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New Product Introduction Strategy

Permanent Link: http://ufdc.ufl.edu/UFE0022011/00001

Material Information

Title: New Product Introduction Strategy The Case of Fusion and Multi-Function Products
Physical Description: 1 online resource (135 p.)
Language: english
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

Subjects

Subjects / Keywords: design, diffusion, fusion, multifunction
Decision and Information Sciences -- Dissertations, Academic -- UF
Genre: Business Administration thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Devices that integrate multiple functions together are popular in consumer electronic markets. Examples include the cellular phone that takes digital pictures and plays MP3's, the PDA with cell phone, and multifunction office machines. We describe these multifunction devices as fusion products since they fuse together products which traditionally stand alone in the marketplace. The first contribution of this study is the guidelines of the optimal product portfolio for a firm who offers two single-function and one multi-function products. We utilize a linear price-demand function which captures the substitution effects between products. We identify the possible product portfolios and the corresponding condition which favor each of them. The fusion product with higher profit margin and less cannibalization of the single-function products is more likely to be included in the optimal portfolio. The single-function products that have low profit margins and can be easily substituted are often replaced by the fusion products. This provides a potential explanation for the proliferation of multi-function products in the market coupled with the simultaneous reduction of single-function products offered. The second contribution of this study provides insights of what fusion products should be designed and offered and what product portfolio should be chosen when there are more than two functions can be integrated into any combination of fusion product. Even though the number of possible portfolios can be extremely large, we propose an algorithm which efficiently identifies the optimal solution. The optimal product portfolio is often a small subset of all product variants and offering all-in-one product is not always optimal. The third contribution of this study is building a product diffusion model which considers the switching from single-function products to fusion product. This model assumes two single-function products are already in the market and the firm tries to find the optimal launch time for the fusion product. Based on Bass diffusion model, we conclude that the firm should consider the diffusions of all related products. We identify some factors that are unique to the whole diffusion of single-function and fusion products: the competitive role of the supplier, the development cost, the switching rates from single-function products to the fusion product, and how many users who will eventually buy one fusion product instead of two single-function products.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Thesis: Thesis (Ph.D.)--University of Florida, 2008.
Local: Adviser: Vakharia, Asoo J.
Local: Co-adviser: Carrillo, Janice E.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2010-05-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0022011:00001

Permanent Link: http://ufdc.ufl.edu/UFE0022011/00001

Material Information

Title: New Product Introduction Strategy The Case of Fusion and Multi-Function Products
Physical Description: 1 online resource (135 p.)
Language: english
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

Subjects

Subjects / Keywords: design, diffusion, fusion, multifunction
Decision and Information Sciences -- Dissertations, Academic -- UF
Genre: Business Administration thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Devices that integrate multiple functions together are popular in consumer electronic markets. Examples include the cellular phone that takes digital pictures and plays MP3's, the PDA with cell phone, and multifunction office machines. We describe these multifunction devices as fusion products since they fuse together products which traditionally stand alone in the marketplace. The first contribution of this study is the guidelines of the optimal product portfolio for a firm who offers two single-function and one multi-function products. We utilize a linear price-demand function which captures the substitution effects between products. We identify the possible product portfolios and the corresponding condition which favor each of them. The fusion product with higher profit margin and less cannibalization of the single-function products is more likely to be included in the optimal portfolio. The single-function products that have low profit margins and can be easily substituted are often replaced by the fusion products. This provides a potential explanation for the proliferation of multi-function products in the market coupled with the simultaneous reduction of single-function products offered. The second contribution of this study provides insights of what fusion products should be designed and offered and what product portfolio should be chosen when there are more than two functions can be integrated into any combination of fusion product. Even though the number of possible portfolios can be extremely large, we propose an algorithm which efficiently identifies the optimal solution. The optimal product portfolio is often a small subset of all product variants and offering all-in-one product is not always optimal. The third contribution of this study is building a product diffusion model which considers the switching from single-function products to fusion product. This model assumes two single-function products are already in the market and the firm tries to find the optimal launch time for the fusion product. Based on Bass diffusion model, we conclude that the firm should consider the diffusions of all related products. We identify some factors that are unique to the whole diffusion of single-function and fusion products: the competitive role of the supplier, the development cost, the switching rates from single-function products to the fusion product, and how many users who will eventually buy one fusion product instead of two single-function products.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Thesis: Thesis (Ph.D.)--University of Florida, 2008.
Local: Adviser: Vakharia, Asoo J.
Local: Co-adviser: Carrillo, Janice E.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2010-05-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0022011:00001


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Iwanttothankmywonderfulparents.Theyprovidedmethegreatesteducationinmylifeandgenerouslyletmepursuemydreamswithunconditionalloveandsupport.Iwanttosay"thankyou"tomyfriend,Eric.Hislifeandbusinessexperienceshelpedmetorevisemyresumeandshowmyfullpotential.WhenIwaslessthanpositiveinmyoutlook,Ericpatientlylistenedtomyfrustration,sharedwithmehislifestories,guidedmetoseelifeandviewtheworldwithadierentlens,andhealsotaughtmehowtowindsurf.Fromhimandmypersonalexperience,Ialsohavelearnedthat\inlife,thingshappenforareason."Formydissertation,IespeciallyappreciateDr.Vakharia'sfullysupportingmetopursuethisinterestingtopic.Hebelievedinme,encouragedmetokeepgoing,andprovidedopportunitiestobefreeofnancialworries.IwanttothankDr.Carrilloforpatientlyreadingthroughmynumerouseditionsandprovidingmewithhelpfulcomments.Aspecialthank-youtoDr.Alptekinoglu.Hisrigorouscritiquesandcontributionresultedinasuccessfulpublicationofourpaper.Manythanksgotoalloftheprofessors,whohaveassistedmetonishthisdissertation.IwanttothankallthestaandschoolmatesofISOM,andfriendsinGainesville,myTangofriends,myonlineandoverseasfriends.Itwastheywhogavemehelp,laughs,entertainment,andunderstandingwhenIneedthem. 4

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page ACKNOWLEDGMENTS ................................. 4 LISTOFTABLES ..................................... 7 LISTOFFIGURES .................................... 8 ABSTRACT ........................................ 9 CHAPTER 1INTRODUCTION .................................. 11 1.1FusionProducts:AnOverview ........................ 11 1.2MarketImpactofFusionProducts ...................... 15 1.3PortfolioDecisionsofFusionandSingle-FunctionProducts ......... 18 1.4DesigningFusionProducts ........................... 19 1.5DiusionofFusionandSingle-FunctionProducts .............. 21 1.6FocusofThisResearch ............................. 23 2OPTIMALPRODUCTPORTFOLIOSTRATEGY:TWOSINGLEFUNCTIONPRODUCTSANDONEMULTIFUNCTIONPRODUCT ............ 25 2.1Introduction ................................... 25 2.2Literature .................................... 26 2.2.1FusionProducts ............................. 26 2.2.2ProductBundling ............................ 28 2.2.3VerticalDierentiation ......................... 32 2.2.4Summary ................................. 34 2.3Preliminaries .................................. 35 2.4OptimalProductPortfolioStrategies ..................... 38 2.5NumericalAnalysis ............................... 43 2.6ImplicationsandSummary ........................... 49 3FUSIONPRODUCTDESIGN ........................... 51 3.1Introduction ................................... 51 3.2Literature:ProductVarietyandProductLineSelection ........... 52 3.3GeneralModel ................................. 55 3.3.1Preliminaries ............................... 55 3.3.2DominantPortfolios ........................... 61 3.4OneAll-in-OneModel ............................. 64 3.5NumericalExamples .............................. 66 3.6Conclusion .................................... 71 5

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..................................... 74 4.1Introduction ................................... 74 4.2Literature .................................... 76 4.3DiusionofSingle-FunctionProducts ..................... 80 4.4AftertheAvailabilityoftheFusionProduct ................. 83 4.5NumericalAnalysis ............................... 91 4.5.1MarketPenetration ........................... 93 4.5.2RoleoftheFusionProductSupplier .................. 95 4.5.3SynergyoftheFP:FasterDiusionSpeed,HigherMargin,andMarketExpansion ................................ 96 4.5.4MaturityoftheFusionTechnologyandtheDevelopmentCost ... 99 4.5.5TimeRelatedFactors .......................... 99 4.5.6MarketSizeandSubstitution ...................... 101 4.5.7MarketOverlap:FromTwoSPstoOneFP .............. 101 4.5.8SummaryoftheOptimalLaunchTime ................ 102 4.5.9ImpactsontheTotalProt ....................... 103 4.6Conclusion .................................... 106 5SUMMARY ...................................... 109 5.1KeyResultsinChapter2 ............................ 109 5.2KeyResultsinChapter3 ............................ 110 5.3KeyResultsinChapter4 ............................ 111 5.4FutureResearch ................................. 112 APPENDIX ACONCAVITYOFTHEPROFITFUNCTION ................... 115 BPROOFFORTHEOREM2.1 ............................ 116 CHESSIANMATRIXFORCHAPTER3 ...................... 120 DTHEOPTIMALQUANTITIES ........................... 121 EQUANTITYANDPROFIT ............................. 122 FPROOFFORTHEOREM3.1 ............................ 123 GPROOFSUPPLEMENTFORTHEOREM3.1 .................. 124 REFERENCES ....................................... 127 BIOGRAPHICALSKETCH ................................ 135 6

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Table page 1-1ExamplesofSingle-FunctionProductsandCorrespondingFusionProducts ... 12 2-1ResultsofTheorem2.1. ............................... 40 2-2DominantProductPortfolioStrategies. ....................... 40 2-3ComparativeStatics. ................................. 42 3-1ComparisonofProductLineSelectionModels ................... 55 3-2VariableNotationforChapter3 ........................... 57 3-3CongruentSubstitutionMatrix ........................... 70 3-4IncongruentSubstitutionMatrix .......................... 70 3-5OptimalProductPortfolioReactingtoParameterValueChange ......... 70 4-1NotationandAcronymsforChapter4 ....................... 82 4-2OptimalLaunchTimeinVariousCases ....................... 93 7

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Figure page 2-1r13:PriceversusMarketEectsatDierentLevels ................ 45 2-2r23:PriceversusMarketEectsatDierentLevels ................ 45 2-3r13andr23:CostversusMarketEectsatDierentLevel ............. 46 2-4r13andd3:DominantRegions ............................ 47 2-5r23andd3:DominantRegions ............................ 48 2-6r13andr23:DominantRegions ........................... 48 4-1DevelopmentCostatDierentLaunchTimeofFP ................ 84 4-2ExamplesofCumulativeSales ............................ 94 4-3OptimalLaunchTimeoftheFusionProductversusVariousFactors ....... 97 4-4ImpactofParameterChangeonTheProt .................... 104 8

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Devicesthatintegratemultiplefunctionstogetherarepopularinconsumerelectronicmarkets.ExamplesincludethecellularphonethattakesdigitalpicturesandplaysMP3's,thePDAwithcellphone,andmultifunctionocemachines.Wedescribethesemultifunctiondevicesasfusionproductssincetheyfusetogetherproductswhichtraditionallystandaloneinthemarketplace. Therstcontributionofthisstudyistheguidelinesoftheoptimalproductportfolioforarmwhooerstwosingle-functionandonemulti-functionproducts.Weutilizealinearprice-demandfunctionwhichcapturesthesubstitutioneectsbetweenproducts.Weidentifythepossibleproductportfoliosandthecorrespondingconditionwhichfavoreachofthem.Thefusionproductwithhigherprotmarginandlesscannibalizationofthesingle-functionproductsismorelikelytobeincludedintheoptimalportfolio.Thesingle-functionproductsthathavelowprotmarginsandcanbeeasilysubstitutedareoftenreplacedbythefusionproducts.Thisprovidesapotentialexplanationfortheproliferationofmulti-functionproductsinthemarketcoupledwiththesimultaneousreductionofsingle-functionproductsoered. Thesecondcontributionofthisstudyprovidesinsightsofwhatfusionproductsshouldbedesignedandoeredandwhatproductportfolioshouldbechosenwhentherearemorethantwofunctionscanbeintegratedintoanycombinationoffusionproduct.Eventhough 9

