon into an opportunity that benefitsthemselves.Kuksovetal.[2]believethatconsideringthemanufacturer’sdecision,theabilityofconsumers to participate in the showrooming phenomenonmay lead to an increase in theprofitability of offline retailers rather than a decrease. Existing research on showroomingmostly focuses on short‐term operation strategies, ignoring the long‐term dynamics ofenterpriseoperations.Moststudiesfocusonpricecompetitionandignoretheimpactofnon‐pricefactorssuchasproductqualityandservicequalityonthesupplychainsystem.Gensleretal. [10]found that non‐price factors play a key role in consumers’ showrooming decisions.

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Therefore, it isnecessary topayattention tonon‐price factorswhenstudying theDecision‐makingofsupplychainmembersinthecontextofshowrooming.

2.2. Dual‐channelSupplyChainCoordinationThere have been many studies on Dual‐channel supply chain, including channel selectionresearch,channelpricingresearch,channelcoordinationresearch,consumerchannelselectionresearchandotheraspects.Theresearchinthisarticlemainlyinvolveschannelcoordination.Regarding channel coordination, the main consideration is the competitive relationshipbetweenonlineandofflinechannels.RelatedscholarshavedesignedandanalyzedtheinfluenceofdifferentincentivemechanismsontheDecision‐makingandprofitfunctionofsupplychainmembers.TheresearchofYanetal.[11]showedthatretailerswereunwillingtocooperatewithmanufacturerstorealizeprofitsharing,andproposedacombinationmechanismoffinancialsupportandprofitsharing,whichprovedthat thismechanismcaneffectivelysolvetheO2Ocompetition problem and create higher profits for the supply chain participants. Pei et al.[12]propose an innovative and positive strategy can be utilized to solve the issue of O2Ocompetitionandconflictandhelpimprovethechannelmemberperformance.Theinnovativestrategyconsistsoftheretailer’ssaleseffortandthemanufacturer’smonetarysupporttotheretailer’slocaladvertising.

2.3. QualityResearchinDual‐channelThe research in this article also involves the relationship between the quality decisions ofsupply chainmembersandcorporategoodwill.Giovanni[13] formulatedanoptimal controlmodel, which considered the negative impact of product defects on goodwill. Relevantliterature mostly considers a single participant, such as a monopoly company or differentdepartments of the same company, but rarely considers the influence ofmembers’ qualitydecisionsondifferentparticipants in the context of aDual‐channel supply chain.Moreandmoremanufacturing companies have established dual channels for sales. Comparedwith asinglesaleschannel,Dual‐channelinvolvespricegamesbetweendifferententities.Atthesametime,inthepresenceoftheshowroomingphenomenon,demandbecomesmorecomplicatedthanunderasinglechannel.ItisofpracticalsignificancetostudythequalitydecisionsofsupplychainmembersunderthebackgroundofaDual‐channel. Basedontheexistingresearch, inthecontextofaDual‐channelsupplychaincomposedofasinglemanufacturerandasingleretailer,thispaperaimsatthequalityDecision‐makingandcoordinationproblemsof theDual‐channel supplychain,andconstructsadifferentialgamemodel, taking the corporate goodwill as a state variable. We consider the impact of themanufacturer’s product quality decision and the retailer’s service quality decision on themanufacturer’scorporategoodwill,aswellasontherevenueoftheoverallsupplychainanditsmembers. First, a differential game model considering the showrooming phenomenon isconstructedasthebasicmodel,whichconsiderstheimpactofthequalityofservicepaidbytheretaileronthesalesoftheonlinechannel.ThroughthesolutionfromHJBequation,weobtainthe optimal quality decisions of the manufacturer and the retailer respectively undercentralizedDecision‐makinganddecentralizedDecision‐makingscenarios.Then,consideringthemanufacturer’sincentivetotheretailer’sservicequality,themanufacturer’sservicecostsharingcontractwiththeretailerisdesigned.Finally,thenumericalanalysis is investigated,whichverifiestheeffectivenessofthecontracttocoordinatetheDual‐channelsupplychain.

