3 New-Product Strategy and Industry Clockspeed

Industrial Engineering

Vol.50,No.4,April2004,pp.537–549

issn0025-1909 eissn1526-5501 04 5004 0537

MANAGEMENT SCIENCE

inf®

doi10.1287/mnsc.1030.0172

©2004INFORMS

New-ProductStrategyandIndustryClockspeed

TheRobertH.SmithSchoolofBusiness,UniversityofMaryland,CollegePark,Maryland20742-1815,gsouza@umd.eduKenan-FlaglerBusinessSchool,TheUniversityofNorthCarolinaatChapelHill,ChapelHill,NorthCarolina27599

{barry_bayus@unc.edu,harvey_wagner@unc.edu}

GilvanC.Souza

BarryL.Bayus,HarveyM.Wagner

W

estudyhowindustryclockspeed,internal rmfactors,suchasproductdevelopment,production,andinventorycosts,andcompetitivefactorsdeterminea rm’soptimalnew-productintroductiontimingandproduct-qualitydecisions.Weexplicitlymodelmarketdemanduncertainty,a rm’sinternalcoststructure,andcompetition,usinganin nite-horizonMarkovdecisionprocess.Basedonalarge-scalenumericalanalysis,we ndthatmorefrequentnew-productintroductionsareoptimalunderfasterclockspeedconditions.Inaddition,we ndthata rm’soptimalproduct-qualitydecisionisgovernedbya rm’srelativecostsofintroducingnewproductswithincrementalversusmoresubstantialimprovements.Weshowthatatime-pacingproductintroductionstrategyresultsinaproductionpolicywithasimplebase-stockformandperformswellrelativetotheoptimalpolicy.Ourresultsthusprovideanalyticalsupportforthemanagerialbeliefthatindustryclockspeedandtimetomarketarecloselyrelated.

Keywords:speedtomarket;timepacing;Markovdecisionprocesses

History:AcceptedbyTeckH.HoandChristopherS.Tang,specialissueeditors;receivedJune2001.Thispaperwaswiththeauthors7monthsfor2revisions.

Intoday’smarketplace, rmscompeteinadynamicenvironmentinwhichthevelocityofchangeisoftenswift.Notsurprisingly,timeasastrategicsourceofcompetitiveadvantageisreceivingincreasingatten-tionfromresearchersinoperations,marketing,andstrategy(e.g.,Blackburn1991,Dataretal.1997,EisenhardtandBrown1998,Hult2002).

Onerecentlineofresearchinthisareaarguesthatindustriesarecharacterizedbyaninternalclock-speedthatin uencesa rm’snew-productdevel-opmentactivities(e.g.,MendelsonandPillai1999).Althoughvariousindustrycharacteristicshavebeenproposedtocaptureclockspeed,changesinindustrypriceplayaprominentroleinallmeasures.1Thus,rapidlydecliningpricesareconsideredtobecloselyassociatedwithfast-clockspeedindustries.

AsoriginallyproposedbyFine(1996,1998),fast-clockspeedindustries(personalcomputers,semi-conductors,cosmetics)requiredifferentproduct,process,andsupplychaindesigndecisionsthanmedium-clockspeed(computeroperatingsystems,

Forexample,Williams(1992)empiricallyde nesfast-,medium-,andslow-cycleindustriesintermsofaverageobservedchangesinindustryprices.MendelsonandPillai(1999)includechangesinindustrypricesintheircompositemeasure.Fine(1998)proposesthatcompetitiveintensity,whichisoftenre ectedindownwardpressureonindustryprices,isamajorcomponentofindustryclockspeed.

537

1

1.Introduction

pharmaceuticals,automobiles)andslow-clockspeed(aircraft,petrochemicals,steel)industries.Becausesustainingacompetitiveadvantageisdif cultintur-bulentenvironments,thefrequentintroductionofincrementallynewproductsisgenerallyobservedinfast-clockspeedindustries(e.g.,Williams1992,Hult2002).Basedonself-reportedsurveysofmanufactur-ersintheelectronicsindustry,MendelsonandPil-lai(1999)con rmthatmanagersbelievethatfasterindustryclockspeedisrelatedtoshorterdevelop-mentcycletimesandreducedtimebetweenproductredesigns.Weareunawareofanypublishedresearch,however,thatanalyticallyestablishesalinkbetweenindustryclockspeedanda rm’sdecisiontobringnewproductstomarket.Consequently,thereisanincompleteunderstandingoftheconditionsinwhicha rmshouldfrequentlyintroducenewproducts.

Ourworkbuildsonprioreffortsaddressingthetrade-offsbetweenthetimingofnew-productintro-ductions,productquality,andproductdevelopmentcosts(Cohenetal.1996,Bayus1997,Bayusetal.1997,Morganetal.2001).2Studyingtheintroductiontiming

Thereareotherindirectlyrelatedpapersaswell.Emphasizingtheimportanceofcannibalizationwithinaproductline,WilsonandNorton(1989)andMoorthyandPng(1992)studythetimingofasinglenew-productintroduction.Machinereplacementmodels(seeNairandHopp1992,Nair1995forreviews)andtechnologyadop-tionmodels(e.g.,BalcerandLippman1984,McCardle1985)focusontheroleofobsolescenceintheproductreplacementdecision.

2

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ofandasingleproduct,Cohenetal.(1996),Bayus(1997), rmBayusshouldshouldet“takeal.its(1997)timeessentiallyconcludethatatialintroduceanewproductanddowithitright”;i.e.,a rmsituationqualityaspossible.Extendingthesetheeffortshighesttoini-theuctconditionsgenerationsinwhichovera rmtime,canMorganintroducemultipleprod-mal;whena“rapidinch-up”etstrategyal.(2001)isopti- ndwithi.e., ndincrementala rmshouldimprovements.frequentlyintroduceInparticular,productstheyproductthatintroductionslargelya rm’sdeterminesinternalcostofintroducinganewresultand,asaresult,thefrequencyproductquality.ofproductThistionations,(priceisnotmarginssurprisingareconstantgiventheiracrossmodelformula-butnouslynotmarketshareisafunctionofproductproductqualitygener-tantly,improvingprice,andindustryataconstantproductrate).qualityisexoge-forsuchthethesebeliefresultsdonotprovideanalyticMoresupportimpor-timingasthatexternalindustrycharacteristics,decision.

clockspeed,drivetheproductintroductionsiderUnlikeortheroletheexistingofexternalliterature,industryweanalyticallycon-development,changesincompetitiveproduction,price),internalfactors(clockspeedand rmfactors(productintroductionfactorsBasedtimingininventorycosts),andanddetermininga rm’soptimalthattionsa rm’sonalarge-scaleoptimalpacenumericalproduct-qualityofnew-productanalysis,decisions.introduc-we ndconditions:isprimarilydeterminedbyexternalindustryareaddition,optimalMore-frequentqualityweundernew-productintroductions ndfasterclockspeedconditions.Insuchdecisionisgovernedthata rm’sbyitsoptimalinternalproduct-factors,withasments.incrementaltherelativeversuscostsofmoreintroducingnewproductsfor(1999).theOursuchFinally,basicresultssurveythusprovidesubstantialanalyticalimprove-supportweshowresultsthatofaMendelsontime-pacingandstrategyPillai(1998)asperformisthewellnotonenecessarilyproposedbyEisenhardtandBrownundermanyoptimal,conditions.

butgenerallydoes2.