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Thethirdcontributionofthisstudyisbuildingaproductdiusionmodelwhichconsiderstheswitchingfromsingle-functionproductstofusionproduct.Thismodelassumestwosingle-functionproductsarealreadyinthemarketandthermtriestondtheoptimallaunchtimeforthefusionproduct.BasedonBassdiusionmodel,weconcludethatthermshouldconsiderthediusionsofallrelatedproducts.Weidentifysomefactorsthatareuniquetothewholediusionofsingle-functionandfusionproducts:thecompetitiveroleofthesupplier,thedevelopmentcost,theswitchingratesfromsingle-functionproductstothefusionproduct,andhowmanyuserswhowilleventuallybuyonefusionproductinsteadoftwosingle-functionproducts. 10

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36 ]. Wecallintegratingandconsolidatingallfunctionsintoanall-in-onedevicefusiontechnology.Fusionproductsprosperswhenthefusiontechnologybecomesmatureandisacceptabletotheendusers.Inthedigitalelectronicsmarket,theemergenceofstandardsandprotocolsinnetworking,interfaceandwirelesstechnologymakesproduct-fusionpossibleandattractive[ 36 ].Fusionproductscapturethestrongdemandofelectronicusers:elminatingtheneedformultipledevicesbyconsolidatingseamlesslyallthedierentfunctions;computing,organizing,communication,input/outputtransforming,andtransmitting,datastorage,andentertaining,intoasingledevice.Purchasingafusionproductnormallycoststhebuyerlessthanthetotalcostofseveralsingle-function 11

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Examplesofsingle-functionproductsandcorrespondingfusionproducts. single-functionproductsExamplesoffusionproducts Copymachine,printer,scannerandfaxmachineDierentcombinationsofall-in-oneocemachines CDplayerandradioCDandradiostereo Cellphone,digitalcamera,digitalmusicplayer,PDA,hand-heldPCDierentcombinationsofmulti-functionpersonaldevices TVandDVDplayerTV/DVDcomboset SunglassesanddigitalmusicplayerDigitalmusicplayerembeddedsunglasses Refrigerator,TV,ComputerRefrigeratorwithbuiltinTV&internetaccess products.Insomecases,whenthebuyerevaluatesfunctionconsolidationwithahighpremium,thepriceofafusionproductmaybegreaterthanthesumofsingle-functionproducts,suchasPalmOne'sTreo700. Werefertothesenewmulti-functiondevicesasfusionproductsforseveralreasons.First,\multi-functionproduct"(sometimescalled\multi-functionperipheral"andbothareabbreviatedasMFP)hasbeencommonlydescribedinbusinessandtechnologyjournals([ 16 ],[ 25 ],[ 3 ],[ 4 ],[ 36 ])toindicateamulti-functionocemachinewhichputsacopier,aprinter,afaxmachine,andascannerintoanall-in-onedevice.Second,`Integration'iswidelyusedinnewproductdevelopmentanddesign.Inmanynewproductdevelopmentpapers([ 20 ],[ 23 ],[ 35 ]),theintegrationfocusesonthedevelopmentprocessorcross-functioncooperation,whichcentersonproductdevelopmentoperations.Betterintegrationofmulti-functiondesignteamandfasterproductdevelopmentarethemajorconcernsofthesepapers.However,`integration'innewproductdevelopmentisaverydierentconceptfromthe`integration'offunctionalitiesintoaproduct.Weavoidusing`integration'todesignatemulti-functiondevices.Third,accordingtotheMerriam-Websterdictionary,`fusion'means\amergingofdiverse,distinct,orseparateelementsintoauniedwhole."Wethink`fusion'moreproperlyspeciestheharmonizing,integrating,andconsolidatingofavarietyoffunctionsinanall-in-onemulti-functiondevice. InTable 1-1 ,welistsomeexamplesoffusionproductsandtheircorrespondingsingle-functionproducts.OneinterestingfusionproductistheOakleyTrumpPolarized 12

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Flip-uplenseswithcontoursthatmaximizeprotectionagainstsun,windandsideimpact.PatentedXYZOpticsrforrazorsharpclarityatallanglesofvision,evenatlensperiphery.Plutoniterlensmaterialtolterout100%ofallUVA,UVB,UVCandharmfulbluelight.DurableOMatterrframewithlessthan1.8-ouncetotalweightforall-daycomfort....Absolutemusicfreedomwithnowiresorcordstodangleortangle.[It]storesupto120songsonthe512MBversionorupto60songsonthe256MBversionSolid-stateNANDashmemory Rightafterthelaunchin2004,wearingsuchapairofsunglassesandenjoyingdigitalmusicisassociatedwithahighpremium.InNovember2004,onepairofOakleyTrumpPolarizedSunglasseswaspricedatapproximately$500USD,whichiscostlierthanapairofpremiumsunglasses,approximately$150USD,plusa512MBiPodShuemusicplayer,whichcostsapproximately$100USD. Manymarketanalystspredictthatamulti-functionpersonalgadgetwilleventuallyreplacemanypersonalelectronicproducts.InGartner'sreport 5 13

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Rustetal.[ 80 ]pointoutseveraldriversforoftheproliferationoffusionproducts.First,addinganewfeatureoranextrafunctioncostslittleorevennothing,suchthat\engineerscan'tresistthetemptationtoequipexistingelectroniccomponentswithmorefunctions."Second,themanufactureris\aimingtohittwobirdswithonestone."Third,themarketersbelievethat\moreisbetter"andaddingadditionalfeatureswillmaketheproductmoreappealing.Fromthedemandside,Thompsonetal.[ 82 ]ndthatmostconsumers 82 ]mentionthattheproductdesignengineersdonotforeseethisproblemintheearlydevelopingstageoffusionproductdesign. Notethateachmajorfunctionintegratedinafusionproducttypicallyhasanassociatedsingle-functiondeviceavailableinthemarket.Thefusionproduct,asaresultofcoexistencewiththesingle-functionproduct,substitutesthedemandofitscorrespondingsingle-functioncomponentproductstosomedegree.Fromtheviewpointofaggregatedemand,somebuyersoffusionproductswillnotbuysome(orall)single-functionproductsthathavebeenintegratedintothefusionproducts.Conversely,somebuyerswhohavecertainsingle-functionproductsmaynotpurchasethefusionproducts,whichconsolidatethosesingle-functionproducts,becausethosesingle-functionproductshave 14

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Thereismoreevidenceshowingthemarketexpansionandgrowthofthefusionproducts.AbusinessmobilitysurveyconductedbyNOPWorldTechnologyin2005showsthatsixtypercentoflargeorganizations(1000-plusemployees)haveusedPDAphonesandmorethanone-thirdoflargecompaniesusesmartphones.Approximatelytwo-thirdsoflargeorganizationsuseorplantousewirelesstechnologytoaccesscompanydatabasesandles.Email,calendaring,andschedulingareseenasthemostimportantfunctionsforwirelessdatacommunicationintheserms[ 29 ].AmarketresearchreportreleasedbyIDCinNovember2004projectsthattheaveragegrowthrateofmulti-functionperipheralsfrom 15

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Itisnotsurprisingthatfusionproductsenterintothemarket(s)ashigh-enddevicessincetheyputsomanyfunctionstogether.Therefore,initiallythepriceofthefusionproductistypicallyatapremiumtoitscorrespondingsinglefunctionproducts.Thefusionproductmaygothroughseveralgenerationsofupgradesanddevelopmentsbeforeitevolvesintoafullyacceptablefusionproduct.EarlyversionsofTreoandBlackberryhadmanydefectswhichwereremovedinnewversionsofthesameproducts.WhileaPDA-phoneandamulti-functioncopier-printerhavebecomepopularinthemarket,otherfusionproductsarestillstrugglingformarketpenetration.Smartphones,whichemergedlaterthanthePDAphone,trytoconsolidatepocket-PCfunctionintoacellular-phone,buttypingonsuchasmalldeviceasalaptopsubstituteisdicult;hence,smartphonesarenotaspopularasPDAphones[ 47 ].Somefusionproductshavebeenlaunchedforyearsbuttheyarenotacceptedbythemarket(i.e.,InternetTV)orstayinnichemarket(i.e.,DVD-TVcomboset.) Asthecomponentandproductioncostsdecrease,thepricesoffusionproductsdecreaseandbecomemorecompetitivewiththesingle-functionproducts.Intermsofunitvariablecost,amulti-functionprintercostisapproximately25%greaterthanaquality-comparablesingle-functionprinter.Themoderatevariablecostincreaseofthefusionproductcomesfromsharingthesameinterfaceamongmultiplefunctions.However,thermhastoinvestasubstantialamountofmoneyinfusionproductdevelopment.Afterseveralgenerationsofimprovementandcostreductionsinmulti-function-relatedcomponents,thepricesofthefusionproductsarecompetitivecomparedwiththe

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Therearefewerandfewersingle-functionproducts,andmoreandmorefusionproductsintheocemachineandcellularphonemarkets.Oneevidenceofthisistheshelfdisplayoftheretailstores.Now,buyingapurecellphonewithouttheadditionalfunctionsleadstolimitedchoices.Buyersarestillabletondasingle-functiondocumentscannerorradiotunerintheretailstores,butthechoicesavailablearefewerthaninthepast.Fusionproductshavegraduallybecomeamainstreamchoiceinmanymarkets. Toresisttheencroachmentofthefusionproducts,thesingle-functionproductshavetoimprovetheirquality,whichwillvalidatetheirvalueandprolongthelifecyclesofthesingle-functionproducts.Oneexampleisthedigitalcamera.Cellphoneswhichcontainadigitalcamerafunctionarepredictedtooutsellthenon-cameraphonein2006worldwide[ 86 ].Cameraphonesarenowequippedwith3-megapixelresolutionorabove(i.e.,SonyEricssonK800andNokiaN80,N93),ashlightanddigitalzooming.Themarketoflow-endsingle-functiondigitalcamerashasdeclined.SamsungB600'scellularphonecontaininga10-megapixelresolutionsurpassesmanymid-levelsingle-functiondigitalcameras.Tocombatthecameraphone'sencroachmentintotheirmarket,themakersofdigitalcamerashavenotonlyincreasedtheresolution,theopticalzooming,andtheLCDscreensize,butalsoaddedmorefeaturessuchasimagestabilization,high-sensitivitymode,andconsecutiveshooting.However,someindustryforecastersstillpredictthefusionproductwilleventuallycausethedemiseofsingle-functiondigitalcamera[ 8 ]. Single-functionPDA'sshipmentsalsosuerfromthegrowthofPDAphonesandsmartphones.AccordingtoIDC'ssurvey,single-functionPDAshipmentsweredown22.3%intherstquarterof2006comparedtothesamequarterayearagoandthatwas 17

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ThefollowingexcerptfromPurchasingmagazine[ 4 ]pointsoutthedesirabilityoffusionproductsandtheirimpactsontheconsumersandthemarket: ...AnMFP(multifunctionproduct)combinescopiers,faxmachinesandprintersintooneunit,whichmeanslesshardwareandlowercostpercopy(CPC)forbuyers.So,acompanycansavemoneybycombiningallfunctionsintoonedevice....CustomersarebecomingmorecomfortablewithMFPssoweseedemanddecliningforsingle-functionfaxmachinesandcopiers...AreportontheMFPmarketpublishedrecentlybyGartnershowsthatwhiledemandisrising,it'smorerobustinsomesegmentsthanothers.MuchofthegrowthinsalesofMFPsfortheoceisforprinter-basedunits,whicharetakingvolumeawayfromsingle-functionprinters.