3. ProblemDescriptionandBasicAssumptions

ThisarticleconsidersaDual‐channelsupplychaincomposedofamanufacturerandaretailer.Theretailersellsinanofflinechannel,andthemanufacturersellsthesameproductthroughitsonlinedirectsaleschannel.Themanufactureristheleaderandtheretaileristhefollower.The

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twocompete inStackelberg.Themanufacturerdeterminesproductquality, and the retailerpays a certain service quality effort to provide services to consumers.The improvementofproductqualitywillhaveapositiveimpactonthegoodwillofthecompany.BasedontheN‐Amodel[14], this paper considers the impact of product quality on goodwill, and obtains thechangeofgoodwillovertimeasshowninthefollowingformula

, 0 0(1)

Among them, is themanufacturer’s product quality decision. is the product quality’sinfluencecoefficientongoodwill. istheretailer’sservicequalitydecision. istheservicequality’s influence coefficient on goodwill. is the natural decline rate of goodwill, whichrepresentstheforgettingeffectofconsumersonthegoodwill.High quality can increase goodwill and sales. However, while improving quality, it alsoincreasesthecostofthemanufacturer.Therefore,themanufacturerneedstochoosethebestqualitydecision toachieve thegoalofmaximizingprofit.At thesame time, theretaileralsoneedstodetermineitsservicequalitylevelwiththegoalofmaximizingtheinterests.Duetotheshowroomingphenomenon, someconsumers are more inclined topurchaseonline channelwithlowerpriceafterexperiencingofflinestores.Therefore,itisassumedthattheretailer’ssaleseffortcannotonlyincreasethesalesofofflinechannel,butalsoincreasethesalesofonlinechannel.Weassumethatthesalefunctionofonlinechannelis

thesalefunctionofofflinechannelis

1 1 (3)

Amongthem, isthemarketshareofonlinechannel,and1 representsthemarketshareoftheofflinechannel.Respectively, , arethesellingpricesofonlineandofflinechannels.Weassumingthatthecross‐priceimpactonsalesislessthantheimpactofchannelpricesonsales,

1. istheservicequalityoftheretailer. representstheshowroomingeffectcoefficient,whichmeans thatamong theconsumersattractedby theretailer through improvingofflineservices, ratioofpeoplechoosetobuyonline,and1 ratioofpeoplechoosetobuyofflineand0 1issatisfied. , aretheinfluencecoefficientsofgoodwillononlineandofflinesales.Assumingthatthewholesalepriceis andthemanufacturer’sunitproductioncost is.Therevenuefunctionsofthemanufacturerandtheretailerarerespectively

Inordertosimplifythecalculation,wesupposethemanufacturer’sunitproductioncost0.[15‐17]Inadditiontounitproductioncost,themanufactureralsobearthecostofproductquality.Suchcostfunctionsareassumedtobequadraticfunctions.Weassumethatthecostof

productquality isrelated tothemanufacturer’squalitydecision,setas )(2

1 21 tqC .Themodel

doesnotconsiderthesalescostoftheonlinechannel.Thesalescostoftheofflinechannelis

related to the retailer’s service quality, which is set as )(2

1 22 tqC .Simplify cost parameters

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withoutlossofgenerality,suppose 1.[13]Thetimevariabletwillbeomittedbelow.Then the profit functions of the manufacturer, retailer, and supply chain as a whole arerespectivelyWhere isthediscountfactorand 0isthediscountrate.

4. ModelSolutionandAnalysis

As consumers havemore andmore channels for obtaining price information,market pricegraduallybecometransparent,andcorporatepricing isbasicallydeterminedby themarket.Therefore,thisarticleassumesthatthesalesprice oftheonlinechannel,thewholesaleprices,andretailprice oftheofflinechannelareallsettoconstants[18,19].Thedifferentialgame

model consists of a state variable and two decision variables. The manufacturerdeterminestheproductquality andtheretailerdeterminestheservicequality .

4.1. CentralizedDecisionModelInthecaseofcentralizedDecision‐making,themanufacturerandtheretailertogethermakethedecision.Theprofitmaximizationofthesupplychainsystemisregardedasthedecisiongoal.Thedifferentialgamemodelofthesupplychaincanbeexpressedas

, 0 0(7)

Proposition1. UnderthecentralizedDecision‐makingsituation,themanufacturer’soptimalproductqualitystrategyandtheretailer’soptimalservicequalitystrategyarerespectively

Proof. Let denote the optimal profit function of the overall supply chain undercentralized Decision‐making. According to the Bellman dynamic programming theory,constructtheHJBequationundercentralizedDecision‐making

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1 1 2 1 2 1 2 1 1 21

1 (10)

(11)Substituteequations(10)and(11)intoequation(9).AccordingtotheformoftheHJBequation,assumingtheformofthevaluefunctionis

(12)Where , istheundeterminedcoefficient,then

Substitutingequations(12)and(13)intothesimplifiedHJBequation,thesolutionis

Substitute intoequations(10)and(11)toget

Proposition1isproved.Substitutingtheaboveoptimalstrategiesintotheexpression(1)ofgoodwillandsolvingtheunivariatelineardifferentialequation,wecanobtainthechangeformofgoodwill.