InModelFormulation

malthissection,etnew-productwestrategies.developaInmodelcontrasttostudytoopti-weal.cessstudy(1996),Bayus(1997),andBayusetal.Cohen(1997),bythatallowsanin nite-horizona rmtomaximizeMarkovdiscounteddecisionpro-Morganintroducingnew-productetal.(2001),multipleweexplicitlyproductgenerations.Unlikepro tityproducttobeintroductiondecisionintroductionvariables.timingconsiderandproductthe rm’squal-underdemandInaddition,uncertainty,weconsiderand

ManagementScience50(4),pp.537–549,©2004INFORMS

thereforeandmodeltheeffectsofproduction,inventory,effectsobsolescence. rms,ConsiderinourFinally,weincludecompetitiveamodel.

marketcomprisedoftwocompetingfromunboundedFirmAandA’sB.perspective.WeformulateThetheplanningdecisionhorizonproblemlengthanddividedintotimeperiodsofisEvery(e.g.,considerperiodlengthsasquarters).equalcompetingperiod,levelproduct rmsthatmakeischaracterizedavailableunitsbyofitsaqualitysingleperiodsandrespectively.anditsdenotedtimeinbymarket,iandwhichismeasuredinproductTherearetwopossiblejforlevelsFirmsforAFirmandA’sB,byintroductionq=qqualitysandqq=:standardqpandpremium,denotedimprovementofimprovement.andastandard,respectively.Weidentifytheaproductasanincremental(1997),FirmandMorganSimilarpremiumtoCohenproductetal.as(1996),asubstantialBayusassumptionB’sproductqBatetanyal.(2001),periodtheisqualitylevelforgenerationetinthatanyeachperiod rmaparameter.3TheismarketsasingleproductMorganal.(1996),etBayus(1997),Bayusinkeepingetal.with(1997),Cohenanducts,Our rms’andfocusal.henceis(2001).

onwethetimingandqualityofnewprod-timeanddimensionalFirminproductsmarketareconsidergivenfunctionsthattheofpricestheproducts’forbothB’spriceandquality.policyPFirmA’spricepolicyPqijB

qij

binationcompetitiveofqarrayscompetitiveprice,qB,thatassigndesignateapriceforgiveneachmulti-com-policyi,andisj.Thus,eventhoughtheframework(e.g.,isenvironment.moregeneralThisexogenous,thanaspectofitre ectsourmodeltheandMorganCohenetetal.1996,Bayus1997,theBayusrelatedetliteratureal.1997,policy.Wemakeal.2001treatpricesasconstant).

productFirst,onlytwoassumptionsregardingapriceproductpriceweisatassumeleastthataslargeFirmasA’sitspremium-standard-thatreasonablePprice,isgivenqB,i,andj.Second,weassumeqijresearchassumptiondecreasingini,givenq,qB,andj.This(e.g.,tionsKrishnanonoptimaliswellgroundedinanalyticaletpricingpoliciesfornewproductsobservations(e.g.,Bayusal.1999)andnew-productgenera-andof1992),aswellasthroughempiricalBayusthe1992).

pricesofnew-productsuccessiveproductprices(e.g.,generationsBayus1993)(e.g.,3

itlyForningmodelreasonsproductofmodelqualitytractabilityasacumulativeandparsimony,wedonotexplic-dohorizon.Wenotethatourconclusions,functiontobediscussedovertheinplan-§3,improvingnotchangeingoveriftimethe(i.e.,overallqqualityofallproductsisconstantlythetimetrend).Wefocusourisananalysisexogenousonthefunctionofanincreas-petitorrelativeremainqualityconstant.

levelsbetweenstandard,premium,situationandinthewhichcom-

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Souza,Bayus,andWagner:New-ProductStrategyandIndustryClockspeed

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prices,Consideringhaveweconsidertheprecedingassumptionsaboutuesingofaprobabilitydistributionmarketdemandthatinre ectsanyperiodtheval-topotentialvaluesq,qB,i,andj,and,implicitly,thecorrespond-thatdemandforprices.forWeeachpostulate rmisthatthetheproductexpectedofmarket rm’seraturedemandmarketforsharetheperiod.multipliedInlinebythewithexpected1997)etandinoperationsmarketing(e.g.,(e.g.,CohenBayus1997,Bayustheetlit-al.shareal.1999,Morganetal.2001),weetassumeal.1996,thatKrishnanmarket(i.e.,and qijisishigherpositivelyforrelatedq=toownproductqualityqijtoj andcompetitorprice,qpthanforq=qs,giveniically,own(1997), priceg andq competitorandnegativelyrelatedqij=qB Pqij PqijB

product ,where,quality.asinSpecif-BayustoinFirm Bis(ifFirm =A’s1,thenmarketingcompetitorseffectivenessrelativeisfromstrictlytermsofandjour.Firmassumptionincreasingmarketingineffectiveness).Wearenotesymmetricthat qijB’smarketthati,sharePgivenqandj;thisfollowsqijdecreasesis1 withigivenqqijsimultaneouslyAtthestartofintroduceandeachwithoutperiod,Firms.

collusion,AandwhetherBdecide,soldopmentintheafollowingnewproductperiod.thatThus,wouldbeproducedandtomadeassumetotimekeepis xedatoneperiod;thethisproductassumptiondevel-isproductthattheourmaximumanalysistimefocusedinmarketandtractable.isnforWerateandtheproductdoesnotphysicallyanyforFirmoverAtime.

deterio-alsodecidesonFirmitsiblebetoB’scurrentFirmproductionproduct.WethedolevelnotofmakeproductionexplicitA.Productiondecision,occursasitquicklywouldnotenoughbevis-toassumeavailabletionthatforbothdemandproductinintroductionthecurrentandperiod.produc-Weanduncertainbeforedecisionsdemandinaoccursperiodinarethatmadeperiod.simultaneouslyBecauseofitlydoesincludemarketFirmA’sdemand,inventoryitisinnecessarythemodel.toexplic-FirmnotisBbehaveshaveknowledgeaccordingoftoFirmB’sinventoryFirmlevel.AassumptionknowableintoFirmA;weaelaboratecontingentmorestrategyonthatthisforTosummarize,§2.2.

thesequenceofdecisionsandis1.FirmAinaperiodis:

eventsjobservedTimein(amarketnewforproductFirmhasB’stimecurrentinproductreviewed=1).FirmandA’sholdinginventorycostsforthecurrentproductmarketisnext2.Firmthecurrentperiod,Aperiod.

itsdecidesquality,whetherareandhowtoincurred.

introducemuchtoproduceaproductinavailable.

3.Theproductionofthecurrentproductbecomes539

is4.demand lled,FirminventoryAobservesisitsreduced,potentialanddemand.anyDemandun llednext5.IfFirmislost.

Adecidestointroduceaproductinatperiod,thenitsellsitsthetoInasalvageend-of-periodinventorythevalue.

bypopulatenextsections,weprovidefunctionalformsproblemtheabovethemodelmathematicalrelationshipsimplied(§2.1),costFirmrequiresB’sstrategyspeci cationdescription.FirmA’sdecision(§2.2),ofmarketparametersrizedparametersinTable1.