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Asaresult,fordierentindividuals,theutilityofafusionproductmightnotbethesumoftheutilitiesfromallitscomponentproducts.SomeconsumersarewillingtopaypremiumforthePDAphonebecausetheyreallyneedwell-integratedPDAphonesthatcansendemails,integrateaddressbook,andaccessdatabases.Someconsumersjustutilizethebasicsoftheextrafunctionsbecausetheyusetheminfrequently.Incontrast,someconsumersarejustmoreadventurousandtheyareearlyadaptersfornewproducts.Fusionproductsgivetheseconsumersnewexperiences,trendiness,andconvenience.Otherconsumersaremoresuspiciousaboutnewproductsandtheyareimitatorsintheproductdiusionprocess.Hence,someconsumersarewillingtopayahigh-premiumforaTreo650butothersarenot.Theconsumer'sutilityheterogeneitywithregardstofusionproductsgeneratesmorecomplexityindemandanalysis. 19

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Therstthreequestionsforthemanufacturersaretechnologylevelrelated.Themostimportantcriterionofavailabilityoffusionproducts,especiallyinelectronics,isthetechnologyadvances.Thesetechnologyadvancesneedcertaininvestmentinproductdesignanddevelopment,whichnormallyisassumedtobeaxedcost.Similartoanynewproductdevelopmenteort,fusionproductsnormallyneedsometimetogothroughseveralgenerationsbeforebeingwidelyacceptedinthemarket.Ifthefusionproductisjustattheinitialstage,thenseverefunctionalitydiscountoftencomesfromimmaturityofthenewcombinedtechnology.Normally,eachgenerationoffusionproductshasimprovedconsolidationinfunctionalitiesthatmakethatfusionproductmoreattractiveandcompetitive.However,thedicultyofintegrationforallinvolvedmanufacturersmightnotbesymmetrical.Thedigitalcameracaneasilybeaddedtothecellularphoneandthisideahasbecomeverypopularinthemarket.But,embeddingacellularphoneintoadigitalcameraisstillrare Inaddition,thexeddevelopmentcostandthevariablecosttodesignafusionproductvaryanddependsonthedegreeoffunctionalityoftheadditionalfunctionsandhowwellthesefunctionsareintegratedtogether.Thecostofaddingafaxfunctiontoaprinterislessexpensive,becausetheextravariablecostmightnotbemuchmorethanacontrolintegratedcircuit(IC).Sizeisanotherissueregardingportablefusionproducts.Addingsomanyfunctionalitiesintoonesmalldeviceisachallengeinproductdesign.As 20

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Thequestionaboutwhatleveloffunctionalityineachfunctionshouldbeintegratedisalsocriticaltothemanufacturers.Normally,theaddedfunctionwillnotworkbetterthanthesingle-functionproduct.Forexample,thescanningfunctionofamulti-functionprintermighthaveasmallerscanningsizeorlowerresolution,andafax-machine-basedfusionproductcannotcopyabook.Themanufacturersmayalsohavedierentfusionoptionstointegratethefusionproducts.Eachfusionproductmodelhasdierentlevelsofextrafunctionsandattractsconsumerdemandinavarietyofways. Technologyadvancesandcompetitionmakeproduct-fusionaninvertabletrend.Ifarmisnotaleaderinoeringfusionproducts,itmightbeencroachedbyothercompetitorsthatoerfusionproducts.Asaresult,manufacturingfusionproductsmightbeasurvivalstrategyforeveryrm.Allrmshavetoevaluatethepenetrationoffusionproducts,theimpactonthedemandofsingle-functionproductsandamarkettransitionprocessfromsingle-functiontomulti-function.Ofcourse,notallsingle-functionproductswillbereplacedbyfusionproducts.However,whattypeofsingle-functionproductcansurvivealonewillremainaconstantquestion.Astechnologyadvances,morermsmaychoosetobecomefusionproductprovidersrealizingthatproduct-fusionmightbeacontinuousandunboundedprocess. 1.2 wepresentedevidenceofshipmentdeclinesofsomesingle-functionproductsafterthelaunchofthefusionproducts.Thereisalsoplentyofevidenceindicatingmanyelectronicproductsareconvergingtofusionproducts.Ifweanalyze 21

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Oneexampleofafusionproductwhichhasalmosttakenoveritscomponentsingle-functionproductsistheportableradiotuner/CD(radio/cassette)stereo.Nowitisdiculttobuyasingle-functionportableradiotuner,single-functionportablecassette,andsingle-functionportableCDplayer.Itshowsthatthesingle-functiontomulti-functiontransitionhasalmostnishedintheportableradiotuner/CD(radio/cassette)market. However,noteveryfusionproductwilleventuallycausethedemiseofitscomponentsingle-functionproducts.TheTV-DVDcombosetisanexampleofafusionproductthatonlyhasanichemarket ThediusionandsubstitutionprocessthatanFPgraduallyreplacesitscomponentproductsispredictedbuthasnotbeeninvestigated.Manyquestionsrelatedtofusionproductdiusionareinneedofinvestigation.Thesequestionsinclude:whenshouldarmintroducethefusionproductandinwhatconditions?HowdoestheavailabilityoftheFPaectthediusionoftheseSPsaswellastheFP?Whatotherfactorsareinuentialto 22

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82 ]haveshownthattoomanyfeaturesmakethefusionproductlessattractive.Marketingorientedresearchcanstartfromconsumer'sutilityanalysistodiscussfusionproductsandsingle-functionproducts.Fromproductdesign'spointofview,howmanyfunctionsshouldbeconsolidatedintoasizelimitedall-in-onedeviceisanimportantquestion.Afterintegratingseveralfunctions,howtodesignamoreuserfriendlyinterfacetoincreasetheusabilityofthefusionproductisalsoachallengingwork.The60MinutesshowonCBS(GetMeTheGeeks!,Jan.28,2007)reportsthatnewhigh-techelectronics(HDTVorcablenetworking)havebecomesocomplicated,thatevenhightechgeekshavedicultiestosetupanewproduct.Productdesignorientedresearchisanotherdirectionoffusionproductresearch. However,thisdissertationinvestigatesthefusionproductphenomenafromthepointofviewofthemanufacturer. First,weanalyzetheproductportfoliodecisionforamanufacturerproducestwodistinctsingle-functionproductsandonetwo-function(multi-function)productinChapter2.Wecharacterizethedemandsinaprice-linearformsuchthatthepricefunctionofaproductdependsonhowmuchquantitytheproductisoeredaswellasitssubstitutes.Thesubstitutioneectsbetweentwoproductsdependsonthefunctionalitiesinthem.Weidentifyvepossibleproductportfoliosandcharacterizetheconditionswhichfavoreachofthem. Second,wefocusonthedesigndecisionforfusionproducts.Asmoreandmorefunctionscanbeconsolidatedintoanall-in-onedevice,thenumberofpossibleproductsgrowsexponentiallybecausedierentfusionproductscanbedesignedwithseveral 23

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Finally,thelaunchofthefusionproductwillchangethediusionprocessforsingle-functionproducts.Ifafusionproductislaunchedearly,thesingle-functionproductsmaycompletetheirlifecyclesearly.However,launchinganewfusionproductearliermayrequiremoreR&Dinvestment.Itshouldalsobenotedthatsubstitutioneects,relativeprotabilityandpotentialmarketsizemayalsoplayaroleintherm'slaunchdecision.Weproposeaproductdiusionmodelthatreviewstwosingle-functionproductsandonefusionproductandincorporatesthefactorsaboveintothemodel.Weinvestigatefactorsthatimpactthelaunchtimedecision. 24

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Weobservethatthebuyersofmulti-functionocemachinesoftenusetheall-in-onedevicestoreplacesomeorallsinglefunctionproductsofthemultiplefunctions.Forexample,mostconsumersandSOHO(Smalloce/homeoce)buyjustall-in-oneocesmachinestosavespaceandthetotalpurchasecost.Forthesebuyers,thescanningandfaxfunctionsontheall-in-oneocesmachines,eventhoughnotsogood,areacceptablefortheirlowvolumeofusage. Butforalargerbusinessortheconsumerswithhighvolumeofusageonthescanningandfaxfunctions,theall-in-oneocesmachinesfallshortoftheirneeds.Theadd-onfunctionsonall-in-oneocemachinesareoftendiscounted.Forexample,thescanningfunctionoftenhasalowerresolutionandthefaxfunctionislackofauto-redialandmultiplereceiversfeature.Asaresult,thesehigh-volumeusersmaystillpurchasesingle-functionproductsforeachfunctionbecausesingle-functionproductshavecompleteandhigh-endfeatures. Fromtheanalysisabove,thermwhichoerssinglefunctionandmulti-functionproductsmustevaluatethesubstitutioneectsbetweenasinglefunctionandamulti-functionproducts.Notethatthedegreesofsubstitutioneectsvaryinfunctionsandthatmaydependonthedesignofthemulti-functionproductandthefunctionitself.Intheall-in-oneocemachineexample,theprintingfunctionbetweenasinglefunctionprinterandamulti-functionocemachineareprettysimilar;butthescanningfunctionbetween 25

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Duetothesubstitutioneects,thedemandofasinglefunctionproductandamulti-functionproductoverlaps.Whilethemulti-functionproductgrabsthedemandfromitssingle-functionsubstitutes,italsoexpandsthemarket.Someconsumersonlypurchasewhenthemulti-functionproductisavailable.Butsomebuyersofsingle-functionproductschooseto`upgrade'tothemulti-functionproduct.Thishasbeenobservedinthemulti-functioncellphonemarketandApple's`iPhone'isanexample.Asaresult,thedemandofeachproductshowssomedegreeofoverlappingwithothersubstitutesbutithasitsowncharacteristics. Intermsofthevariablecost,asinglefunctionproductandamulti-functionproductmaysharesomecommoncomponents.Flat-bedstylescannersusethesameat-bedskeleton,glassandandsomeopticalcomponentsinallsinglefunctionandmulti-functionscanners.Butthemulti-functionscannerneedsamorecomplexcontrolcardtoexecuteotherfunctions.AswediscussinChapter1,thevariablecostofamulti-functionproductdoesnotequaltothesumoftotalcostofitscomponentfunctions. Now,letusdiscusssomeliteraturerelatedtomulti-functionproducts. 2.2.1FusionProducts 3 ],to\strategyofthemanufacturer"[ 4 ],to\newmarkettrend"[ 22 ][ 31 ],to\productdesigncritique"[ 25 ],andto\fusionproductreview"[ 28 ][ 37 ][ 13 ]. Fusionproductssuchasocemachinesandcellularphonesarebecomingmorematureinmarkets.Severalarticles[ 4 ][ 28 ][ 41 ]reportthedemandofthefusionproductsincreasedwhenthequalityoffusionproductsbecamemoreacceptable.Schonfeld[ 41 ]pointsoutthatBlackberryevolvedfromresembledpagerswithminiaturekeyboardsinthe 26

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28 ]impliesearliermultifunctiondevicesbeforethenhad\toomanycompromisesinatleastoneofthefunctions."Afterovercominginitialcompromises,fusionproductshavenowshownthattheyarestrongsubstitutesofsinglefunctionproducts. Here,wesummarizethesebusinessandtechnologyreportsonfusionproducts.First,asthepricesoffusionproductsdecline,thefusionproductsaremoreaordabletoconsumers.Havingafusionproductmeans\lessmachinecount"(totalnumberofsinglefunctiondevices)andlowercostforconsumers[ 4 ].Second,therearealmostlimitlessfunctionalitieswhichcanbeintegratedintooneunit[ 4 ][ 48 ].Astechnologyadvancescontinue,product-fusionwillemergeandprosperinmoreproductelds.Third,fusionproductsnormallyworkwellinoneortwofunctionsbutnotallofthemandtheconsumersshouldevaluatewhatlevelofperformancetheyrequireandhowmuchtheyarewillingtopay[ 25 ][ 28 ]. Therearesomedisadvantagesassociatedwithfusionproducts.First,Magid[ 28 ]mentionsthat\Ifyourstand-alonescannerorfaxmachinebreaks,youcanstillprint.Butifanycomponentgoesdownonamultifunctionmachine,thewholesystemmaybeunusableuntilthemachineisxed."Second,itisdiculttondouthoweveryfunctionworksinamultifunctiondeviceandthelearningcurvecanbesteep[ 13 ].Third,BreedenandSoto[ 13 ]pointoutsomefusionproductscannotmultitask,whichisdierentfromusingseveralsinglefunctionmachines.Evenifsomefusionproductscanhandlemultitaskssimultaneously,thelengthoftimetocompletethetaskisgreaterduetosharedmemory. Productdesignintegrationisanothertopicinproduct-fusionthathasbeeninvestigated.Thoughintegrationofdesignisoneaspectofproduct-fusion,currentliteratureaboutintegrationofproductdesignfocusesonmaximizingtheperformance.Theresearchfrom[ 6 ],[ 5 ],[ 45 ]discusstheintegrationissueofICandcomponent.Allawi[ 6 ]studiestheintegrationofanalog-digitalIPblocks.Thefocusofthepaperisontheperformanceanddesignissueofcircuitrouting.Allan[ 5 ]discussesthesuperiority 27