Thestablestateofgoodwill is

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FromProposition 1, in the case of centralizedDecision‐making, from the expression of themanufacturer’s optimal product quality decision , it can be seen that themanufacturer’squality decision is related to the sellingprices of the two channels. It is also related to theinfluencecoefficientsofgoodwillonthesalesofthetwochannels.Themanufacturerneedstocomprehensivelyconsiderpriceandtheinfluencecoefficientsofgoodwillonthetwochannelsbefore deciding its optimal quality strategy.Whenonline andofflinemarket prices change,manufacturermustmakecorrespondingadjustments.Thequalitydecisionofthemanufacturerispositivelycorrelatedwiththeinfluencecoefficient ofproductqualityonthegoodwill,thatis, the greater the influence of product quality on the goodwill, the more willing themanufacturer to increase quality investment. The reason is that the greater the influencecoefficientofproductqualityongoodwill,theeasieritisforthemanufacturertoincreaseitsqualityinvestmenttoincreasegoodwill,andtheincreaseingoodwillwillincreasethesalesofonlineandofflinechannelsandbringhigherreturnstomanufacturer.Businessesaremotivatedto increase quality investment. Manufacturer’s product quality decision affects corporategoodwillthroughtheequationofstate(1),whichinturnaffectsthesalesofonlineandofflinechannels.From the expression of the retailer’s optimal service strategy , it can be seen that theretailer’sservicequalitydecisionisrelatedtothesellingprices , ofthetwochannels,theinfluencecoefficients , ofgoodwillonthesalesofthetwochannels,andtheshowroomingeffectcoefficient .Theretailer’sservicequalitydecisionispositivelycorrelatedwiththeinfluencecoefficient ofservicequalityongoodwill,thatis,thegreatertheinfluenceofservicequalityongoodwill,themorewillingtheretailertoincreaseservicequalityinvestment.Thesameastheproductqualityofthemanufacturer,theretailer’sservicecanalsoindirectly increasedemandbyimprovinggoodwill.Differentfromtheproductqualitydecisionofthemanufacturer,theimprovementofthe retailer’s service quality can directly increase demand, not only increasing the sales ofoffline channel, but also increasing the sales of online channel due to the existence of theshowroomingphenomenon.Therefore,theretailershouldcomprehensivelyconsiderthedirectandindirecteffectsonthetwochannelswhenmakingitsservicequalitydecision.Corollary1. The partial derivatives of themanufacturer’s product quality strategy , theretailer’s service quality strategy , and the steady state goodwill with respect to theshowroomingcoefficient arerespectively

0， 0， 0

Corollary1showsthatunderthecentralizedDecision‐makingsituation, theinfluenceoftheshowrooming coefficient on the steady state of goodwill and the retailer’s service qualitystrategydependson thepricedifferencebetween the two channels. Specifically,when

0 , that is, when the online price is lower than the offline price, the larger the pricedifference,thesmallertheretailer’sservicequality,andthelowerthecorporategoodwilllevel.The greater the online andoffline price difference, themore sensitive the retailer’s servicequality and corporate goodwillwill be to the showrooming coefficient. Themanufacturer’sproductqualitydecisionhasnothingtodowiththesizeoftheshowroomingcoefficient.The

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reasonisthattheshowroomeffectwillonlyallowthemanufacturertosharepartofthesalesincreasedbytheretailer’sservice,andwillnotaffectthemanufacturer’squalitydecision.Corollary2. The partial derivatives of themanufacturer’s product quality strategy , theretailer’s service quality strategy , and the steady state goodwill with respect to theinfluencefactor ofproductqualityongoodwillarerespectively

0， 0，2

Corollary2 shows that in thecaseof centralizedDecision‐making, thegreater the influencefactor of product quality on goodwill, the higher the quality of product provided by themanufacturer,andthehigherthegoodwillofthecompany.Thisisbecausetheimprovementofthemanufacturer’squalitylevelwillfurtherincreasethecompany’sbrandreputation,therebyincreasingtheonlineandofflinesalesof theproduct.Theretailer’sservicequality levelhasnothingtodowiththisimpactfactor.Corollary3. The partial derivatives of themanufacturer’s product quality strategy , theretailer’s service quality strategy , and the steady state goodwill with respect to theinfluencefactor ofservicequalityongoodwillarerespectively