(§2.3).Themodelandnotationitsownissumma-internal2.1.TotalDemand

amarketdemandinaperiodXqijismodeledasPrstochasticcomparison Xvariablewithprobabilitymassfunctiont=w =aqij w ,inministic.§3.3theEacheffectswiththew=0 1 Forpurposesofunitofpriorofallowingliterature,marketdemanddemandwealsorepresentstobeconsiderdeter-an

Table1Notation

Symbol

Description

StateqvariablesQualityofFirmA’sproduct:q=qs(standard)orq=qp

ijTime(premium)

xTimeinFirmA’sinmarketmarketforFirmA’sproductinperiodsinventoryforlevelFirmB’sproductinperiodsParametersnMMaximumtimeinmarketforaproduct MaximumqBFirmA’smarketinginventoryeffectivenessquantityKsQualityK

p

FirmA’sof(relativetoFirmB) xedFirmB’sproduct FirmDiscountA’s xedproductfactorproductintroductionperperiodintroductioncostcostforforaastandardpremiumproductproductArrays,Pfunctions,andrandomvariablesPqijB

PricePriceofofFirmFirmA’sB’sproductproductgivengivenqq,,ii,,andandjjhqij

qInventoryholdingcostperunitperperiodforsvq

Inventorygivenq

aproduct

salvagevalueperunitofaproductgivenqpqB

Variablecostperunitofqij

ProbabilitythatFirmBintroducesaproductagivenproductqnextperiod,givenpB

Arrayq,i,ofandpBj

qijXqijFirmqij

MarketA’sexpectedpotentialmarketsharegivenq,i,andj

probabilitydemandmassineachfunctionperiod,(p.m.f.)arandomPrvariablewith w=0 1 givenq,i,andj

Xqij=w =aqij w ,DqijMeanmarketdemandqij

FirmandA’sj

demandineachperperiod,period,aE Xrandomqij ,givenvariable,q,i,givenandj

q,i,Decisiondecisions)variable(inadditiontotheproductintroductionandqualityyFirmdecisionA’sinventoryisy xon),handwhereaftery≥productionx

(production

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opportunityproduct.

forFirmAorFirmBtosellaunitofFirmAsimpleassumesA’sdemandapproachDthatsplitsmarketdemandsetsqij= qijXqij.siderwhichXinteger-valued=3and =0demand.Our 5.ThenDFormodel,example,however,con-qijqijqij= qijXqij=1 5,integerWeuseisnotdemandvaluesanintegral.

alternativeforDformulationthatgeneratesqij.IfmialforFirmA’sproductmarketismodeleddemandisaswa,bino-thenThissimilarallocationrandomvariableofmarketwithdemandparameterstoFirmswAand qij.Lippmantothe2000).andincrementalMcCardlerandom-splittingandBis1997,SmithandruleAgrawal(e.g.,FirmA’sThedemandprobabilityis:massfunction(p.m.f.)forPr Dqij=d =

Pr Dqij=d Xqij=w Pr Xqij=w

w=0

= w d

qij 1 qij w daqij(1)

w=d

d w

Hereured qijis erbyFirmtheA,expectedsinceE Dpotentialmarketsharecapt-qij = qijmarketpotentialisappropriatebecause E Xqij .Thequali-qijistheexpected

inventoryshareonlyifFirmAalwayshassuf cientFirmtomeetdemand.WeassumethatwhendemandAthisishaslostinsuf cientanddoesnotinventory,gotoFirmitsnonsatis edB.RelaxingresultsassumptionmodelpresentedhasherenobecauseeffectonwethedomodelandthethenDFirmB’sinventory.WhenXnotexplicitlyqij～Poisson qij ,qij～Poisson qij qij (Kulkarni1995).

2.2.WeedgeassumeCompetitivethateachBehavior

seemsaboutConsequently,reasonableitsrival’s rmdoesnothaveknowl-inpracticeinventorylevel.Thisassumptionbehavioructsmodel i j basedFirmandFirmonA’stheAisonlyandableprovidestoassesstractability.FirmB’sexistingagesofproductthecompetingqualityprod-q.We

FirmgivenBFirmFirmqintroducesB’sstrategy,i,andj.Weaproductasallow0ofthequalityprobabilitypB

qijthatB

qBnextperiod,

inventoryAhasincompleteinformation≤pqij≤1abouttore ectFirmthatB’stolevel,whichmayimpactFirmB’sdecisionFirmTointroduceillustrate,aproduct.

supposethatforzeroBdecidestointroduce q i j = 1 1 2 ,tory.inventory,butnotwhenitahasproduct100unitswhenofinven-ithasisrepresentsrandom.ViewedbyFirmA,FirmB’sstrategyat 1 1 2 noteFirmThearrayB’splanpBofisactionacontingentforeverystrategy;ittheythatsomevaluesof q i j arevirtual q ini thatj ;decisionsmaynevertobein uencedberealized.byThus,FirmweA’spermitdecisions.

FirmB’sManagementScience50(4),pp.537–549,©2004INFORMS

assumeIncontrast,Cohenetal.(1996)anduct(2001)inthethatwindowthecompetitoroftimedoesstudied.notintroduceBayusMorgana(1997)

prod-etal.aassumethatthecompetitoractsaccordingtopendentperiodicegyofproductFirmA’ingstrategyacontingentthatisinde-strat-WepartassumepBforFirmthatBFirmpermitsamoregeneralscenario.incorporatesonobservedAhypothesizespBbasedinperspective.4

competitionhistoricalbehavior.fromadecision-theoreticThus,ourmodel2.3.Wediscounted-pro tformulatePro tMaximization

FirmA’soptimizationproblemasovervaluesanin nitehorizon.MarkovAdecisionstateisprocesscomprised(MDP)aof ciently0 1 for n 2 q × i 0 j 1x .ThestatespaceisS=2×resultslargesuchthat Firm M ,A’swhereoptimalMisstrategyavalueneversuf -theForininitialinventorythatexceedsM.

wherevalueeachwhethery≥ofstate,x(FirminventoryFirmAAproducesonhashandthreedecisions.Oneisy afterx).productionThey,qualityleveltointroduceqsanewproduct.Thethirdsecondistheisucts,respectively,orqpwhenforstandardaproductandisintroduced.

premiumprod-ETheexpectedperiodsalesquantityisS q i j y =is

Dqij min y Dqij .Thecurrentperiodexpectedpro tr q i j x y

PqijS q i j y vq y x hqx noproductintroduction; = PqijS q i j y vq y x hqx+s y S q i q

j y Ks

(2)

standard-productintroduction; PqijS q i j y vq y x hqx +sq y S q i j y Kp premium-productintroduction.

Thetermsqissalvagerevenueperunit;Ksthepremium xedproductandKpareuctunit;developmentproducts,introductionandrespectively,costsforstandardandlaunch;vwhichincludeprod-beginningandhqisproductioncostperofqistheholdingperiodcostbeforeperproduction.

unit,appliedatthe4

becauseWedonotconsideragame-theoreticmodelofnecessarynumerousandBayus(e.g.,pareadditional1997).SeetheSouzamodelssimplifying(2000,andassumptionsassumptionscompetitionwouldbe2004)forfurtherinBayusdetails.

1997

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pro tLetfTheextremalat q statei j x denotethetotalexpecteddiscountedequation q i j x is

overanunboundedhorizon.f q i j x

r · + E pBf+

Dqijqij q i+1 1 y Dqij + 1 pBqij f q i+1 j+1 y Dqij + =xmax r · + pBqijf qs 1 1 0

≤y≤M + 1 pBqij f qs 1 j+1 0

r · + pBp qijf q 1 1 0 + 1 pB qij f qp

1 j+1 0

forq=qs qp i=1 2 n 1 j=1 2 n

x=0 1 M

(3)

Ini(3),pB

qij=1forj=n.Theextremalequation rst=nofrowissimilarinsidetheto(3)bracesexceptin(3).fortheabsenceoftheforassumeDNotethatthep.m.f.qijgivenandthat by(1)requiresknowledgeB

of qij.We

componentsj.Weconsiderqijdependsspeci confunctionalqBandPqijforallq,i,(1997),inandMorganof(3)similaretal.(2001),toCohenandetweal.forms(1996),forthesespecifyBayusresultWedetailshouldin§3.2.

theseexampleinasimplepointdecisionoutthatthestructure,solutionastothe(3)followingdoesnotXExampleillustrates.