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45 ]showthatamultifunctionltercanperformthreebasicfunctionssimultaneously.However,thesepapersconcentrateontheperformanceordesignissueoftheproductinsteadoffusionproducts'impactonthemarket.Also,theproductsdiscussinthesemodelsarecomponentsofothernalproductsanddonotrelatetothenalmarketdemanddirectly. Ingeneral,bundlingmodelsoriginatefromeconomicstheory.Allmodelsassumeeachconsumerhasareservationvaluevectorforallproductsandthermknowsallthereservationvaluevectors.Rationalconsumerschoosecombinationsofsinglecomponentsorabundledpackagebymaximizingtheirutility.MostmodelsexceptthosepresentedbyHansonandMartin[ 24 ],DansbyandConrad[ 18 ],andBakosandBrynjolfsson[ 9 ]assumeproductcostsandreservationvaluesofconsumersareadditive.Forthebundledproducttobestrictlycompetitive,thebundledpricehastobelessthanthesumofallcomponentprices.Allmodelsassumethattheresaleofcomponentsfromtheconsumersisnotallowed.Itisastrongassumptionbecauseintherealworldconsumersoftentakeadvantageofbundlingorpromotionsbyaggregatingdemandtogether. ProductbundlingwasrstsuggestedbyStigler[ 44 ],whovieweditasastrategyforarmtoaccomplishpricediscriminationwhenheterogeneousconsumershavedierent 28

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Earlyresearchinvestigatedtheissuesoftheoptimalstrategyofsellers,consumersurplusandtheeectsoncompetition(e.g.,[ 1 ],[ 18 ],[ 39 ],[ 40 ][ 30 ],and[ 24 ]). AdamsandYellen[ 1 ]rstdenetwobundlingstrategiesforamonopolyproducer.Purebundlingstrategymeansthermonlysellsgoodsinpackageandmixedbundlingmeansthermsellsthecomponentsseparatelyaswellasinpackages.Theyshowthatbundlingcanbeprotablewithouttheassumptionofproductioncostsaving.Theyconcludethat,inmostcircumstances,bundlingcanbemorelucrativethansimplemonopolypricing. DansbyandConrad[ 18 ]considertwootherpossibilities:subadditiveandsuperadditive.Subadditive(superadditive)meansthetotalcostofthebundleisless(more)thanthesumofthecostsofallcomponents.Theyalsoallowtheconsumerstobuytwocomponentproducts,calledself-bundle,insteadofbundleonewhenmixedbundleisadapted.Ifallbuyersareutility-additive,oered-bundleandself-bundlewillnotexistsimultaneously.Theyndwhentheutilityofconsumersissubadditivethebundlepriceundermixedbundlemightbehigherthanthatunderpurebundle. Schmalensee[ 39 ]analyzesabundlingmodelthatamonopolistcombinesasingleproductwithanotherproductinacompetingmarket.Schmalenseealsondsiftwoproductsarenegativelycorrelatedthemonopolistcanprotfrompricediscriminationwhenthebuyersrevealtheirreservationvalues.Schmalensee[ 40 ]ndsthatwhiletheaveragewillingnesstopayishighandthecorrelationcoecientispositive,purebundlingdominatespurecomponentstrategyinasymmetricnormalcasebecauseitincreasesprotbyextractingmoreconsumersurplus. McAfeeetal.[ 30 ]ndthat,inamonopolysituation,thepurecomponentwillneverbeoptimalifthemonopolistcanmonitorapurchasemadebyconsumers.Oeringmixedbundleallowsthemonopolisttosegmentgroupsofcustomers.Ifthemonopolist 29

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HansonandMartin[ 24 ]developageneralizedbundlinganalysiswhenthemonopolistsellsmanyseparatecomponentsinthemarket.Theybuildacomplicatedlinearprogrammingmodelandshowthatiftheconsumersarerationalandwishtomaximizetheirutility,theconsumersineachmarketsegment(segmentedbytheirreservationvaluesandmarketpricesofallcomponents)willpurchaseexactlyonebundleorwillnotmakeapurchase.Thispropertycanbeformulatedasadisjunctiveconstraint. Salinger[ 38 ]analyzestheimpactofthecorrelationofreservationvaluesonoptimalbundlingstrategy.Whenthereservationvaluesoftwoproductsarenegativelycorrelated,highunitcostsmakebundlingunattractivecomparedtocomponents'aggregation.Whenthereservationvaluesoftwoproductsarepositivelycorrelated,thenbundlingneedslargercostsavingtobetheoptimalstrategy.Whenthereservationvaluesoftwoproductsareperfectlynegativelycorrelated,whichreducesthevariationofreservationvalues,thermcanusebundlingtoextractallconsumersurpluses. Chen[ 14 ]investigatesthebundlingstrategywhentheprimaryproductisinaperfectlycompetingduopolymarket.Eachduopolistcanbundlewithoneormoreofthegoods.Hendsthatbundlingworksasaproductdierentiationdevicefortherms. Somemarketingorientedresearchfocusesonretailorinformationgoodsbundling(e.g.,[ 34 ][ 10 ].Eventhoughknowingthattheconsumer'sutilityfunctionisawidelyacceptedassumptioninbundlinganalysis,howconsumersjudge,andhowtheyperceiveandevaluatethebundledealarenotstudiedtillrecently(e.g.,[ 51 ],[ 26 ],and[ 42 ]). MulhernandLeone[ 34 ]pointoutinsomesensepromotionisaformofpricebundling.Discountpromotionsforsomeitemsarecommonlyusedtodrivethedemandsofothernon-discountproductsintheretailers.Theycallthisapproachimplicitprice 30

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BakosandBrynjolfsson[ 9 ]studythebundlingofinformationgoods.Duetoverylowmarginalcost,theyndbundlingalargenumberofinformationgoodsmakesiteasiertopredicttheevaluationofconsumers.Themultiproductmonopolistcanextractmoreprotbysellingbundlesofinformationgoods.BakosandBrynjolfsson[ 10 ]extendtheirpreviousbundlingofinformationgoodstoacompetitivesetting.Whenthemarginalcostsarelow,theyconcludethatthereexisteconomiesofaggregationevenwithoutnetworkexternalityoreconomiesofscaleorscope.Byaddingnewinformationcontentstothecurrentone,thermcanemployeconomiesofaggregation. YadavandMonroe[ 51 ]conductanexperimenttoexplorehowbuyersperceivethesavingsinabundlingprice.Theiroutcomesshowtheseller'spricingstrategysignicantlyinuencesthebuyers'perceptionontwosavingsandtheirpurchasingbehavior.Twosavingsarebothimportanttothebuyersalthoughthebundlesavingismoreinuentialtothetotaltransactionvalue. SimoninandRuth[ 42 ]useaquasi-experimenttoinvestigatebundlingstrategyusedintheintroductionofthenewproductanditsimpactonconsumerpriceperception.Bundlinganewproductwiththecurrentbrand(orproduct)reducestheriskandisstronglyrelatedwithbrandextension.Bundlinganewproductwithawell-linkedbrandgeneratesafavorableattitudetowardthebundle.Thebrandofthenewproducthasgreaterinuenceontheattitudetowardthebundlethanthebrandofthetie-inproduct. Kaickeretal.[ 26 ]investigatethechoiceofthebuyers'componentversusbundlingpurchasebycomparingtherealpriceandthepriceexpectation.Theyndthatsubjectspreferabundlewhenfacedwithmixedgainsandlownetmixedlosses,andsubjectspreferacomponentspurchasewhentheyperceivedmultiplegainandhighnetmixedlosses.Onemajorconstraintoftheirresearchistonotconsideramixedbundlingstrategy. 31

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11 ],VandenboschandWeinberg[ 46 ]).Themodelsassumetheconsumershavethesamerankingofthevariantsofthisproduct.Ifallvariantshavethesameprice,allconsumerswillchoosethebestqualityproduct.Theheterogeneityofconsumerscanbeonincomebudgetdistribution(e.g.,[ 11 ],[ 21 ])orontastedistribution.Mostmodelsassumingdierenceintastealsoassumethedistributionisuniform(e.g.,[ 32 ],[ 46 ],[ 50 ]).Ansarietal.[ 7 ]relaxthetastedistributiontoageneralizedbetadistributionthatshowstheresultsareverydierentfromuniformdistribution.Twopapersinvestigatedverticaldierentiationovertime,whichmeansthatintertemporalcompetitionexists([ 33 ]and[ 19 ]). Baumol[ 11 ]analyzestheoptimalpostureofanewproductoranewstorealongtwodimensionsofproductcharacteristicsorretailerstance.Theresultsshowthatthenewproduct(shop)mustexistabovetheboundaryofaconvexregionformedbycurrentproducts(shops).Alltheconsumersduringacertainrangeofattributeslopebuythesameproductorshopinthesamestore. GabszewiczandThisse[ 21 ]investigateanon-cooperativeduopolygamefacingalargenumberofconsumerswithidenticalrankingofproductsbutdierentincomes.Higheraverageincomehelpstheprotabilityofbothrms;however,uptoacertainpoint,thelowerqualityrmwillbeoutofthemarketsinceallconsumerscanaordhighqualityproducts.Ifthehigherqualityrmimprovesitsproductquality,bothequilibriumpricesgoup.Surprisingly,whenthelowerqualityrmimprovesitsproductquality,itmightreduceitsequilibriumpricewhichmakesitselfworse-o. Moorthy[ 32 ]relaxesastrongassumptionofPigouvianthird-degreepricediscriminationconsumer-isolationandinvestigatedtheimpactofconsumerselectiononsupplier'smarket 32

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BoltonandBonanno[ 12 ]exploretheverticaldierentiationtwo-layersupplychainstructure.Whenthesupplychainisnotverticallyintegrated,alinear-pricecontractbetweenthemanufacturersandretailersgivesrisetoverticalineciency.Theyderiveanoptimalcontractbyrestrictingthesetofretailpricesandprice-dependentfranchisefees.Theyndwhenthewillingnesstopayforqualitydoesnotvarymuchwithincome,therearefewerincentivesforretailerstousepricediscrimination. Waterson[ 49 ]discussesoligopolymodelsofverticaldierentiationinquality.Ontheproducerside,undercertainconditionofincomerange,duopolyequilibriumholds.Largermarketsizeleadstohigherqualityproductsandthehigherqualityproducerearnsmorerevenue.Hendsthelowerqualityproducerisinanunderdogsituation;however,changeofincomedistributionmighthaveadierentconclusion. Choietal.[ 15 ]investigatetheNashequilibriumoftheduopolyproblemwhiletheindividualconsumer'spurchasingbehaviorisheterogeneousandinlogitmodelform.ConcaveprotfunctionofsinglermisanecessaryconditionofNashequilibriumwhilelowpricesensitivityofconsumersisasucientcondition.Theyndthathigherqualitywillincreasehigherequilibriumprice,butthatmakesthecompetitor'spriceindeterminant. CremerandThisse[ 17 ]studytwotypesofproductdierentiation:horizontalandvertical.Theyprovethatalargeclassofhorizontaldierentiationmodelsisaspecialcaseofverticalproductdierentiationmodel,butnotviceversa.Theresearchalsondsthatinverticaldierentiationthetopandbottomqualityrmsearnthesameprotthatishigherthantherm'sprotbyprovidingmediumquality. 33