0， 0，

Corollary3 shows that in thecaseof centralizedDecision‐making, thegreater the influencefactor ofservicequalityongoodwill,thehigherthelevelofservicequalityprovidedbytheretailer and the higher goodwill of the enterprise. This is because the improvement of theretailer’sservicequalitywillincreasethegoodwill,andtheimprovementofthegoodwillwillincrease the retailer’soffline channel sales.The larger the factor , themoremotivated theretailertoincreasesalesinofflinechannelbyincreasingtheinvestmentinservicequality.Themanufacturer’sproductqualitydecisionhasnothingtodowiththisimpactfactor.

4.2. DecentralizedDecisionModelIn thecaseofdecentralizedDecision‐making,both themanufacturerandtheretaileraimatmaximizingtheirownprofitsandeachformulatetheiroptimalstrategies.Themanufacturermakes product quality decisions, and the retailer makes service quality decisions. UsesuperscriptDtoindicate.Usingdifferentialgametheorytosolvetheoptimaldecisionofthemanufacturerandretailer.Wecangetthefollowingproposition.Proposition2. TheoptimalstrategiesunderdecentralizedDecision‐makingare

1 (16)

Proof. Let and denotetheoptimalprofitfunctionsofthemanufacturerandtheretailerunderdecentralizedDecision‐making.AccordingtotheBellmandynamicprogramming

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theory, construct the HJB equations of the manufacturer and retailer under decentralizedDecision‐makingasfollows

1 1 (18)

Solvingtheoptimizationproblemontherightsideoftheequation,themanufacturer’soptimalproductqualitystrategyandtheretailer’soptimalservicestrategyare

1 (19)

Substituteequation(19)intoequations(17),(18)andsimplify.AccordingtotheformoftheHJB equation, it is assumed that the value functions of the manufacturer and retailer arerespectively

Where and 1,2 areundeterminedcoefficients,thenthereare

Substitutingequations(20)and(21)intothesimplifiedHJBequations,thesolutionsare

Substituting , intoequation(19),weget

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Proposition2isproved.Substituting the above optimal strategies into the expression of goodwill and solving theunivariatelineardifferentialequation,wecanobtainthechangeformofgoodwill.

(24)Thestablestateofgoodwill is

ItcanbeseenfromProposition2thatthemanufacturer’sproductqualitydecisionisrelatedtothepriceandwholesalepriceoftheonlinechannel,buthasnothingtodowiththepriceoftheofflinechannel.Theretailer’sservicequalitydecisionisrelatedtotheofflinechannelpriceandthewholesaleprice,nottotheonlinechannelprice.Themanufacturer’squalitydecisionisnotonly related to the influence coefficient of goodwill on online channel sales, but also theinfluencecoefficient ofgoodwillonofflinechannelsales.This isbecauseofflinesaleswillalsoaffectthemanufacturer’srevenue.Thebigger is,themoreofflinesales.Thatmeansthemore wholesale revenue the manufacturer receives from the retailer, and the greater themanufacturer’stotalprofit.Theretailer’sservicequalitydecisionhasnothingtodowith ,butonlywith .Underthesameconditions,thegreatertheinfluencecoefficient ofgoodwillonofflinechannelsales,thehighertheretailer’sservicequality.Corollary4. The partial derivatives of themanufacturer’s product quality strategy , theretailer’s service quality strategy , and the steady state goodwill with respect to theshowroomingcoefficient arerespectively

0， 0， 0

Corollary 4 shows that in the case of decentralized Decision‐making, the steady state ofgoodwill and the retailer’s service quality strategy are all negatively related to theshowroomingcoefficient.Themanufacturer’sproductqualitydecisionhasnothingtodowiththesizeoftheshowroomingcoefficient.InthecaseofdecentralizedDecision‐making,withtheenhancementof showrooming,moreconsumerswill choose theonlinechannel topurchaseamong theconsumersattractedby the retailerby improvingofflineservices.This leads theretailertoreduceserviceleveltoreducecosts.Itwillalsoreducethegoodwillofthecompany.Corollary5. The partial derivatives of themanufacturer’s product quality strategy , theretailer’s service quality strategy , and the steady state goodwill with respect to theinfluencefactor ofproductqualityongoodwillarerespectively