1.Considern=8,astationarymarketaqijproduct～Poisson(5)forandqBis0.6,periodicallyallandqprelativeeveryq,i,andtoq vej;Bis1;periods;FirmBintroducesPqstorelativeqij=i 0 1for0is 09,j;hPqijB

=j 0 1013forforallallqqand;Kpi=; 1= 00and 96,vallq

Kqs==00 35,81;sq =q=0 qijpetitorproportionalproductproductto(seepricerelativequalityproductqualityrelativetothecom-toandtheinverselycompetitorproportionalproducttopolicy(5)premiumdependsbelow).Theoptimumproductintroductionprice tion1 7 5 4 producton.Further,atinventory:inventory q i j x =Firmon 1hand 7 A5 introducesafter2 butproduc-notata 1 7 does5 · ,noty=5followforx=a4,base-stockbuty=3<policy:5forxFor=2.

states2.4.Inoptimalgeneral,TheOptimalProductionDecision

decisionproduction(3)mustbepolicy.solvedtodetermineFirmA’sisistrivial,however,ThewhenoptimalFirmA’sproductiondemandperiod.deterministic—producealwaysThisalsooccursaccordingtodemandinaronment.betheInmet—forthisspecialexample,whencase,inFirmA’sdemandcanxacanmake-to-orderbeenvi-ablestatebecausespaceFirmandA’syonlyisnodecisionslongeraremovedfromaredecisiontheproduct

vari-541

introductionindecisions.WefurtherstudythissituationductionIn§3.3.

addition,productpolicyifindependentFirmAusesofax xed,productintro-§3.6,introductionpolicythatwesuchstudyasafurtherperiodicinfollowsthenTheproofabase-stocktheconstrainedisavailableformintheasoptimalappendix.

describedproductioninTheorempolicy1.FirmTheoremtory,Ais xed1.andIfindependenttheproductofintroductionFirmA’spolicyforductionthenforeachy*theconstrainedoptimalinventorystartinglevelafterinven-pro-(q,ini,j).(3)Thatisabase-stockis,forstatepolicy(q,i,withj,x),parametery*satis es:

Rqij

y q i j x =Rqijifx≤Rqij

x ifx≥R(4)

qij

3.InAnalysisandstrategiesthissection,encebydeterminingweexploreResults

theoptimalconditionsnew-productqualityFirmnumberofitsA’sdecisionsaboutthefrequencythatin u-andTableinsights1,analyticofmodelnew-productparameters,introductions.assummarizedGiventheinapproachabouttheresultsimportantcannotbefactors,derived.weTodevelopofmodel.

conductingofBayusalarge-scale(1997)andnumericalMorgananalysisetfollowal.of(2001)theourweIn§3.1,wedescribeoursolutionapproach.buildingdescribeFirmatestafull-factorialIn§3.2,populationexperimentaldesignforofA;theseparametervaluesofoptimalcoverasolutionswidevarietyforbetweenconditions.ministicthestochasticWecomparedemandthedifferencemodelinresultsargumentdemandmodelin§3.3.Wemakeandaastrongdeter-tic,andespeciallyforinconsideringfast-clockspeeddemandindustries.tobestochas-In§§3.41995)3.5,thetowedetermineuseglobalthesensitivityfactorsanalysis(WagnermanceoptimalforFirmofsolution.In§3.6,wethatstudymostthein uenceperfor-A.

atime-pacingproductintroductionstrategy3.1.WePutermansolveSolutionApproach

program1994theMDPfordetails).(3)asWealinearprogram(seetionsusingaCprogram,andgeneratesolveitusingthelinearfunc-ageneratesgivenofthesetCplex7.0callablelibrary(Cplex1998).For1994).aofdiscrete-timeparameters,theMarkovoptimalchainsolution(Putermanof(3)variablesTheableiandstatejspaceis nitebecausethestatebilityxdistributionisboundedarebyboundedbyn,andthestatevari-canMbe.Thecomputedchain’sreadilystationary(Kulkarni

proba-

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1995).inWeuseGaussianeliminationasimplementedciatedForMATLABagiven(MATLABstationary1996).

techniqueswithperiodtoasolution,computeweprobabilitydistributionasso-equivalentusestandardMarkovchain1994),productand(Pro t)thestationaryoveranunboundedaveragepro tperprobabilitieshorizonof(Putermaninstateabestintroductionsproduct-introductionbyFirmA.decisionSolvingtime(3)betweenforresultseachtimeFirmbetween q i j x consecutiveoveranunboundedproductintroductionshorizon.ThebyoptimalA,however,isprobabilisticbecauseFirmA’sinventoryproductdemandxintroductiondecisiondependsonthe(see,whichSouzavaries2000asforadetails).resultofWestochasticdenoteETBPexpectedtimebetweenproductintroductionsasproduct.Similarly,introductionswedenotebyFirmtheAfractionasQP.

ofpremium-3.2.DuedemandtoStudycomputationalDesign

constraints,wechooseortheproductdistributionquality.ThisthatassumptiondoesnotdependamarketisonpricesBayusrelatedmodeletal.literature1997,Morgan(Cohenetetal.al.2001).1996,inkeepingToBayuskeep1997,withthetime inreasonablysized,wesetthemaximumproducttional=E X markettorysimplicity).=5(weatn=8andmeanmarketdemandatWedropsetthethesubscriptsmaximumonlevelXforofinven-nota-thatassuringstationaryatM=2 inventorybecauseourlevelsnumericalneverresultsindicateproblemthatthatisthethesamesolutionasthetotheboundedreachthisinventoryvalue,PWithimposesregardnotouppersolutiontotheproblemFirmA’sboundpricingoninventory.

policy,weusePqij=forqi withi ≤ijj,.whereHereP ij= fori>j,0< ≤1,and ij=1qistheinitialpriceofadeclinequalitycompetitivebythatq, isapricetrendparameternewproduct(pricesnewerpricefractiondiscountineachappliedperiod),whenandFirm1 isatotherebyFirmproductB’sthanFirmA.Thus,FirmAmayBhasreactasuresTheparameterincreasingproductintroductionbyreducingitsprice, itsresemblesmarketshare.

severalproposedspeed),ofandasindustryarguedclockspeedin§1.In(higher ～fasterclock-mea-developmentPillai(1999,correspondingofthep.underlying2)relateparticular,clockspeedMendelsontechnology,to“rapidfollowdoesMendelsonfallinandthePillaicost/performancebyassumingthatratio.”andtheWeqandnotj.FordependFirmonB,iprices,butpricesaresetdeclineaccordingwithtoiquality,given

PB

PBB

qij=

eterj Bforneedalli,whereFirmB’spricetrendparam-weSimilartonotCohenbeequaletal.to(1996) .

andBayus(1997),tionusethemarket.amarketTheshareapproachattractionissimplemodelandtointuitive,

appor-ManagementScience50(4),pp.537–549,©2004INFORMS

and,etqualityal.importantly,1992).hasempiricalsupport(e.g.,LilienThus,relativeFirst,todenoteFirm k,k=s p B,asproductk’sis p≡1;if B=1,thenA’spremium-qualityFirmB’sproductproduct.qualitymodelidenticalitstoitsrelativeFirmtoFirmA’spremium-qualityproduct.WerelativeproductA’smarketshareasbeingproportionaltoprice:

qualityandinverselyproportional

1

qij=1+1 BPqij

··forq=qs

(5)

qij

similarlystantToandvaluessimplifyforq=qp.

forourinventoryanalyses,weconsideronlycon-etervariableonlyvaluesdiffercostperbyproductunit.holdingOfcourse,cost,ifsalvagetheseparam-value,innaturethisthepaperspeci cwillnumericalchange,resultsquality,weexpectthatbutthatarereportedquality rmdecisionofourconclusions,willcontinuesuchnottobethatthequalitativedriventhebyproduct-internaluct’sIfwefactors.