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33 ]examinethetimingofproductintroductionwhiletherearetwosegmentsinthemarket.Ifthesellerintroducestwoproductssimultaneously,itshouldlowerthequalityofthelow-endmodelandreducethehigh-endprice.However,thesellercanalsocommittothemarketaboutitslaunchingscheduleifthesellerintroducestwoproductssequentially. Ansarietal.[ 7 ]investigatetheone-dimensionproductdierentiationinanon-uniformlydistributedconsumermarket.Theyanalyzethepositioningandpricinggamewhenthemarkethastwo,three,andfourbrandsandthermsmakethedecisionsimultaneouslyorsequentially. VandenboschandWeinberg[ 46 ]analyzetwo-dimensionalverticaldierentiationinatwo-rmsituation.Theydeterminethattherearethreetypesofresults.Therstresultisthatthetwormswillmaximizedierentiationinonedimensionandminimizedierentiationinanotherdimension,whichiscalledMaxMinproductdierentiation.Thesecondresultisthatonermtakesamax-maxqualitypositionandanothertakesamin-minqualityposition.Thethirdresultshowstwormsmaximallydierentiatedinonedimensionandpartiallydierentiatedinanotherone.MaxMindierentiationisthenormalcase. Wauthy[ 50 ]assumesthattwormsdierinlevelofqualityandtheconsumersdierintheirtastesofquality.HeconcludesthattheNashequilibriumpricesarefunctionsofthedegreeofpopulationheterogeneityandthedegreeofproductdierentiation.Onemajorcontributionofthispaperisitincludescoveredanduncoveredmarketcongurations. 34

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Afusionproductmaybeseenasahigh-endversionofitssinglecomponentproducts.However,viewingthefusionproductasahigh-endsubstituteoftheoriginalproductwillignoretheimpactofthefusionproductontheothersingle-functionproductmarket.ItislikelythateveryunitsaleofTreo650displacesapotentialbuyerofacellularphone,aPDA,andalow-enddigitalcamera.Thedynamicbroughtbyfusionproductsismuchmorecomplex.Wethinktheproblemofproduct-fusionwillnotbesucientlyexplainedbyverticaldierentiationandshouldbeanalyzedseparately. 35

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Weassumealinear,downward-slopingdemandcurveasafunctionofprice.Asanapproachtomodelprice-demandrelationships,lineardemandcurvesarequitecommonintheliterature([ 43 ],[ 74 ][ 27 ][ 58 ][ 77 ][ 66 ]).Besidesanalyticaltractability,lineardemandcurvesalsopossessseveralattractivefeatures.First,thepriceelasticityofdemandisincreasinginprice,i.e.,thehighertheprice,themoresensitivethedemandistochangesinprice(thisisnottrueforotherpopularformsofprice-demandfunctionssuchasCobb-Douglas).Second,thelineardemandfunctionhasautilitybasedexplanationfromrstprinciples[ 72 ].Foracompletediscussionofwhenlineardemandcurvesareappropriate,thereaderisreferredtoLaFrance[ 63 ].Thespecicinversedemandfunctionsweassumeforeachproductareasfollows: whereai>08icanbeinterpretedasthemaximumpriceforproducti;qiisthequantityofproductisoldbytherm;ri3(0
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Thevariablemanufacturingcostforproductiisciandtoruleouttrivialcases,weassumeci
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Maximize=q1(d1q1r13q3)+q2(d2q2r23q3)++q3(d3q3r13q1r23q2) (2{4) subjectto:qi0fori=1;2;3 (2{5) wheredi=aici8iandcanbeinterpretedasthemaximumprotmarginforproducti.Itisrelativelystraightforwardtoshowthatisstrictlyandjointlyconcaveinthedecisionvariables(seeAppendixA)andthus,therst-orderconditionsarenecessaryandsucienttoidentifyanoptimalsolution(q1;q2;q3)toourproblem.However,thereisnoguaranteethatthissolutionisfeasible(i.e.,qi08i).Hence,thereareseveralpotentialproductportfoliostrategiesthatemergeasbeingoptimalfortherm.Thesestrategiesare: 38

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1.Ifd32(0;1],theoptimalproductportfoliostrategyisNMFPS; 2.Ifd32(1;2],theoptimalstrategyisAPS. 3.Ifd32(2;3),and 4.Ifd32[3;1),thentheoptimalstrategyisSMFPS. Table 2-1 summarizestheoptimalproductportfoliostrategiesbasedontheresultsstatedinTheorem2.1.Foreachofthesestrategies,detailsontheproductquantityoerings,resultingrmprots,andcorrespondingpricesforeachproductforeachareshowninTable 2-2 TheresultsofTheorem2.1areintuitivelyappealing.Recallthatd3isthemaximumprotmarginforthemulti-functionproduct.Itisonlywhenthismaximumprotmarginislessthanorequaltotheweightedaverage(wherethe\weights"arethesubstitutabilityparametersintheinversedemandfunctions)maximumprotmarginofbothsinglefunctionproducts,thatthermshouldnotincludethemulti-functionproductinitsproductportfolio.However,ifthemaximummarginonthemulti-functionisgreaterthanthisweightedaverage,themulti-functionproductisalwayspartoftheproductportfolio 39

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ResultsofTheorem2.1. ParameterSettingOptimalProductPortfolioStrategyCorrespondingProductPortfolio DominantProductPortfolioStrategies. APSNMFPSSMFPSPMFPS1PMFPS2 P3i=1[0:5qidi]0:25(d21+d22)0:25(d23)0:25y40:25z5 40

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AnanalysisoftheimpactofeachparameteronthechangesinoptimalquantityoeringsandchangesinthecorrespondingprotforeachproductportfoliostrategyisshowninTable 2-3 .Examiningthistable,weobtainthefollowingadditionalinsights: 41

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ComparativeStatics. APSNMFPSSMFPSPMFPS1PMFPS2 Theanalysisoftheoptimalproductportfoliostrategiessofarhasbeenfocusedonprovidingparametricguidelinesforthermtochooseaspecicstrategy.Furtherinsightsintothechangesinthequantityoeringsandrmlevelprotswithchangesinkeyparametershavealsobeendiscussed.Oneissuewhichhasnotbeenexploredistheimpactofsimultaneouschangesinthesekeyparametersonchoicesbetweenthesetofportfoliostrategies.Inordertodothis,thenextsectionpresentsanumericalanalysisbasedonsecondarydatafortwosinglefunctionproductsandonemulti-functionproductcurrentlyavailableinthemarket. 42

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1.MaximumProtMarginsversusMarketEects:ThemaximumprotmarginfortheMFPisrepresentedbytheparameterd3andisdeterminedasafunctionofthemaximumprice(a3)andcost(c3).Thus,keyquestionsinthiscontextwouldbe: 2.StrategyRegionsandMarketEects:Howaretheoptimalstrategyregionsmoderatedbythesubstitutabilityparameters?Thiscouldprovideinsightsintohowmarketeectsimpacttheoptimalproductportfolio. Inordertoaddressthesequestions,weuseocemachines(specicallyprintersandscanners)asourproductsforanalysis.Thereisassumedtobeasinglemanufacturer(e.g.,HP)whohasthecapabilityofoeringaprinter(baseproduct1),ascanner(non-baseproduct2),andaprinter-scanner(MFP-product3)toasinglemarket.Pricequotesfromwww.Ocedepot.comandwww.Nextag.comandthegrossmargindatafromHP'snancialreportareusedtosetthemaximumprices,unitcostsandthemaximumprotmarginsfortwosinglefunctionproducts(products1and2).Theseparametersvaluesaresetas: Product1(Printer):a1=$680,andc1=$240whichimpliesthatd1=$440;and Product2(Scanner):a2=$580,andc2=$280whichimpliesthatd2=$300. Sinceprotmarginsareafunctionofmaximumpricesandcosts,wegeneratethreegures.InFigures2-1and2-2,wesetcostoftheMFP(c3)tobeequalto$400andthen 43

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44

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PriceversusMarketEects:Optimalstrategywhena1=680,c1=240,a2=580,c2=280,c3=400,andr23=0.4. Figure2-2. PriceversusMarketEects:Optimalstrategywhena1=680,c1=240,a2=580,c2=280,c3=400,andr13=0.6. forthesinglefunctionproducts,theninternalcostcontrolsneedtobemorestringenttoensurethattheMFPisincludedintheoptimalportfolio. 45

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CostversusMarketEects:Optimalstrategywhena1=680,c1=240,a2=580,c2=280,a3=900. Insum,theseresultsindicatethatwhensubstitutioneectsarehigher,theMFPneedstocommandahighermaximumpricetobeincludedintheproductportfolio.However,oncethisisachieved,highersubstitutioneectsactuallyleadtotheMFPincludedintheproductportfolioeitherwithoneofthetwosinglefunctionproductsorbyitselfwithlesserrequiredincreasesinthemaximumprice.Inasimilarvein,wealsoseethatwhensubstitutioneectsarehigher,thebasecostfortheMFPcanbelowerforittobeincludedintheproductportfolio.However,oncethisisachieved,highersubstitutioneectsactuallyleadtotheMFPbeingincludedintheproductportfoliowithoneormoreofthesinglefunctionproductswithsmallerreductionsinMFPcost. Inordertoillustratetheseregions,westartbysettingd1=$440andd2=$300.Inaddition,Figure2-4isgeneratedbyxingr23=0:4andsimultaneouslyvaryingr13intherange[0.5,0.95]andd3intherange$[380,800];Figure2-5isgeneratedbyxingr13=0:6andsimultaneouslyvaryingr23intherange[0.1,0.5]andd3intherange$[380,800];andFigure2-6isgeneratedbyxingd3=$600andsimultaneouslyvaryingr13intherange(0,1)andr23intherange(0,1).Figures2-4and2-5illustratethefollowingkeyresults: 46

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Figure2-4. Dominantregionswithd1=440,d2=300,andr23=0.4 ManageriallytheresultsinFigures2-4and2-5canbeinterpretedtoformulatethefollowinggeneralguidelinesforstrategychoices: 1.APSismorelikelytobetheoptimalchoicewhendemandsubstitutioneectsaresmallandtheprotmarginoftheMFPisnottoolargeortoosmall.TheprotmarginoftheMPFmustbeleastequaltothelinearcombinationoftheprotmarginsandthesubstitutionindicesoftheSFPs; 2.PMFPS1and/orPMFPS2aremorelikelytobetheoptimalchoicewheneitherthedemandsubstitutioneectsarelargeor themaximumprotmarginfortheMFPislarge;and 47

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Dominantregionswithd1=440,d2=300,andr13=0.6 3.SMFPSismorelikelytobeoptimalwhenboththedemandsubstitutioneectsarelargeandthemaximumprotmarginfortheMFPislarge. ThenalsetofresultsinFigure2-6oeradierentperspectiveonthestrategyregionswhichallincludetheMFPintheoptimalproductportfolio.Givenourassumptionsthatr13>r23andr213+r223<1,thedarkdashedlinesinthisgureindicatetheboundsforthefeasibleregionforstrategychoices.Giventheparametersettingsofthemaximumprotmarginsforthethreeproducts,managerialguidelinesbasedontheseresultsare: Figure2-6. Dominantregionswithd1=440,d2=300,andd3=600 48

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Weareabletoidentifythekeyparametersdrivingthechoicebetweenthesedominantstrategies.Tostartwith,itisnecessaryforthermtounderstandandparameterizethedemandsubstitutioneectbetweeneachsinglefunctionproductandtheMFP.Assumingthisinformationisavailable,weareabletoshowthattherm'soptimalchoiceofaproductportfoliostrategyisdrivenprimarilybythemaximumprotmarginassociatedwiththeMFP.Atoneextreme,ifthismaximumprotmarginfortheMFPislessthanorequaltotheweightedaverageprotmarginforthetwosinglefunctionproducts,thentheMFPshouldnotbeincludedintheoptimalproductportfolio(i.e.,NMFPSisoptimal).Ontheotherhand,theotherextremecaseisthatifthemaximumprotmarginfortheMFPdominatestheadjustedmaximumprotmarginsforbothsinglefunctionproducts,thenitisoptimalforthermtoincludeonlytheMFPinitsproductportfolio 49

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Ananalysisofthedemandsubstitutioneectsalsoleadstosomeinterestinginsights.Iftheseeectsarehigher(forboththebaseandnon-baseproductinrelationtotheMFP),thenthelikelihoodoftheMFPbeingincludedintheoptimalproductportfolioislower.Thus,thereisanecessitytofocusonbothquantityandmargineectsinmakingthedecisiontoincludeanMFPintheoptimalproductportfolio.Further,thereareinteractionsbetweenthedemandsubstitutioneectsandthemaximumprotmarginoftheMFPwhichmoderatethechoiceofthepartialMFPstrategies.Inessence,smaller(larger)valuesofthedemandsubstitutioneectbetweenthebase(non-base)productandtheMFPtendtoincreasethepossibilityofthebaseproductandtheMFPbeingincludedinanoptimalproductportfolio.Ontheotherhand,larger(smaller)valuesofthedemandsubstitutioneectbetweenthebase(non-base)productandtheMFPtendtoincreasethepossibilityofthenon-baseandMFPbeingincludedinanoptimalproductportfolio. 50