0， 0，2

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Corollary5showsthatinthecaseofdecentralizedDecision‐making,thegreatertheinfluencefactor ofproductqualityongoodwill,thehigherthequalityprovidedbythemanufacturer,and the higher the goodwill of the company. This is because the higher , the higher themanufacturer’s quality levelwill further improve the company’s brand reputation, therebyincreasingtheonlineandofflinesalesof theproduct.Theretailer’sservicequality levelhasnothingtodowiththisimpactfactor.Corollary6. The partial derivatives of themanufacturer’s product quality strategy , theretailer’s service quality strategy , and the steady state goodwill with respect to theinfluencefactor ofservicequalityongoodwillarerespectively

Corollary6showsthatinthecaseofdecentralizedDecision‐making,thelevelofservicequalityprovidedbytheretailerandthegoodwilloftheenterprisearepositivelyrelatedtotheimpactfactor of the retailer’s service quality on goodwill. The manufacturer’s product qualitydecision has nothing to do with .This is because after retailer’s service quality level isimproved,theofflinephysicalstorecanbringconsumersmoreinformationaboutproductsandbettershoppingexperience.Thelarger ,theeasieritistoincreasethegoodwillofthecompanyandpromotethesalesofonlineandoffline.Corollary7.Comparing themanufacturer’s optimal product quality decision, the retailer’soptimal service quality decision, corporate goodwill and the respective sales of the twochannelsinthetwosituationsofcentralizedanddecentralizedDecision‐making,wecanobtain

, , , , Corollary7showsthatinthecaseofcentralizedDecision‐making,thecorporategoodwill,thequality effort of the manufacturer and the retailer are greater than that of decentralizedDecision‐making. The demand for online and offline channels under centralized Decision‐makingisgreaterthanthatunderdecentralizedDecision‐making.InthecaseofdecentralizedDecision‐making,thestrategiesofthemanufacturerandtheretaileraretomaximizetheirowninterests. The retailer will be affected by consumers’ showrooming behavior and willcorrespondinglyreduceservicecosts,whichwillleadtoadeclineingoodwill.Thedeclineingoodwill will lead to a decline in sales in both channels. This is not conducive to theimprovement of the overall profit of the supply chain, so it is necessary to introduce acooperationcontracttorealizethecoordinationandimprovementofthesupplychaininthecaseofdecentralizedDecision‐making.

4.3. ServiceQualityCostSharingModelFromtheaboveanalysis,itcanbeseenthatthequalitydecisionofthesupplychainmembers,thegoodwillofthecompany,andthesalesoftwochannelsunderthedecentralizedDecision‐makingsituationarelowerthanthoseunderthecentralizedDecision‐makingsituation,andthesupplychainsystemcannotachievetheoptimalstate.Retailer’simprovementinservicequalitycandirectlyincreasethesalesofofflinechannel.Atthesametime,duetotheexistenceoftheshowroomingphenomenon, itcanalso indirectly increasethesalesofonlinechannel.WhileincreasingDual‐channel revenue, it also intensifies competition between online and offline

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channels.InordertoalleviatechannelcompetitionandachieveParetoimprovement,thispaperdesigns an incentive mechanism for the manufacturer to provide the retailer with certaintransferpayments.Thatis,themanufacturersharespartofretailer’sservicequalityinvestmentunderdecentralizedDecision‐making.Assumingthesharingratio isγ, the transferpaymentprovidedbythemanufactureris .Themanufacturerisinaleaderposition,andfirstmake product quality and sharing ratio decisions. The retailer determines service qualitystrategybasedonthemanufacturer’sstrategy.Usingthereverse inductionmethod,wefirstsolvedtheretailer’sstrategy,andthenbringitintothemanufacturer’sHJBequationtoobtaintheoptimalservicequalitycostsharingratio.Themodelis

1 (25)

Proposition3. Undertheincentivemechanismthatthemanufacturersharespartoftheservicequalitycost,themanufacturer’soptimalproductqualitystrategy,theretailer’soptimalservicequalitystrategyandthecostsharingratioarerespectively

1 (26)

2 3 1 2 32 1 2

Proof. Let and respectively denote the optimal profit functions of themanufacturerand theretailerunder theservicequality cost sharingmode. In this case, thevaluefunctionoftheretailersatisfiestheHJBequationis

1 1 1 (27)

Solvingtheoptimizationproblemontherightsideoftheequation,theretailer’soptimalservicequalitystrategycanbeobtainedas

TheHJBequationsatisfiedbythemanufacturer’svaluefunctioninthecaseofservicequalitycostsharingis