Denotetimeassumeinmarketthateachdoesperiodisaquarter,aprod-1the/ 1+ /the4 .Weyearlysethinterestratenotbyexceed ,sotwothatyears. =q= vq/4forallq.(analysesfollowingfactor,notreportedparametersherefortheanalysis:Wealso(i) choose=0 15the(iii) rm’satreasonableproductPoptimalpolicy),levels,indicate(ii)hasthatthediscountvnegligible=0 35forimpactallq,andonqq=1forallq—althoughthedardhigherproducthasahigher(seebelow),introductionFirmA’scostpremium-qualitymarketthanthesharestan-productwithapremiumproductbecauseofidenticalisthecomplexityprices—thisoffocusestheanalysisandreducesPoisson.WeconsidersiderWithrespectdemandthenumericaltotoFirmbeA’sdeterministicstudy.

parameters,aswellasproduct:twoas slevels=0 6andofrelativequalityforthestandardwecon-marketafractiontwoshare):ofKnetp/ Prevenues0.8;twolevelsvforifor=1Kpgiven(expresseda50%q q /2 =0 5andTherelevelsforKsrelativetoKp Ks/Kp=0 1.0;and faster-clockspeed=0 1areandtwo0.3,levelsforthepricetrendparameter,3and0.7.pricingthestrategybyindustrywheretheFirmA.andlargervaluere ectsaWepossiblyanaggressiveWepricediscount1 =0 15,andassumenopricetwolevelsdiscount.forandconsiderproduces0.75forconsideronlyalltwotoq.levelsWeofsalvagevaluesq/vq=0 25disposenoteofthatthesq/vq<1,elsethe rmodicallyWeassumethreethatlevelsFirmfor B=introduces0 7 1product. 0,and1.3.

Finally,weB

pB

everyTperiods(thatis,pqij

=a0productifj=T,peri-andweqiTanalyze=1foralltheqcaseandwherei),whereFirmTB’s=1,actions5,anddepend7(in§3.6on

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thoserelativeofFirmofqualityA). WeB=study0.7,1.0,threeandlevelsforProductB’sFinally,FirmpriceweB’ssetprice-trendPB=1,soparameter,1.3,thatFirm Band=0 two1andlevels0.3.rizedTheisgenerateindesignequaltoB’snew-productTable2.ofFirmA’snew-productprice.

Theseournumericalselectionsforanalysesparameterissumma-valueshalfatotalof33×28=6 912halfoftalassumethesecellsPoissonassumeexperimentalcells;demand.deterministicdemandandhascellUltra1,248withstochasticdemand,Fortheeachlinearexperimen-program25station,variablesatypicalandsolution21,648constraints.timeforForaSuncomputingsecondsforthelinearprogram,and50eachsecondscellforisrelatedperformancethestationarymeasures.

probabilitydistributionand3.3.InDeterministicvs.StochasticDemand

productthisPoissonstrategiessection,webetweenconsiderthedeterministicdifferencesinnew-preferencedemandissuesforthecases.Thepurposeistojustifyandourtheperformrelativetoclockspeedstochasticassumptionandproductinquality.addressingWebetweenacasesthepairwisecaseswithcomparisondeterministicforthedemandvalueofETBPPro t.withwisetwocomparison.Tablestochastic3summarizesdemand,similarlyforQPandandtheThedifferencethestatisticsinETBPfortheforpair-theincreasedemanddifferencerepresentsmodels0.76issigni cant.periods;inOverallthe32%eachexceeds50%.Wealso nd25%thatofETBPcellstheforthancase.ETBPdeterministicAsindicatedforthecorrespondingdemandcaseinTable3,thestochasticisalwaysdifferencedemandsmallerinQP

Table2NumericalStudyDesign

Parameter

SymbolValuesMarketdemanddistributionDistributionofX

Deterministic,FirmPoissonFirmA’sA’sprice-trendrelative

parameter s

0.1,0.6,0.30.8Firmstandard-productpremium-productA’snormalizedqualitycostofaKp/ Pq vq /2

0.5,1.0Firmintroduction

standard-A’srelativevs.costofaKs/Kp0.3,0.7Firmqualitysq/vq0.25,0.75FirmfractionA’ssalvageproductpremium-introductionA’srelativeofvariablevalueasamarketingcost 0.7,1.0,1.3Firmeffectiveness

1 0,0.15FirmFirmA’sBpricehasdiscountwhenFirmB’sB’srelativeanewerproducttimebetweenproductproductquality BT0.7,1,1.0,5,71.3Firmintroductions

B’sprice-trendparameter

B

0.1,0.3

543

Table3

ComparingDemandModels

ModelResultsforthePoissonandDeterministicbetweenExpectedintroductionsproducttimepremium-productFractionofStatistic

FirmA(ETBP)

byintroductionsFirmA(QP)

byPro tMeanPoissonvalue

Deterministicdemand54 568000 73690modeldemandmodel1 8801MeanPoisson%differencerelativeto324 13Std.deterministicdifference

deviationof%58

21

5

betweenitstandardiszerotheinalmosttwodemand95%ofmodelscases.Theaveragesrelativelyonlylarge4%;cellsmalthetwodeviation,demandhowever,modelssuggeststhatinsomedetailsproduct-qualitydecisions.indicateWedonotoppositereportopti-thedeviationhere,andconditionsstochasticinbutETBPitisimportanttonotethatthelargestdemandandQPcasesbetweenoccurstheunderdeterministicrapidingly,obsolescenceoffastclockspeed(lowvalue(highofsvalueofindustry )andq/vq .Notsurpris-deterministicTable3showsdemandthatpro tsareusuallylargerfornew-productOverall,thesestochasticintroductionresultscases.

implystrategythataismoreconservativedemandinformulation.demandasThiscomparedtoapreferreddeterministicwithvalue.inventoryholdingcost,resultlostre ectssales,anduncertaintysalvagegiesdemandinEvenavariationassumptions,majoritythoughofthewecellsoptimalnew-productstrate-believearesimilarthatthereforisthetwoformulationtoapproachmendingisalsoinwarranttheconsistentremainderusingthestochasticdemandenoughwithoftheourliteratureanalyses.recom-Thisdecisionsthatimpactbemodeleda rm’sjointlynew-productbecauseandproductionBillingtonintroductionetal.1998).

timingandqualitydecisionsinventory(e.g.,can3.4.TheisationtoobjectiveSensitivityanswertheoftheAnalysisquestion:sensitivityofModelHowanalysisParameters

muchobservedinthissectionvari-Pro t)inofinthemodeliseachindependentlyperformancemeasure(ETBP,QP,andparameters?causedWeconsiderbyvariationineachstudywhichvalues,designdemandisPoisson.Giventheonlyfull-factorialanalysesincludeeffectivewherewayseachofvariableansweringhastwoorthreeR2(Wagner1995):(i)computingtthisstatisticsquestion(oreach)forpairsingle-variableofindependent-dependentsimplelinearregressionsvariables,and

for

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SensitivityAnalyses(AbsoluteValueoftStatisticsforSingle-VariableLinearRegressions)

ExpectedtimebetweenproductintroductionsbyFirmA(ETBP)

Fractionofpremium-productintroductionsbyFirmA(QP)t18 10 416 634 323 81 82 33 12 55 3