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Fusionproductswithmultiplefunctionsarethrivinginthemarket.Multi-functionocemachinesareoftenequippedwiththreeorfourfunctions.Amulti-functioncellphonecannowintegratefunctionsofcellphone,digitalcamera,PDA,musicplayer,andGPSallintoasingledevice.Apple'siPhoneisadvertisedtoreplacefoursingle-functiondevices.Thereareseveralfactorsthatcontributethepopularityoffusionproducts.Amulti-functionportabledevicehastheadvantageofspacesavingandisfreeofintegrationhasslesbetweenfunctions.Themulti-functionocemachinesarenormallypricedjustslightlyhigherthansingle-functionproductssincetheyhavebeeninthemarketforalongtime.Butawell-integratedmulti-functioncellphonecanbepricedwithahighpremium. Theavailabilityofthefusiontechnologyincreasestheproductvarietyandthecomplexityofproductportfoliodecisionsfortherm.Forexample,whenafusiontechnologywhichintegratesvefunctionstogetherisavailable,thereareinfact31dierentfunctioncombinationsofproductsthataretechnologicallyachievable.Intermsofpossibleproductportfolio,therearetotally2311portfoliostochoosefrom.Howeverwedonotobserveallsortoffunctioncombinationsinthepersonalportabledevicemarketifweonlyconsiderthesevefunctions:cellphone,digitalcamera,PDA,musicplayer,andGPS.Forexample,thecombinationsofdigitalcamerawithmusicplayer,PDAwithGPS,orGPSwithdigitalcameraarenotavailableinthemarket.Thereisnoexplanationaboutwhythesefunctioncombinationsarenotattractivetothemanufacturersofpersonal 51

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Fromatechnologydevelopment,productdesign,andproductintroductionperspective,weaddressestheseconddecision.Thus,weexplicitlyassumethatthermhasaccessto(throughself-developmentorexternalsources)thetechnologyrequiredtooeranFP.Giventhatthisisthecase,theproductdesigndecisionisaddressedusingaproductportfolioperspectiveandthus,thegeneralapproachweproposewouldalsohelparmmakethestrategicdecisionontheoptimalcombinationofSPsandFPs(whichdenesaproductportfolio)tointroducetothemarketplace.Thefollowingliteraturereviewstheresearchofproductlineselectionandproductportfolioasproductvarietyincreases. 64 ],productvarietyinmostpapersreferstothenumberofvariantswithinaspecicproductgroup,buttheviewofproductvarietyandthequestionsbeingaskedvariesalot.Therearefourdierentviewsconcerningproductvariety:theindividualconsumer,theindividualrm,marketequilibrium,andthesocialoptimum. Sorenson[ 71 ]usesanevolutionaryperspectivetotesttheproductvarietystrategyinthecomputerworkstationindustry.Theauthorexamines179rmsand1,276productsfrom1980to1996.Theresultsillustratethatproductvarietybecomeslessvaluablewhenthetotalnumberofproductsinthemarketincreases.Productcullingcanremovebadly-performedproductsbutalsodecreasestheabilityofthermreactingtothechangeofconsumers'preference. RamdasandSawhney[ 67 ]developmeasurementproceduresforlife-cyclesalesvolumeandcostforlineextensionofassembledproducts.Sharingcomponentscanbringacostbenetbecauseofdemandpoolingforcomponent.However,similarityamongassembledproductsdecreasestherevenuebecausetheseproductssubstituteeachother's 52

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Ramdasetal.[ 68 ]identifythreeorganizationalapproachesforcomponentsharing,whichachieveproductvarietywithlowercomponentvarietyandcostforassembledproducts.Threeconceptualconstraints-component-to-productfeasibility,system-to-productfeasibility,andcomponentinteractivity-arealsodiscussed. LochandKavadias([ 62 ])recognizetheinherentcombinatorialcomplexityofoptimallydeterminingaprojectportfoliowhenanalyzingthisdecisionfromthetechnologydevelopmentandR&Dinvestmentlevel.Theyfocusonthedynamicallocationofresourcesoveraxedplanninghorizonwhichcanguidemanagersinthedevelopmentofanewproductwithseveralassociatedproductlines. Otherpapershaveaddressedtheproductlineandpricingproblem.DobsonandKalish[ 57 ]formulateamathematicalprogramwhichassumesthatthecustomersincertainmarketsegmentsarehomogeneousandcanbeaggregated.Theyndthat,duetoxedcostofassortmentandthecannibalizationeects,havingtoomanyvariantsmaydecreasethetotalprot.Despiteadierentmodelingapproach,ournumericalexamplesalsosuggestthattheoptimalproductportfolioisnormallyasmallsubsetofallpossibleproducts.ChenandHausman[ 56 ]proposeaparsimoniouschoice-baseconjointanalysiswhichleadstoanecientalgorithmtosolvetheproductline/priceproblem.Dierentfromranking/ratingbasedconjointanalysisthatoftendependsonenumerationorheuristicprocedurestoselecttheproductline,theirmethodcanbeappliedtoaproblemwithrealisticsizeofproductlineandsolvedbycommercialmathematicalprograms.HoppandXu[ 61 ]investigateproductlineselectionwhilethermusesmodularitytoreducetheintroductioncostofnewproduct.Assumingexistenceofeconomyofscopewithouteconomyofscale,theyndthatmodularityoersmorevarietyintheproductline,whichalsobenetsahighermarketshareandapricepremium.Itwasobserved,in 53

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Onetrackofproductassortmentmodelsutilizesmultinomiallogit(MNL)tomodeltheconsumer'sutilitiesandpurchasingchoices.Cachonetal.[ 55 ]investigatetheretailer'sassortmentproblemwhenconsumersearchispossible.Theydierentiatethreemodelsofconsumersearch:nosearch,independentassortmentsearchandoperlappingindependentassortment.Insomecases,theoptimalassortmentiswithinadenedpopularsetofproductsfornosearchandindependentsearchmodels.Ourmodelconrmsthisresultutilizingadierentdemandbasedapproach.Whileincludingthecostofassortment,theyndthattheoptimalassortmentcanbefoundbyfullenumeration.Incontrast,weprovidestructuralresultstoaidintheidenticationoftheoptimalproductportfolio. OtherpapersalsouseMNLchoicemodelstoinvestigatetheproductlineandstockingproblem.AydinandRyan[ 53 ]analyzetheproductlineandpricingdecisionsinthreesituations.Theyndthatwhentheshelfspaceislimited,theoptimalproductlineconsistsofanumberofmodelswiththehighestaveragemargins.SmithandAgrawal[ 70 ]developamulti-iteminventorysystemtomeettheindividualitem'sservicelevel.VanRyzinandMahajan[ 75 ]analyzeaninventorymodelinwhichasequenceofconsumerarrivalspurchasesonlytheirrstchoice.MahajanandvanRyzin[ 65 ]issimilartovanRyzinandMahajan[ 75 ]exceptthattheconsumerssubstituteamongproductvariantsiftheirrstchoiceisnotavailable. ThecomparisonofproductlineselectionmodelsabovewithourmodelislistedinTable 3-1 Wecandierentiateourfusionproductproblembycontrastingtotheproductlineselectionmodelsintermsofthetimingofdecision.Fromproductdevelopmenttoproductdisplayintheretailshop,thisrststageofFPdecisionmakingconcernsitselfwithsuchtechnologydevelopment.TheresearchisexempliedbyLochandKavadias([ 62 ]).Afterward,thermmakesastrategicdecisionatthemarketlevelconcerningboth(a) 54

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Comparisonofproductlineselectionmodels. ModelStructure DemandMNLSubstitutionFixedcostInventoryCharacteristics DobsonandKalishAggregateNoNosubstitutionYesNo(1998)DemandVanRyzinandIndividualYesNosubstitutionNoYesMahajan(1999)discretechoiceAydinandRyanIndividualYesSubstitutionbasedNoYes(2000)discretechoiceonavailabilitySmithandIndividualNoSubstitutionbasedYesYesAgrawal(2000)discretechoiceonavailabilityChenandHausmanAggregateYesNosubstitutionNoNo(2000)demandMahajanandvanIndividualYesSubstitutionbasedNoYesRyzin(2001)discretechoiceonavailabilityCachon,TerwieschIndividualYesSubstitutionbasedYesYesandXu(2005)discretechoiceonavailabilityThismodelAggregateNoSubstitutionbasedNoNodemandonfunctionality whichFPstobringtomarketand(b)howmuchofeachproductvarianttoproducebasedonaggregatedemandprojections.Thisisthefocusofthemodelintroducedhere.Atlast,thermdecidestheproductionandinventorystockingissues,whichareinvestigatedasin[ 55 ],[ 70 ],[ 75 ],and[ 65 ]. Foramorethoroughliteratureviewofproductvariety,wereferthereaderstoLancaster[ 64 ],HoandTang[ 60 ],andRamdas[ 69 ].Regardingapplyingnancialportfoliotheorytoproductportfolio,seeCardozoandSmith[ 76 ]andDevinneyandStewart[ 78 ]. 3.3.1Preliminaries

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Whenthefusion-technologymakesFPspossible,thenthedemandsforallproductsaremoredynamicduetosubstitutioneects.Consequently,theoptimalquantitydecisionforeachproductisinuencedbythesubstituteproduct.Becausenotwoproductsareexactlyidenticaltoeachother,weassumeeachproductkhasitsownmarketpotentialakandvariablecostck.Wedenoteaandcasthem1marketpotentialvectorandm1variablecostvectorofmproducts,respectively.ThevariablenotationsusedinthispaperaresummarizedinTable 3-2 Ifanytwoofthesemproductspossesssimilarfunctionality,thenthereexistssomedegreeofsubstitutionbetweenthetwomarketsfortheseproducts.Usingthemanufacturerofocemachinesasanexample,single-functionproductswhichcouldpotentiallybeoeredarethefaxmachine,copier,printer,andscanner(i.e.,n=4).Givennooverlapinfunctionalitiesbetweeneachoftheseproducts,theyarenotconsideredsubstitutes.Withtheavailabilityoffusion-technology,themanufacturernowhasthecapabilityofoering11FPs(i.e.,24(4+1))anddependinguponthefunctionalitiesincludedineachofthem,thesecouldbeconsideredsubstituteproducts.Forexample,assumethatthemanufacturerintroducesanFPwhichintegratesthefunctionalitiesassociatedwithaprinterandacopier.Inthiscase,thisproductwouldbeasubstituteforthesinglefunctionprinter,thesinglefunctioncopier,andotherFPswhich 56

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VariableNotationforChapter3 SPSingle-functionproductFPFusionproductpkPriceofproductkqkQuantityofproductkoeredbytherm(decisionvariable)akMarketpotential(themaximumamountofwillingness-to-pay)ofproductkckUnitvariablecostofproductkdkScaledprotmarginofproductk,dk=akck incorporatethefunctionalityofaprinterand/orthescanner(e.g.,printer/fax;copier/fax;printer/copier/fax). Todierentiatevariouslevelsofcombinationsoffunction,inthispaper,afusiondeviceequippedwithallfunctions,iscalledall-in-one,andafusiondevicewithonlysomefunctionsiscalledsome-in-one.Forexample,considerafour-functionsetcontainingfunctionsofcopying,scanning,printingandfax.Then,acopier/printerandaprinter/copier/faxareexamplesofsome-in-one,andadevicewithfourfunctionsisanexampleofanall-in-oneproduct.Duetothecomplexityofthemodel,weassumethatthefusiontechnologyisexogenouslygiven. Beforespecifyingtheinversedemandfunction,werstdescribesubstitutioneects.Thesubstitutionamongmproductscanberepresentedbyammasymmetric 57