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Substituteequation(28)intoequation(29)tosimplifyandsolvetheoptimizationproblem.Themanufacturer’soptimalproductqualitydecisionandoptimalservicequalitycostsharingratioareobtainedrespectively

Assumethatthevaluefunctionofthemanufacturerandretailerareasfollows

Among them, and 1,2 are undetermined coefficients, then there are ,.Let

Then22

Substitutingequations(30),(32),(33)intotheHJBequationsofthemanufacturerandretailer,wecanget

Substituting , , into(30)and(33)togetproposition3.Substituting the above optimal strategy into the expression of goodwill and solving thedifferentialequation,wecanobtainthechangingformofgoodwill

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Thestablestateofgoodwill is

2 22 2

Corollary8. Comparingthemanufacturer’soptimalproductqualitydecisionunderthecostsharingsituationandthedecentralizedDecision‐makingsituation,thereare .Thatis,compared with the decentralized Decision‐making situation, the introduction of the costsharing contract does not affect the manufacturer’s optimal product quality decision.Comparingtheretailer’sservicequalitydecisionsandthesteady‐statevalueofgoodwillinthetwo Decision‐making situations, when the showrooming coefficient satisfies

, introducing the cost sharing contract in the case of decentralized

Decision‐makingcanimprovetheservicequalityoftheretailerandthecorporategoodwill.Corollary9. Thepartialderivativeoftheservicequalitycostsharingratio withrespecttothe

showroomingcoefficient is 0.

Corollary9showsthatthemanufacturer’sshareratiooftheretailer’sservicequalitycost ispositively related to the showrooming coefficient. The larger the coefficient, the higher theproportionofconsumersattractedby the improvementof theretailer’sservicequalitywhochoosetheonlinechanneltopurchase,andthemorethemanufactureriswillingtoincreasetheshareratioinordertoobtainhighersales.

5. NumericalAnalysis

WeanalyzedtheinfluenceofdifferentstrategiesmadebysupplychainmembersoncorporategoodwillandsupplychainprofitsinthecaseofdecentralizedandcentralizedDecision‐making.Theservicequalitycostsharingcontractisestablishedtoachievesupplychaincoordination.Inthis section, numerical analysis is used to visually demonstrate the impact of relevantparametersonthesupplychainsystem.Theparametersaresetas 0.4, 0.5, 3,4, 2, 1, 1.2, 0.1, 0.5, 1, 1.2, 0.TheeffectoftheshowroomingcoefficientontheoverallsupplychainandtheprofitofmembersisshowninFig.1,Fig.2,andFig.3.TheParetoeffectofthecostsharingcontractontheprofitofmembersisshowninFig.4.

Fig1.Theinfluenceofthecoefficient ontheoverallprofitofthesupplychain

0 0.2 0.4 0.6 0.8 1

πC πD πB

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Fig2.Theinfluenceofthecoefficient onthemanufacturer’sprofit

Fig3.Theinfluenceofthecoefficient ontheretailer’sprofit

ItcanbeseenfromFigs.1,2and3thatwiththeincreaseoftheshowroomingcoefficientinthethreecases,theoverallprofitofthesupplychaingraduallydecreases.Therespectiveprofitsofthemanufacturerandretailerdecreaseastheshowroomingcoefficientincreases.Underthecostsharingcontract,theoverallprofitofthesupplychainishigherthantheprofitinthecaseof decentralized Decision‐making, and the respective profits of the manufacturer and theretailerarehigherthantheprofitinthecaseofdecentralizedDecision‐making.ThisindicatesthatthecontractcanhelpmanufacturerandretailerachievetheParetoimprovementofthetotalprofitofthesupplychainandtheDecision‐makingparties’profitlevel.ButthetotalprofitisstilllowerthantheprofitunderthecentralizedDecision‐makingsituation,whichindicatesthat the contract to share the retailer’s servicequality cost is nothelpful for themaximumParetoimprovement.

0 0.2 0.4 0.6 0.8 1

πMD π

0 0.2 0.4 0.6 0.8 1

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Fig4.Theinfluenceofthecoefficient ontheParetoimprovementeffectofthecostsharing

contractFig.4showsthatregardlessoftheshowroomingcoefficient,thecostsharingcontractachievesthe Pareto improvement in the profits of the manufacturer and retailer in the case ofdecentralizedDecision‐making,andtheeffectof improvingtheprofitofthemanufacturerismoreobviousthanthatoftheretailer.Withtheincreasingoftheshowroomingcoefficient,theParetoimprovementeffectofthecontractontheprofitofthemanufacturerisincreasing,whilethe improvement effect of the retailer’s profit is decreasing. This indicates that theshowroomingphenomenonhasacertainimpactontheimplementationeffectofthecontract.Thedecisionmakersneedtoconsiderthesizeofthecoefficientinthemarketwhenformulatingtheservicequalitycostsharingcontractanddeterminingthecostsharingratio.