LargerLHLHLLLLHH

t33 98 44 94 03 64 836 77 836 93 7

Pro tLargerLLLLHHHLLL

NrParameterSymbol B

Kp/ Pq vq /2

Ks/Kp

ssq/vq 1 BT

t56 72 512 513 08 07 611 011 810 37 1

LongerLHHHLLLLHH

Industryclockspeed

1FirmA’sprice-trendparameter2FirmB’sprice-trendparameter

Internal rmfactors

3FirmA’snormalizedcostofapremium-productintroduction4FirmA’srelativecostofastandard-vs.premium-quality

productintroduction

5FirmA’srelativestandard-productquality

6FirmA’ssalvagevalueasafractionofvariablecostCompetitivefactors

7FirmA’srelativemarketingeffectiveness

8FirmA’spricediscountwhenFirmBhasanewerproduct9FirmB’srelativeproductquality

10FirmB’stimebetweenproductintroductions

(ii)computingtstatisticsinstandardizedmultipleregressionsforeachdependentvariableasafunc-tionofallindependentvariables.Weperformedbothanalyses;ourconclusionsarethesameusingeitherapproach—forbrevitywepresentonlytheresultsof(i)inTable4.Thetableentriesareinterpretedasfollows.ForRow1,thesimplelinearregressionETBPon hasanabsolutevalueoftequalto56.7,andalow(L)valueof impliesalongerETBP.Similarly,forRow7,theregressionPro ton hasanabsolutevalueoftof36.7,andahigh(H)valueof impliesalargerPro t.

Notethatallbuttwoofthetvaluesaresigni -cant(seeRows2and6).BasedontheabsolutevaluesofthemagnitudesinTable4,we ndthatindustryclockspeed,asre ectedby ,hasthegreatestin u-enceonETBP,followedbyotherinternal rmfactorsandcompetitivefactors.FromRow1,alowvalueof (lowerclockspeed)isassociatedwithlongerETBP.Thus,itisoptimalfor rmstofrequentlyintro-ducenewproductsinenvironmentswherepricesaresharplydeclining(i.e.,fast-clockspeedindustries).AssuggestedbyRow2 B ,deviationsofFirmBfromtheindustryclockspeed havelittleeffectonFirmA’sdecisions.

Theobservedin uenceofinternal rmfactorsonETBPisasexpected.Inparticular,less-frequentnew-productintroduction(longerETBP)isoptimalwhenintroductioncostsforpremium(Row3)andstandard(Row4)productsarehighandwhentheunitsalvagevalueforolderproductsislow(Row6).Inaddition,itisoptimaltoshortenthetimebetweennew-productintroductionswhenthequalitygapbetweenstandardandpremiumproductsishigh(low s,Row5).Finally,thein uenceofcompetitivefactorsonETBPisrelativelysmall—theeffectsaresimilartothe rm’sinternalcostfactors.Less-frequentproductintroduc-tionisoptimalifthe rmhasaninherentmarket-ingdisadvantage(Row7),ifthe rmoffersalowerpricediscountafterthecompetitorintroducesanewproduct(Row8),ifthecompetitorhasrelativelyhighproductquality(Row9),orifthecompetitorintro-ducesproductslessfrequently(Row10).

Table4alsoindicatesthatinternal rmfactorshavethegreatestimpactontheproduct-qualitydecisionQP.Itmakessensetointroducepremiumproducts(largerQP)whentheintroductioncostforapremiumproductislow(Row3),whenthe rm’sintroductioncostsforstandardandpremiumprod-uctsaresimilar(highKs/Kp,Row4),andwhenthequalitygapbetweenstandardandpremiumproductsishigh(low s,Row5).Also,itisoptimalfor rmsinslow-clockspeedindustriestoemphasizepremiumproducts(Row1),thatis,emphasizeproductswithsigni cantqualityimprovements.

Intermsofpro ts,Table4revealstheimportanceofindustryclockspeedandcompetitivefactors.FirmA’spro tsarelargerwhenitsclockspeedislow(Row1),whenFirmAhasaninherentmarketingadvantage(Row7),andwhenFirmBhasarelativelylow-qualityproduct(Row9).

Insummary,thesenumericalresultssupportman-agerialbeliefsabouttherelationshipbetweenindus-tryclockspeedandtimetomarket(e.g.,MendelsonandPillai1999).Ouranalysesdemonstratethatunderfast-clockspeedconditions(i.e.,sharplydecliningindustryprices),itisindeedoptimalfora rmtofrequentlyintroducenewproducts.Moreover,itisoptimaltointroduceincrementallyimproved(i.e.,standard)productsinthissituation.Concomitantly,we ndthatpro tsinfast-clockspeedindustriesarelowerthanthoseinslow-clockspeedindustries.

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3.5.InwiththeOptimalpreviousNew-Productsection,Strategies

mostPoissonWein uentialdemandtowedetermineexaminedthethefactors3,456thatcasesaredividingnowexaminewiththerespectrobustnesstoETBPof,theQP,andPro t.whetherthesepremium,the5optimalcasesintoqualityfourdecisionstrategiesinsightsbyisaccordingtoorWelongerthanandthewhethermediantheoptimalETBPstandardisshorterorfourexamineETBP,whichis5.2periods.impactcompetitivetheenvironmentscharacteristicsofthecorrespondingtimingTwodominantoffactorsstrategiesthataffectpro tandandassessmarkettherelativeshare.productofetintroductionproductintroductionwithrespecttoqualityandliterature.areprevalentintheaallyproductal.(1996)withandsubstantiallyBayus(1997)suggestForexample,thatintroducingCohentime.optimal,tionsIncontrast,despiteMorganthelongerimprovedqualityisusu-etproductdevelopmentimprovedwhentionalproductsthefrequental.(2001) ndcondi-isoptimal.introductionHereofincrementallyintroductioninsightsregardingthejointqualityweprovideandproductaddi-choiceTodeterminetimingdecisions.

employofoneofthethefourkeynew-productfactorsrelatedstrategies,toa rm’swelevel)enceforaeachbinomialmodeltest(atap<0 001signi cancetheirbetweenTablehighlow5.7Alevels.observedparameterbasedonthediffer-6andexpectedproportionsatsmalltThestatisticstatisticalinTableresults5indicatesareshowninoften,andofwhereashighparameteralargetvaluesstatisticoccurnearlythatequallytheoccurstheparametermorevalues(LforlowindicatesandHforthathigh)onestrategyBasedoninfrequentintheoften.

Tablenumber5,ourofresultsnumericalcasesforeachoccurswithmostintroductionoften.This ndingofpremium-qualityindicateisgenerallyconsistentproductsthatthemixourofCohenstrategies,etal.(1996)however,andBayusmaychange(1997).Therelativeunitassumptioneterscostareconstant(handinvtheexperimentalanalysisifwethatrelaxtheqwithq)andrespectsalvagetorevenuesqparam-theInfouraddition,strategiesthemagnitudeinTable5ofquality.

showsthetvaluesthatindustry

across5

productsFirmAfollowsverytoassignfewandcases.sometimesamixedstrategythemintoWeroundintroducing(sometimesintroducingpremiumoneofQPthetotwothealternatives.

neareststandardintegerproducts)fortheseinonlycasesa6parameterBecauseweportionhashavetwoaorfull-factorialthreevaluesstudy(seeTabledesign2),wheretheexpectedeachmodeleachlevels,new-productofcaseswhereaparameterisobservedatitshighlevelpro-inexperimentalwehavecasesconductedstrategyiswhereaa0.5parametersimilaror0.33.analysisForparameterswiththreeisobservedfortheatproportionitslowlevel.of7fromAlthoughamultivariatenotreporteddiscriminanthere,weanalysis.