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81 ],[ 52 ]).Normally,ahigh-endproducthasastrongersubstitutioneecttoitslow-endsubstitutethanvice-versa.Forexample,anall-in-oneprinterhasstrongersubstitutioneectonthesinglefunctionprinterthantheconverse.ManagerscanutilizetheestimationtechniquesshowninBen-AkivaandGershenfeld[ 54 ]andHendel[ 59 ]forassessingthesubstitutionmatrixfortheirrm.Also,atechniquesimilartothatdescribedinChenandHausman[ 56 ]forchoice-baseconjointanalysiscanbeadaptedtoderiveaggregatedemandlevelparameters. Letabethemarketpotentialvector,qbem1quantityvectorandrbethesubstitutionmatrix.Theinversedemandfunctionsareasfollows. (GP):=qT(pc)=qT(acrq)=qT(2drq)s:t:q0:

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Becauseofasymmetricsubstitutioneectsamongallproducts,oeringallmproductsmaynotbeanoptimalstrategyfortherm.Usingocemachineproductsasanexample,eventhoughaprinterwithfaxingfunctionisatechnologicallyachievableproduct,consumerscannotndsuchaproductinthemarket.ThisimpliesthatoeringallFPsmightnotbeanoptimalstrategy.Hence,theobjectiveofthermistondtheoptimalproductportfolioandthequantitiesforproductvariantsthatmaximizeprot.Facingm(=2n1)technologicallyachievableproducts,thermhasatotalof22n11productportfoliostochoosefrom. LetusrststartbyevaluatingwhethertheobjectivefunctiontomodelGPisstrictlyconcaveinthedecisionvariables.Inordertodothis,wenotethattheHessian(seeAppendixC)isdenedas: 2(rk;j+rj;k)(k;j2f1;2;:::;mgandk6=j)representstheaveragesubstitutioneectbetweenproductskandj.Inordertoestablishconcavity,weneedtoshowthattheprincipalminorsofHalternateinsign.Althoughthiscanbeeasilyshownforthecaseofn=2functionalitieswithsomeadditionalrestrictionsonthesubstitutioneects(seeChapter2),itisanalyticallydiculttoreachthisconclusionwhenFPscanbedesignedwithn3functionalities.Alsonotethat,insomecases,concavityoftheobjectivefunctiondoesnotguaranteethatbysimultaneouslysolvingtheFOC,wecandetermine 59

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Basedonthis,westartbyformulatingtheLagrangianforourprotmaximizingmodelasfollows: (GL):GL=qT(pc)=qT(2drq)+qT; 2) (3{1) (3{2) and,ofcourse,foreachproductoeringk,qkk=08k.Thisleadstosomeinterestingobservations.Forsomeproductoeringk,ifqk>0,thenwehavek=0;otherwise,whenk=2(Pmj=1;j6=kk;jqjdk)>0,qk=0.Itisalsopossiblethatboththethequantityoeringandthelagrangianmultiplierarezerosimultaneously,whichoccurswhenthereisaboundarysolution.Thecontentofkimpliesthataproductkwitha\relativelysmall"protmarginismorelikelytohaveapositivelagrangianmultiplierandhence,notbepartoftheproductportfoliowhiletheproductwith\relativelylarge"protmarginismorelikelytobeincludedintheproductportfolio.However,ahighprot-marginproductmaynotbeselectedifthesubstitutioneectswithotherproductsaretoostrong.This`ruleofthumb'withasymmetricsubstitutioneectsresonateswithsomeoftheresultsin[ 93 ]whentheyfocusedonlyonsymmetricsubstitutioneects. Nowthatwehavesomeinsightsintowhichproductoeringswillprobablybeincludedinasolutiontoourproblem,letusturnourattentiontoidentifyingtheoptimalsetofproductoerings.Inordertodothis,werstdeneaproductportfolioSasonewhichconsistsofspecicnon-zeroquantityoeringsforeachproductincludedinthe 60

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S=qTSrTSqS=dTSAdj[S]dS Incaseofsymmetricsubstitutioneects,thenon-zeroquantityoeringvectorqSandtheassociatedprotcanberestatedas: S=dTSAdjr[S]dS whenwehavesymmetricsubstitutioneects. 61

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IftheprotfunctionassociatedwithaparentportfolioSisconcave,thisisanimportantfactorindeterminingtheoptimalityofthatportfolio.Wecanassesstheconcavityoftheassociatedprotfunction,wecandothissimplybyensuringthatallprincipalminorsofShavepositivedeterminants.Asaresult,ifaproductportfolioShasanassociatedprotfunctionwhichisconcave,thethefollowingtheoremestablishesanimportantdominancerelationshipbetweenparentandchildportfolios. 1.IfjS0j>0,thenS0dominatesS;else 2.SdominatesS0. Thekeyimplicationofthisresultisasfollows.AparentportfolioS0dominatesachildportfolioSifandonlyifS0hasanassociatedprotfunctionwhichisconcaveandthequantityoeringsforallproductsincludedinSareallpositive.Inessence,thisalsoimpliesthatS0dominatesall itschildportfolios.Thisresultcanbeusedtoreducethethenumberofpotentialproductportfolioswhichneedtobeevaluatedsothatthermcanidentifyanoptimalportfolioofproducts. WeusethedominancerelationshipestablishedthroughTheorem3.1toproposeasearchalgorithmforndingtheoptimalproductportfolio.Morespecically,bystartingwithsmallerchildrenportfoliosandaddingsingleproductvariantstotheseportfolios,allpotentialportfoliosforevaluationcanbeidentied.Thedeterminantoftheaveragesubstitutionmatrixforeachchildrenportfolioisthebuildingblockofeachpotentialparentportfoliossincethesehavealreadybeenevaluatedandcomputed.Notethata 62

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1.Seti=0atiteration0.MaintainalistthatcontainsanullportfolioS=f;g. 2.ForeachconcaveportfolioSinthelist,addanotherproductjsuchthatj=2S.HenceeveryS[fjgisan(i+1)-productportfolio. 3.If,atiterationi+1,thereisno(i+1)-productportfoliowithconcaveprotfunction,GotoStep6;otherwise,continuetothenextstep. 4.Foreach(i+1)-productportfoliowithconcaveprotfunction,examinetheoptimalquantitiesbysolvingtheFOCsoftheprotfunction.Foreachportfolio,ifallquantitiesarepositive,addthisportfoliotoalistofconcavefeasibleparentportfolioandremoveallchildrenportfoliosofthisnewly-addedportfolio. 5.Seti=i+1,GotoStep2. 6.Comparetheprotsoftheportfoliosinthelistofconcavefeasibleparentportfolio,andtheoptimalproductportfolioistheonewithhighestprot. Eachiterationinthesearchalgorithmsavescomputationtimethroughtwomechanisms.First,itiseasytochecktheconcavityoftheprotfunctioncorrespondingtonewlycomposedportfoliosthroughanevaluationoftheprincipalminorsoftheassociatedmatrix.Thus,ifthisisnotthecase,wesavecomputationtimebynotproceedingtocomputethequantityoeringsofalltheproductsinaportfoliothroughtheFOC.Second,eveniftheobjectivefunctionforagivenportfolioisconcave,itispossiblethatthequantityoeringsforallproductsincludedinthisportfolioarenotpositive.Inthiscaseagain,wedonotincludesuchaportfolioasapossibleonetoevaluateforidentifyingtheoptimalportfolio. Areasonablequestionfollowingtheresultsaboveconcernsthespecicpropertiesoftheoptimalportfolio.Unfortunately,duetothecomplexityofthegeneralmodeland 63

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3.4 ,weinvestigateaspecialcaseofFPdesignwherearmcurrentlyoeringnSPswouldliketoobtaininsightsastowhethertoalsodesignasingleall-in-oneFPandoerittothemarket. AIOM=nXk=1qk(akckqkrk;fqf)+qf(afcfqfnXk=1rf;kqk)(3{7) Tostartwith,wedeneseveralproductportfolios:(a)APS(AllProductStrategy)whichconsistsofallSPsandtheFP(i.e.,APS=f1;:::;n;fg);(b)NFPS(NoFusionProductStrategy)whichconsistsofallSPs(i.e.,NFPS=f1;:::;ng);(c)SFPS(SingleFusionProductStrategy)whichconsistsofonlythefusionproduct(i.e.,SFPS=ffg);and(d)PFPS(Partialfusionproductstrategy)whichconsistsofsomeSPsandthefusionproduct. Forthisspecialsetting,theprocesstoidentifyanoptimalportfolioisrelativelystraightforwardandweproceedasfollows: 1.EvaluateportfolioAPSasfollows. 64

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2.EvaluateportfolioNFPS.Inthiscase,itistrivialtoshowthatforthisportfolioqk=dk8k,qf=0,andSFP=Pni=1d2k. 3.EvaluateportfolioSFPS.Inthiscase,itistrivialtoshowthatforthisportfolioqf=df,qk=08k,andF=d2f. 4.EvaluateallpossibleportfoliosPFPS.UsingthedominancerelationshipestablishedthroughTheorem1,compareallpossibleparentportfoliosinthissettoidentifythe\best"PFPportfolio(denedasonewhichprovidesthemaximumprot).Ifsuchaportfolioexists,gotostep6,elsegotostep5. 5.CompareportfoliosNFPSandSFPSandtheonewiththehigherprotisoptimalandStop. 6.Comparethe\best"PFPSportfolioinstep4totheNFPSportfolioandtheonewiththehigherprotisoptimal. Asisobvious,Step4isthisprocessiscomputationallyintensive.However,giventhesparsityof,itismucheasiertoimplementtheprocesstosearchamongallPFPSportfolios.RecallthateachpotentialPFPSportfoliocontainssomecombinationoftheSPsandthefusionproductf.DeneKasthesetofSPsincludedinaspecicPFPS-callthisportfolioPFPSK.Forthisportfolio,deneK=Pk2Kdkk;fandK=1Pk2K2k;f.ThenifK0,theprotfunctionassociatedwithportfolioPFPSKisconcave.Further,theoptimalquantityoeringsforallproductsincludedinportfolioPFPSK,caneasilybecomputedasqf=dfK 65

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Theresultsforthisspecialsetting(wherearmcanoerasingleFPincorporatingthefunctionalitiesofndistinctSPs)indicatethatitishighlylikelythattheFPwillbeincludedintherm'soptimalproductportfolio(sinceitisincludedinSFPS,APS,andallpossiblePFPS).FromanFPdesignperspective,thisimpliesthatarmshouldmakeanattempttodesignanFPwhichintegratesthenfunctionalitiesincludedineachSP.Inthenextsection,wefocusonthegeneralcasewherethermcandesignFPswithanycombinationofnfunctions.Giventhatthisproblemisanalyticallycomplex,weresorttoanumericalanalysisbasedonsecondarydata. 3.4 isrelatedtotheproductdesigndecisionwhenarmcanoeranall-in-onedevicewhichintegratesnfunctionstogether.SincethermhasthetechnologytofusenSPstogether,itislikelythattechnologyisavailabletofusesubsetsofthecomponentproducts.However,becauseofthecomplexityofthismoregeneralproblem,analyticresultsarediculttoobtain.Inthissection,weperformnumericalanalysistogainfurtherinsightintothisproblem.Specically,thedynamicsofchangesin 66