Fig5.Theinfluenceofthecoefficient ontheretailer’sservicequality.

It can be seen fromFig.5 that the quality of service provided by the retailer in the case ofdecentralizedDecision‐makingislowerthanthatinthecaseofcentralizedDecision‐making.Inboth Decision‐making situations, as the showrooming coefficient increases, the quality ofservice provided by the retailer is both gradually decline, and in the case of decentralizedDecision‐making, thequalityof servicedeclines faster.This isbecausecentralizedDecision‐making is aimed atmaximizing the overall profit of the supply chain, while in the case ofdecentralizedDecision‐making,themembersofthesupplychaineachaimatmaximizingtheirrespective profits.When the retailer dealingwith the negative impact of the showroomingphenomenon,itwillchoosetoreducetheservicequalitycosttoobtainahigherlevelofprofit.Afterintroducingtheservicequalitycostsharingcontract,theretailer’sservicequalityishigher

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πMB -π

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iler’

eC eD eB

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thantheservicequalityinthecaseofdecentralizedDecision‐making.Becausethemanufacturersharestheservicequalitycostoftheretailer. Itboostsretailer’smotivationtoprovidegoodserviceandmakesthelessimpactofshowroomingphenomenonontheretailer.Italsomakesthe retailer’s service quality less sensitive to the coefficient, that is, as the showroomingcoefficientincreases,theretailer’sservicequalitylevelbasicallyremainsunchanged.

Fig6.Theinfluenceofthecoefficient onthegoodwill

Fig.6showsthatthegoodwillunderthethreeDecision‐makingsituationsaredifferent.Amongthem, the goodwill under the centralized Decision‐making is the highest, and under thedecentralizedDecision‐makingisthelowest.InthecaseofdecentralizedDecision‐making,theintroductionofcostsharingcontractfortheretailerhasimprovedgoodwilltoacertainextent.InthecaseofdecentralizedDecision‐making,goodwillismostsensitivetotheshowroomingcoefficient.Aftertheintroductionofthecontract,thesensitivityofgoodwilltothecoefficientisreduced,andtheshowroomingcoefficienthasalmostnoeffectonthegoodwill.Itshowsthatincreasing the contract can increase goodwill and reduce the negative impact of theshowroomingphenomenonongoodwill.

Fig7.Theinfluenceofthecoefficient onthecostsharingfactor

ItcanbeseenfromFig.7thatwiththeenhancementofconsumers’showroomingbehavior,theproportionofthemanufacturersharingtheretailer’sservicecostgraduallyincreases.Thisisbecausewhen the showrooming coefficient increases, consumers attractedby the retailer’sservicesaremorelikelytochooseonlinepurchases.Itmakestheretailerpaytheservicecost

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GC GD GB

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butnotreceivethecorrespondingprofitreturn.Theretailermustreducetheservicequalitytodealwiththenegativeimpactoftheshowroomingphenomenon.Theretailer’sservicequalityaffectsthegoodwillandproductsales.Inordertoenhancetheretailer’sserviceenthusiasm,themanufacturerwillchoosealargershareratiotoencouragetheretailertoprovidehigherservicequality.Considering thatboth themanufacturer’sproductqualitydecisionand theretailer’s servicequalitydecisionwillaffectthecompany’sgoodwill,andovertimewillaffectthesalesof theDual‐channel and the profit level of members, the following first analyzes the changes ingoodwillover time.The trajectory is shown inFig.8.Next, the time trajectoryof theoverallsupplychainandtheprofitsofdifferentparticipantsinthethreeDecision‐makingscenariosisanalyzed,asshowninFigs.9,10,and11.

Fig8.Timetrajectorydiagramofgoodwill

ItcanbeseenfromFig.8that inthethreeDecision‐makingsituations, the levelsofgoodwillcontinueto increaseovertimeandeventuallystabilizes.The levelofgoodwill inthecaseofcentralizedDecision‐makingisthehighest,andinthecaseofdecentralizedDecision‐makingisthelowest.Aftertheintroductionofthemanufacturer’sservicecostsharingcontractwiththeretailer,thegoodwillinthecaseofdecentralizedDecision‐makingisimproved.Itindicatesthatthemanufacturer’s sharing of part of the service quality cost can encourage the retailer toimprovetheservicelevel,therebyincreasingthecompany’sgoodwill.