alsoreachthesameconclusions545

clockspeedintroduction(Rowfactorstiming1)decision,isprimarilywhereasrelatedinternalto rmthe(Rowsdecision.3,like4,5)developmentareassociatedandwiththeintroductionproduct-qualitycostsarehigher-qualityassociatedInparticular,mentproductswithfast-clockspeedfrequentproductintroductionsarerelatedtosituations,andtheconclusionsandintroductionofMorgancosts.etThisal.resultlowerdiffersdevelop-fromtheAlthoughternumericalnotcasesreportedwherehere,thewe(2001).

price-trendcloselyexaminedparame- Firm=for BFirmAisnotequaltothatofFirmB(i.e.,higherA’s).Irrespectivecompetitiveofstrategy,FirmB’sFirmpricingApolicyanddroppingpro tsFirmitspricesfromaggressivefasterthanpricingneverFirm(i.e.,FirmobtainsAqualityA’svaluestrategyproduct-introductionremainunchangedtimingB).regardlessandMoreover,product-oftheFirmperformingA’sof Bprice.Wediscountalsoclosely1 examinedonPro ttheandimpactETBPbyofETBPapairwisecomparison.BothPro tandnopricepricearediscount.

discountalmostalwaysascomparedgreaterwhentowhenFirmitAoffersoffersa3.6.Induction,thisAsection,Time-PacingweconsiderProduct-IntroductionaperiodicPolicy1998).presentThisortime-pacingpolicyneedpolicynot(Eisenhardtproductbeoptimal,andBrownintro-simple.uctDenotetheattractivethenumberpropertyofperiodsofbeingbutdoesbetweenstructurallypolicy,introductionsductionETBP=FforFirmAasF.Foratime-pacingprod-remdecisionishasanaintegerbase-stocknumberformand(seetheTheo-pro-and1).slightly:

product-introductionGivenF,onecancomputedecisionsthebyoptimalmodifyingquality(3)f q i j x

r · + E pBf q i+1 1 y D + = Dqijqij

qij xmax≤y≤M

+ 1 pB

qij f q i+1 j+1 y Dqij + forq=qs qp i=1 2 F 1 j=1 2 n

x=0 1 M

(6)

f q F j x

B r · + pqijf qs 1 1 0

+ 1 pBqij f qs 1 j+1 xmax0

=≤y≤M r · + pBqijf qp 1 1 0

+ 1 pB f q 1 j+1 0

qijp

forq=qs qp j=1 2 n x=0 1 M

(7)

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Table5

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ManagementScience50(4),pp.537–549,©2004INFORMS

KeyFactorsRelatedtoOptimalNew-ProductStrategies(AbsoluteValueoftStatisticsforBinomialProportionsTests)

Strategy1:Infrequentintroductionofpremium-qualityproducts

Strategy2:Frequentintroductionofpremium-qualityproductst18 41 121 013 49 43 0

LevelHLLHLH

Strategy3:Frequentintroductionofstandard-qualityproductst32 30 89 638 117 72 7

LevelHLHLHH

Strategy4:Infrequentintroductionofstandard-qualityproductst16 30 999 927 440 22 3

LevelLHHLHL

NrParameterSymbol B

Kp/ Pq vq /2

Ks/Kp ssq/vq

t30 01 13 010 37 73 5

LevelLHHHLL

Industryclockspeed

1FirmA’sprice-trendparameter2FirmB’sprice-trendparameter

Internal rmfactors

3FirmA’snormalizedcostofa

premium-productintroduction

4FirmA’srelativecostofastandard-vs.

premium-qualityproductintroduction5FirmA’srelativestandard-productquality6FirmA’ssalvagevalueasafractionof

variablecostCompetitivefactors

7FirmA’srelativemarketingeffectiveness8FirmA’spricediscountwhenFirmB

hasanewerproduct

9FirmB’srelativeproductquality

10FirmB’stimebetweenproductintroductionsNumericalcases

1 BT

4 37 73 59 8

LLHH

3 37 33 411 5

HHLL

3 04 02 86 8

HHLL

2 22 62 23 9

LLHH167(5%)

1 561 45% 957(28%)771(22%)

Weassesstheperformanceofatime-pacingpolicyasthepercentdeteriorationinaveragepro t: F Pro t =100% Pro topt/Pro tF 1 ,wherePro toptisPro tforanoptimalpolicy,computedfrom(3),andPro tFisPro tforthetime-pacingpolicythatintroducesaproducteveryFperiods,computedfrom(6)and(7).De netheoptimalFforatime-pacingpolicyasF =argminF F Pro t .

WeusethestudydesigninTable2withPoissondemandand1 =0,exceptthatnowweconsiderthatFirmBactsaccordingtoarandomizedproduct-introductionstrategywithaprobabilityofproduct

B

introductionnondecreasinginbothiandj pqij=min 0 1 i+j 1 1 0 forallq,i,j).

WeobservefromouranalysesthatthevalueofF isalmostthesameasroundingETBPtothenearestintegerfortheoptimalpolicyfrom(3).Furthermore,productqualityfortheoptimalandtime-pacingpoli-ciesisthesamein98%ofcases.Finally, F Pro t equals0.0%in89%ofthecasesandaverages0.1%withamaximumof2.2%.Thus,atime-pacingpolicyforFirmAtypicallyperformsverywellrelativetoanoptimalpolicy.FirmA’sperformancemaysufferconsiderably,8however,ifitusesatime-pacingpolicywithaperiodotherthanF .

Forexample,ifFirmAchoosesF 1,thenpro tdeteriorationaverages2.8%,withamaximumof18.4%;thesevaluesarehigherforthe288caseswhere =0 3at3.9%and18.4%,respectively.IfFirmAchoosesF 2,thenpro tdeteriorationhasamaximumvalueof26.5%;itaverages9.2%when =0 3and6.6%overall.

8

4.Conclusions

Shoulda rmfrequentlyintroduceastreamofnewproducts?Shoulda rmemphasizetheintroductionofincrementallyratherthansubstantiallyimprovedproducts?Doesindustryclockspeedhaveastrongin uenceona rm’sdecisiontospeednewprod-uctstomarket?Weexplorethesequestionsbystudy-ingtheroleofexternalindustryclockspeed(asre ectedbyindustrypricechanges),internal rmfac-tors(productdevelopment,production,andinven-torycosts),andcompetitivefactorsina rm’soptimalintroductionandproduct-qualitydecisions.

Usinganin nite-horizonMarkovdecisionprocess,wemodeltheeffectofmarketdemanduncertaintyonnew-productintroductions,productionandinven-torylevels,andconsequentproductobsolescence.Weconcludefromalarge-scalenumericalanalysisthattheintroductiontimingdecisionisprimarilydrivenbytheindustry’sclockspeedandtheproduct-qualitydecisionismostlybasedoninternal rmfactorslikeproductdevelopmentandintroductioncosts.We ndthatcompetitivefactorshavelimitedin uenceonthe rm’soptimalnew-productstrategy,althoughtheysigni cantlyin uencea rm’spro t.Also,weshowthatatime-pacingintroductionstrategyresultsinaproductionpolicywithasimplebase-stockformandperformswellrelativetotheoptimalpolicy,providedthatthetime-pacingdecisionsareoptimized.

