基于需求扩散和随机技术进步的连续产品引入过程

TimingSuccessiveProductIntroductionswithDemandDiffusionandStochasticTechnologyImprovement基于需求扩散和随机技术进步的连续产品引入过程R.MarkKrankelDepartmentofIndustrialandOperationsEngineering,UniversityofMichigan,IzakDuenyas,RomanKapuscinskiRossSchoolofBusiness,UniversityofMichigan,AnnArbor,MichiganPresentbyLiWeiCONTENTSIntroductionLiteratureModelOptimalPolicyComputationalStudyandInsightsExtensionsIntroductionConsideraninnovativefirmthatmanagesthedevelopmentandproductionofasingle,durableproduct.Overtime,thefirm’sresearchanddevelopment(R&D)departmentgeneratesastochasticstreamofnewproducttechnology,features,andenhancementsfordesignintosuccessiveproductgenerations.IntroductionThefirmcapturesthebenefitsofsuchadvancesbyintroducinganewproductgeneration.Duetofixedproduct-introductioncosts,itmaybeunreasonabletoimmediatelyreleaseanewproductgenerationaftereachtechnologydiscovery.Rather,thefirmmayprefertodelayanintroductionuntilsufficientincrementalnewproducttechnologyhasaccumulatedinR&D.Theobjectiveofthispaperistocharacterizethefirm’soptimalproduct-introductionpolicyIntroductionThetotalnumberofproductgenerationsisnotpre-specified;rather,itisdeterminedbythepaceoftechnologyimprovementalongwiththefirm’sdynamicdecisionsonwhentointroduce.Analysisiscenteredupontwokeyinfluencesaffectingtheintroductiontimingdecisions:–(1)demanddiffusiondynamics,wherefutureproductdemandisafunctionofpastsales–(2)technologyimprovementprocess,specificallytheconceptthatdelayingintroductiontoalaterdatemayleadtothecaptureoffurtherimprovementsinproducttechnology.IntroductionPreviousliteratureexaminingincrementaltechnologyintroductionhasfocusedoneither(1)or(2),butnonehaveconsideredbothfactorssimultaneously.Asaresult,thepresentanalysisprovidesnewinsightintothestructureoftheoptimalintroductiontimingpolicyforaninnovativefirm.Usingaproposeddecisionmodelthatincorporatesbothkeyinfluences,weprovetheoptimalityofathresholdpolicy:itisoptimalforthefirmtointroducethenextproductgenerationwhenthetechnologyofthecurrentgenerationisbelowastate-dependentthreshold,inwhichthestateisdefinedbythefirm’scumulativesalesandthetechnologylevelinR&D.IntroductionRelativepapers–WilsonandNorton(1989)&MahajanandMuller(1996)Thesetwopapersproceedunderademanddiffusionframework,butdonotmodeltheprogressionofproducttechnology.Rather,theyassumethatthenextgenerationproducttobeintroducedisavailableatalltimesstartingfromTime0.Asaresult,theyrespectivelyconcludetheoptimalityof“nowornever”(thenewgenerationproductisintroducedimmediatelyornever)and“noworatmaturity”(thenewgenerationproductisintroducedimmediatelyorwhenthepresentgenerationproducthasreachedsufficientsales)rulesgoverningproductintroductions.LiteratureTwomainresearchareasaredirectlyrelevanttothecurrentwork.–Thefirstcentersonmodelsofdemand.Papersinthisareadescribethepatternsofdemandexhibitedbysingleormultipleproductgenerations,specificallyinrelationtonewinnovations.Thesepapersconcentrateonsystemdynamicsand/ormodelfitwithempiricaldata.–Thesecondresearchareaexaminesdecisionmodelsfortechnologyadoptiontiming.Asubsetofthisgroupincludespapersthatmodeltheintroductionofnewproductssubjecttodemanddiffusion.Literature—modelsofdemandBass(1969)initiatesthestreamthatexaminesdemanddiffusionmodelsbyformulatingamodelforasingle(innovative)product.TheBassmodelspecifiesapotentialadopterpopulationoffixedsizeandidentifiestwotypesofconsumerswithinthatpopulation:innovatorsandimitators.Innovatorsactindependently,whereastherateofadoptionduetoimitatorsdependsonthenumberofthosewhohavealreadyadopted.Theresultingdifferentialequationforsalesrateasafunctionoftimedescribestheempiricallyobserveds-shapedpatternofcumulativesales:exponentialgrowthtoapeakfollowedbyexponentialdecay.Literature—modelsofdemandBass,F.M.1969.Anewproductgrowthmodelforconsumerdurables.ManagementSci.15215–227.ProfDr.FrankM.Bass(1926-2006)wasaleadingacademicinthefieldofmarketingresearch,andisconsideredtobeamongthefoundersofMarketingscience.HebecamefamousasthecreatoroftheBassdiffusionmodelthatdescribestheadoptionofnewproductsandtechnologiesbyfirst-timebuyers.HediedonDecember1,2006.Literature—modelsofdemandNortonandBass(1987)extendtheoriginalBassmodelbyincorporatingsubstitutioneffectstodescribethegrowthanddeclineofsalesforsuccessivegenerationsofafrequentlypurchasedproduct.JunandPark(1999)examinemultiple-generationdemanddiffusioncharacteristicsbycombiningdiffusiontheorywithelementsofchoicetheory.WilsonandNorton(1989)proposeamultiple-generationdemanddiffusionmodelbasedoninformationflow.KumarandSwaminathan(2003)modifytheBassmodelforthecaseinwhichafirm’scapacityconstraintsmaylimitthefirm’sabilitytomeetalldemand.Usingtheirreviseddemanddiffusionmodel,theydetermineconditionsunderwhichacapacitatedfirm’soptimalproduction/salesplanisa“build-uppolicy,”inwhichthefirmbuildsupaninitialinventorylevelbeforethestartofproductsalesandalldemandismetthereafter.Literature—technologyadoptiontimingGjerdeetal.(2002)modelafirm’sdecisionsonthelevelofinnovationtoincorporateintosuccessiveproductgenerations.Thepaperdoesnotco