Fig9.Timetrajectorydiagramoftheoverallprofitofthesupplychain

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GC GB GD

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πC πB πD

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Fig10.Timetrajectorydiagramofthemanufacturer’sprofit

Fig11.Timetrajectorydiagramoftheretailer’sprofit

FromFigs.9,10and11,wecanseethatunderthethreemodels,theoverallprofitofthesupplychain, theprofitsof themanufacturerand theretailer, respectively, gradually increaseovertime and eventually stabilize. Theprofit of themembers under the cost‐sharing contract ishigherthanthatinthecaseofdecentralizedDecision‐making.Itindicatesthatthemanufacturersharespartoftheretailer’sservicequalitycost,whichnotonlyincreasestheretailer’sprofit,themanufacturer’sownprofithasnotbeenlost,butalsobeenimproved.Thereasonisthatthemanufacturer sharing part of the retailer’s service quality cost can increase the retailer’senthusiasmforservice,improvetheirgoodwill,andincreasesalesinonlineandofflinechannels.Thiscontractcaneffectivelyincreasetheprofitsofbothpartiesinthesupplychain,andachieveParetoimprovement.ItcanbeseenfromFig.9thattheprofitlevelisthehighestinthecaseofcentralizedDecision‐making.Aftertheintroductionofthecontract,theoverallprofitlevelofthesupplychainissignificantlyhigherthanthatofdecentralizedDecision‐making.Figs.10and11illustratethataftertheintroductionofthecontract,comparedtothecaseofdecentralizedDecision‐making,theprofitlevelsofsupplychainmembershavebeengreatlyimproved.

6. Conclusion

This paper uses the dynamic differential game theory to construct the centralized anddecentralizedDecision‐makingmodels.WeconsidertheinfluenceofshowroomingcoefficientonthequalitydecisionsofsupplychainmembersunderdifferentDecision‐makingsituations,

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andgetthefollowingconclusions.Firstly,themanufacturer’soptimalproductqualitydecisionisindependentofthesizeoftheshowroomingcoefficient.Theoptimalservicequalitydecisionis negatively correlated with the showrooming coefficient. That means the showroomingphenomenonwillnotaffectmanufacturers’qualitydecisions,butwilldampentheenthusiasmof the physical retailer to provide services and crack down retailer’s activeness in servicequalityinvestment.Secondly,throughthecomparisonoftheoptimaldecisionsunderdifferentDecision‐makingsituations,themanufacturer’sservicequalitycostsharingcontractwiththeretailerisdesignedandwegettheoptimalshareratioforthemanufacturerthatwillbemoreeffectiveinmotivatingretailertoincreaseinvestment.TheParetoimprovementoftheprofitsof thesupplychainmembersunder thedecentralizedDecision‐makingsituation is realized.Finally,theimprovementeffectofthecostsharingcontractisverifiedbynumericalanalysis.InthecaseofdecentralizedDecision‐making,themanufacturerandretailerhavereducedtheirrespectivequalitycostsinordertomaximizetheirprofits.Theoptimalproductqualitydecisionandtheoptimalservicequalitydecisionaresmallerthanthatunderthecentralizeddecision.Underthecostsharingcontract,theprofitsofthemanufacturerandtheretailerarebothhigherthanthatinthecaseofdecentralizedDecision‐making,indicatingthattheintroductionofthiscontractcanincreasetheprofitsofbothpartiesinthesupplychainandreducethenegativeeffectofshowroomingeffectonretailer’sactivenessinservicequalityinvestment.

7. LimitationsandFutureDirections

Thispaperstudiestheoptimaldynamicqualitydecisionsofsupplychainmembersundertheshowrooming effect, and gets some valuable conclusions. We have introduced the servicequality cost sharing contract between the manufacturer and the retailer to achieve theoptimizationofthesupplychain.However,therearestillsomeshortcomingsintheresearchofthisarticle.Afterintroducingthecost‐sharingcontract,thetotalprofitisstill lowerthantheprofit in the case of centralized Decision‐making, indicating that only the contract for theretailer’sservicequalitycost‐sharingisnotenoughtoachievetheParetooptimalimprovementeffect. In the future, we can consider introducing other contracts, such as joining a profit‐sharingmechanism,tofurtherrealizetheParetoimprovementofthesupplychain.

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study on quality decision making and coordination in dual

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