Theseresultsaddtoourunderstandingofnew-productintroductionandspeedtomarketasastrat-

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egy.(1996),Extending ndBayus(1997),theresultsandreportedBayusetbyal.Cohen(1997),etweal.quentlyconditionsmentalintroducewhennewitproductsisoptimalandfortofocusa rmontoincre-fre-trastimprovements(standardproducts).Incon-nalproduct-quality rmtoMorgandevelopmentetal.costs(2001),we ndthatinter-videindustryanalyticalsupportdecision.forImportantly,primarilyourimpactresultspro-therelated.

clockspeedandtimethemanagerialtomarketarebeliefcloselythatnotIttallyimplyisimportantthatthetopointoutthatourresultsdoclockspeedimprovedproductsfrequentisintroductionalwaysoptimalofincremen-infast-thatpriseda rm’sindustries.optimalnew-productInstead,ouranalysesstrategyindicateiscom-introductionoftwoclockspeed,timingdistinctisbutdependentrelatedfactors.onWhereassubstantiallytheinternalimproveddecisionnewtointroducetheindustryproductsisincrementalormentlimitations.Asand rmwithintroductionfactorsrelatedtotheproductdependentdevelop-onallresearch,costsourofstudytheseproducts.

isnotwithoutsimplifyingForassumptionsInparticular,inweourhavemodelmadeformulation.severalatheoreticdecision-theoreticexample,weconsiderperspective,competitionnotfromonlyagame-fromallowspoliciesforviewpoint.analyzingAlthoughtheeffectourofgeneraldifferentframeworkpro t,tionouronFirmmodelA’sdoesproductintroductionpolicypricinganduct.Ourmodeldoesnotnotallowincludeforpricevariableoptimiza-resultsdevelopmentdoesassumeatotaltimemarket(crashing),ofandournumericalprod-onlynotre ectpriceelasticity.Inconstantaddition,size,wewhichhavenamely,consideredoneaspectofindustryclockspeed,research.Theseindustrylimitationspricearechanges.

thatperioda rmForexample,naturalextendingdirectionsourmodelforfuturesomayandcancandecideofferaonproductlineineachtimeempiricalgeneratepricesforeachproductgiesanalysesfurtheranalyticalinsights.Inaddition,speedsby rmsacrossofindustriesobservedwithnew-productdifferentstrate-clock-calSuchresultsshouldandtobepotentiallyconductedgeneratetovalidateouranalyti-appropriatelyanalyses rm-levelconstructedmayinvolvecross-industrymanagerialfurthersurveysinsights.datasetsanddotaltioninformationproductintroductionsuggeststhatdecisions.productWhileofprolifera-anec-QuelchisrelatedtestingandKennytohigh1994,costsandlowerpro ts(e.g.,triestrieshaveoflowerour ndingthatMcMathfast-clockspeed1994),empiricalindus-research.

willalsobepro tsaninterestingthanslow-clockspeeddirectionforfurtherindus-547

Acknowledgments

ThethreeauthorsearlieranonymousthankdraftsofthisrefereesChrisTang,paper.

fortheirthehelpfulassociatesuggestionseditor,andonAppendix

ofProoftheMDPof,Theoremasisstandard1.Considerpracticethein nite-horizonMDPtheory:

versionft q i j x

B

r q i j x y + ED qij pqijft 1 q i+1 1 y Dqij + + 1 pBqij ft 1 q i+1 j+1 y Dqij + = r q i j x y + pBqijft 1 qs 1 1 0

xmax≤y≤M B + 1 pqij ft 1 qs 1 j+1 0 r q i j x y + pBqijft 1 qp 1 1 0 + 1 pBqij ft 1 qp

1 j+1 0

forq=qs qP i=1 2 n 1 j=1 2 n x=0 1 M

wheref0 q i j x =maxx≤y≤M r q i j x y ,and

(A1)

PqijS q i j y vq y x h noproductintroduction;qx r q i j x y =

Pqij sq S q i j y vq sq y+ vq hq x Ks

standard-productintroduction; Pqij s S q i j y vq sq y+ vq hq x Kp premium-productq

introduction.(A2)

pendentNow,considera xedproduct-introductionpolicyinde-theproductproduct-introductionofinventory,and,decisionfornotationalbyzsimplicity,denote

qij,wherezqij=0ifduced,alsorewriteandisintroduced,zzstandardproductisintro-noqij=1ifa(A1)qij=2as:

ifapremiumproductisintroduced.Weft q i j x = vq hq x+maxy≥x

Ht q i j y

(A3)

where,fort>0,Ht q i j y =H0 q i j y

+ 1 1 z qij>0 pBqij

E

D Dijft 1 q i+1 1 y qij + + 1 pB

E

qij

Dqij ft 1 q i+1 j+1 y Dqij + + 1 z qij>0 pB

qij

ft 1 zqij 1 1 0 + 1 pB

qij ft 1 zqij 1 j+1 0

(A4)

and

H P

0 q i j y =qi sq1 zqij>0 S q i j y

v1 z q sqqij>0 y Kq1 zqij>0 (A5)thenFromabase-stock(A3),ifHt q i j y policywithisconcaveparameterinyfordependentany q i j on

,

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Souza,Bayus,andWagner:New-ProductStrategyandIndustryClockspeed

548

q i j concavityisoptimal(seeZipkin2000,p.377).WeproveWeWeknowproveofthatthatHthet q i j y S q i j y Husinginduction.

0 q i j y =Eisconcaveiny ,for,whereany q i j D.Dqij min y DqijqijistheisinconcavedemandinforyAforateachstateD q i j .Giventhatmin y Dqij qij,thenS q i j y isconcavePy(seeZipkin2000),forany q i j .From(A2),becausesequently,qij>sq,theHtermthatmultipliesconcaveS q i j y iny,forisanypositive. q i j Con-0 q i j y is;we

de neforWeitsnextunrestrictedprovethatmaximumfassqij

0=maxy H0 q i j y .maxany q i j .From(A3),0 q i j x itsuf cesisconcavetoshowinthatx,theymaxright-hand≥x H0 q i j y Hsideisofconcave(A3)islinear.inx,sincethat

De netheV rsttermin0 q i j x =y≥x0 q i j y .Weprove =V0 q i j x+1 V0 q i j x V0 q i j x

+V0 q i j x 1 ≤0

Considerthreecases:

(i)x≤sqij

qij

quently,0 1.ThenV =H0 q i j x =H0 q i j ssqij

=0 q i j sqijqij

0 .Conse-0 2H0 q i j s0 +H0 q i j (ii)x0 =sij0.

qijqij

0.Then =H0 q i j ss0+1 2H0 q i j sH q i j s0 since0qijqijqij

+

0 =H0 q i j concavity.

Hx isnonincreasing0+1 Hin0 q i j 0 q i j x≥sqij

s0 ≤0,

0duetoits(iii)x>sqij

0.Then,becauseH0 q i j x isnonincreasingin

xj ≥H q x sqij

0.,i Thus,V0 q i j x 1 =j ≤Hx =maxy≥x H0 q i j y =H0 q i 0,0 q fromi thej concavityx+1 2Hof0 q Hi j x +00 q i j x .inductionHencef0yhypothesis q i j x isisconcavethatHinxforany q i j .Thet 1 q i j y isconcaveinforforEt=all1, q i j yby q i j (A3),.Consequently, Dfaswehavejustprovedt 1 q i j x isconcaveinx,andsoDqij ft 1qij + isconcaveinyforany q i j .

Givenarethat 1 1 zqij>0 pBqij

and 1 1 zqij>0 · 1 pB

qij forhorizonanynonnegative, q i j ,whichthencompletesby(A4),Hthet q i j y argumentisconcaveforthe nite-inysiderToable.theextendMDP.

nite-horizontheresultMDPtothe(A1).in nite-horizonThestatespaceMDPiscount-,con-andfaboveTheone-periodby Ppro tr · isboundedbelowby Kpq1.Since0pletes q i j x ast→ (Puterman≤ <1994,1,ft q i j x p.150),convergeswhichcom-toonNotetheproof.

twox,functions,wethatareifnottheasinableproduct-introduction(A3),torewriteandthefpolicyisdependentprooft q i j x doesasnotthehold.sum

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