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3.3 Forthenumericalexamples,weuseSonytoillustratearmwhooersfusionproductsbasedondigitalcamera,MP3musicplayer,andcellphonefunctionalities.SonyisamanufacturerofdigitalcamerasandMP3players,anditalsomaintainsajoint-venturewithEricssontoproducecellphones,whichadoptsSony'stechnologytoprovidemulti-functioncellphone[ 83 ].Sonyowns50%shareofSonyEricsson(SEhereafter);hence,Sonyhasstronginuenceinthejoint-venture'sstrategy.Moreover,recentarticleshavediscussedhowSEhasadjustedthenumberofproductvariantsthatitisprovidingtothemarket[ 85 ].Thepresidentofthecorporationhascommentedthat,\Wearecondentthattheremainderoftheyearwillseeusfurthercapitalizeonthisnewbroaderportfolio,"whichincludescellphone,cameraandMP3productvariants. Weindexthecellphone,thedigitalcamera,andtheMP3playeras(single-function)products1,2,and3,respectively.IntermsofSPs,productmodelsSET105,CyberShot,DSC-S700,andWalkmanNWZ-A816areexamplesofproducts1,2,and3,respectively.SinceallcellphonesoeredbySEin2007haveextrafunctions,weuseanoldermodel(T105)asanexampleofasinglefunctioncellphone.Products4,5,and6aresome-in-oneproductswhichcombinetwoofthesingle-functionproductstogether.SEK550iisanexampleofproduct4thatintegratesfunctionsofdigitalcameraandcellphone.Sonydoesnotprovideproducts5and6tothemarketthatcombineacellphoneandanMP3playeroradigitalcamerawithanMP3player.Forthethree-functionall-in-oneproduct,SEW810iisanexampleofproduct7inourmodel.Notethatsincethecameraphonesnormallyadoptlowimageresolution,wechoosealow-enddigitalcameramodelandonlyanalyzetheimpactoffusionproductsonthelow-endmarket. Regardingprotmarginestimations,weusedatafromSonyandSE'sannualreport.TheaveragegrossprotmarginrateofSEinthelastthreeyearis28%,whileSony'sannualreportshowsthatthecompany-widegrossprotmarginis37%.Thereisno 67

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88 ],Canon'sdigitalcamera[ 87 ],andCreative'sMP3player Tocharacterizetheimpactofthesubstitutionmatrixontheoptimalsolution,weactuallyconsidertwodierentsamplematricesAandBasshowninTable4andTable5.Thesetwomatricesallowustocapturesomeeectsofthelandscapeofsubstitutabilityindicesontheoptimalsolutions.ThevaluesshowninmatrixAaremorerealisticforSony'sthreeproductmarket,inthattherearerelativelyhighsubstitutionindicesbetweentheproductswhichcontainsimilarfunctions.Thesesingle-functionproductsunderconsiderationarefairlycongruent,inthatitiseasytofusethemintoasingleproductandthenewlyfusedproductisservingasimilarmarketastheoriginalsingle-functionproducts.Incontrast,thevaluesshowninmatrixBreectthoseassociatedwithamoreincongruentsetofproducts.Thesubstitutionindicesarelower,asthecombinationproductsseemtocreateanewmarketwithlessoverlapwiththeoriginalmarketsforthesingle-functionproducts. WeconsidersymmetricsubstitutionmatricesforthesevenproductsasshowninTables4and5.Notethatthisanalysisalsoappliestoanyasymmetricsubstitutionmatriceswhichcanbe`averaged'tondthesetwomatrices.Azerointhematrixdenotes

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TheresultsofsixdierentnumericalexamplesareshowninTable6.Asummaryoftheinputparametersaswellasthecorrespondingoptimalportfolioandobjectivevaluesareshownforeachexample.Therstthreecasescorrespondtothecell-phone,digitalcamera,andMP3playermarketsandusematrixAforthesubstitutionmatrix.Case1reectstheinitialscenariousingparametersdescribedinthepreviousparagraphswhereasinglefusionproductistheoptimalsolution.Inthissituation,itappearsthatoeringasingleall-in-oneproductcapturesthemostprotfortherm.Cases2and3showtheimpactofchangesinspecicprotmarginparametersontheoptimalportfolio.Forcase2,anincreaseintheprotmarginfortherstsingle-functionproduct(i.e.,thecellphone)hasnoeectontheoptimalportfolio. Forcase3,anincreaseintheprotmarginforthethirdsingle-functionproduct(i.e.theMP3player)changestheoptimalportfolioslightly.Inthiscase,itisnowoptimaltosellthesingle-functiondigitalcamera,single-functionMP3playerandtwo-functioncameraphonetothemarket.Thisresultissupportedinthepressbyanecdotalevidencewhichpointstothepopularityofcameraphone.TheresearchreportreleasedbyABIResearchin2005[ 86 ]projectsthattheshipmentofcameraphoneispredictedtosurpasstheshipmentofsingle-functioncellphone.Thelow-enddigitalcamerasalesalsoshrinksignicantlybytheencroachmentofthehigh-enddigitalcameraandthecameraphone. TheremainingexamplesutilizethematrixBwhichreectsamoreincongruentproductsetwithlowersubstitutionindices.Ingeneral,theoptimalproductportfoliofortheseexamplesincludesmoreproductvariantsandismoresensitivetoparameterchangesthanthoseshownformatrixA.Incomparingcase1tocase4,theoptimalproductportfolioincludesboththeall-in-onefusionproduct(i.e.product7)andalsoa 69

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MatrixA 11000.80.800.820100.600.60.6300100.90.90.940.80.6010.850.850.850.800.90.8510.90.95600.60.90.850.910.9570.80.60.90.80.950.951 Table3-4. MatrixB 11000.50.500.520100.600.60.6300100.90.90.940.50.6010.60.70.750.500.90.610.90.95600.60.90.70.910.9570.50.60.90.70.950.951 Table3-5. Changingtheprotmargins(d1andd2)andtheresults. Cased1d2d3d4d5d6d7Opt.PortfolioqProt 1Ai;j24383850535867f7gf67g$44892Ai;j30383850535867f7gf67g$44893Ai;j24384450535867f2,3,4gf12.5,44,42.5g$45364Bi;j24383850535867f4,7gf6,62.7g$45075Bi;j24443850535867f2,5gf44,53g$47456Bi;j24384450535867f1,2,3,4gf4.5,14.6,44,39g$4548 some-in-oneproduct(i.e.product4).Specically,thosecustomersinthemarketforonlytherstorsecondsingle-functionproducts(i.e.thosecontainedinproduct1orproduct2)willchoosebetweenthetwodierentproducts(i.e.product4orproduct7).Customersinthemarketforthethirdsingle-functionproduct(i.e.product3)willbuytheall-in-onefusionproduct(i.e.product7). Incases5and6,theprotmarginparametersarevariedforSPs2and3andtheoptimalproductportfolioforthesecaseschangessignicantly.Incase5,theprotmarginforproduct2isincreased.Asaconsequence,theoptimalproductportfolionowincludesthesingle-functionproduct2andthesome-in-oneproduct5,whichindicatestherm 70

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Someadditionalmanagerialinsightsbasedonthisanalysisareasfollows.First,whenthesubstitutioneectsarerelativelyhigh,aportfoliocontainingasmallernumberofproductsislikelytobeoptimal.Ifasingleall-in-onefusionproducthashighmargins,thenthismodeldominatestheproductportfolio.However,whenastandalonesinglefunctionproducthasrelativelyhighprotmargins,thenitislesslikelythatafusionproductcontainingthisfunctionshouldbeoered.Instead,thermshouldsellthesinglefunctionproductindependentlyandcombineotherlowermarginfunctionsintoasome-in-oneproduct.Lastly,smallchangesinparametervaluescancauselargechangesintheoptimalportfolio.Whenthesetofproductsunderconsiderationissomewhatincongruent(i.e.thesubstitutioneectsarelow),thentheproductportfolioingeneralissomewhatlargerandmoresensitivetosmallchangesintheprotmargins. 71

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Thereareseveralmanagerialinsightsgeneratedfromtheanalysisofthemodel.Ingeneral,theoptimalportfolioandhencethe`best'productdesignsareafunctionoftwoimportantparameters:protmarginandsubstitutioneects.Aproductwithhigherprotmarginandsmallersubstitutioneectswithotherproductsismorelikelytobeincludedinanoptimalportfolioandthus,thisproductdesignshouldbeinitiated.However,facinganypossiblecombinationoffunctionintegrations,substitutionandcannibalizationcannotbeavoidedifthermintendstooermanydierentproducts.Sincetherm'sobjectiveisprotmaximization,acarefulinvestigationandevaluationofall(single-function,some-in-one,all-in-one)possibleproductsisthebestwaytoachieveoptimalitywhiletakingintoaccountthecannibalizationeects. Ingeneral,thermshouldnotmanufacturetoomanydierentfusionproducts(FPs)simultaneously.StrongcannibalizationeectsamongtheseFPsimplyselectingtherightfusionproductisimportant.Inessence,thermshouldnotcomplementtheFPwithtoomanycomponentorotherFPswhenthesubstitutabilityindicesarehigh.Itisalsointerestingtonotethatourgeneral-formmodelcanalsobeappliedtotheproblemofproductvarietyinacertainmarketsegment.KraftFoods,Inc.[ 84 ]foundtheyhavelaunchedtoomanysimilarproductsinonemarketsegment.Introducingtoomanyproductsinducesstrongcannibalizationamongtheirownproducts. Incontrast,theproductportfolioandcorrespondingproductdesignismorediculttodeterminewhencannibalizationeectsaresmall.Thissituationcanoccurwhenthesetofsingle-functionproducts(SPs)underconsiderationareincongruent,orwhenthefusionproducts(FPs)createasignicantlydierentmarketthantheoriginalSPs.Numerical 72

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114 ]categorizestheadoptersintovegroupsbasedonthetimingoftheirpurchase:innovators,earlyadopters,earlymajorities,latemajorities,andlaggards. Sofar,productdiusionresearchfocusesonthediusionwithinaproductcategory.AswepointoutinChapter1,thecurrentdiusionmodelsdonotcapturethetransitionfromsingle-functionproductstofusionproducts.Inthischapter,weconstructanewproductdiusionmodelthatisasparsimoniousaspossibletocapturethediusionprocessoftheFPandtheirinteractionswiththediusionprocessesfortheSPs.AfterthelaunchoftheFP,theFPstartsencroachingonthedemandoftheSPsandchangestheirdiusionpaths.Weareinterestedintheoptimallaunchtimedecisionforthefusionproductandthefactorsthatinuencethedecision. WeobservethattheintroductionoftheFPinuencesthediusionofSPsinmanyways.Toillustrate,radioandCDplayerfunctionshavebeenintegratedsoonafterthecompactdiscwasusedasamediaofmusic,andtheradioandCDcombohasbecomeamainstreamproduct.Shipmentsofthesingle-functionPDAalsosuerfromthegrowthofthePDAphonesandthesmartphones.AccordingtoIDC'ssurvey,single-functionPDAshipmentsweredown22.3%intherstquarterof2006comparedtothesamequarterayearagoandthatwastheninthconsecutivequarterofyear-over-yeardecline.AcombinedproductofTVandDVDhasbeenintroducedinthemarketforawhilebutitfailstohave 74

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Thediusionandsubstitutionprocesswhereafusionproductgraduallyreplacesitssingle-functionproductshasnotbeeninvestigatedintheliterature.Thefollowingquestionsrelatedtoproductdiusionstillneedtobeanswered.(a)Howlongwillittaketopenetratetoacertainlevelofmarketacceptance?(b)Whenshouldthermintroducethefusionproduct?(c)Howdoesthemanufacturerspeedupthepenetrationofanewfusionproduct? Thephenomenonaboveissimilartothediusionprocessofseveralgenerationsofproducts,butthereisamajordierence:theresearchonthediusionprocessofseveralgenerationsonlyfocusesononeproductcategory,butthefusionproductsinuencetheproductdiusionacrossseveralproductcategories.Forexample,thecameraphonehaschangedthemarketlandscapeinthecellularphoneandthedigitalcamera.ThediusionmodelwhichtreatstheFPasanewgenerationofanSPmightnotbesucienttocaptureallofthedynamicsbroughtbytheFP.Inaddition,howwellthefusionproductconsolidatesitscomponentproductshasastronginuenceontheadoptionoftheFP.Thus,usingamulti-generationdiusionmodel,thediusionpathsderivedfromtwoSPsmightbeverydierent. Moreover,ifthereissynergyamongsomeSPsthenfusingthemtogetherintoanFPisappealingtothemarket.Fortheconsumer,thesynergyincludesspacesaving,lowertotalcost,andfunctionsynchronization.ThePDAphonescansharethecontactlistwithoutthehasslesofsynchronizationandallowtheuserstocarryonlyonedevice.Fortherm,thesynergyoflaunchingFPsismanufacturingcostsaving.Aprinter,acopier,ascannerandafaxmachinecanallsharethesameplatformandinterfacewhichmakesamultifunctionocemachinecostonlyatasmallpremiumcomparedtoasingle-functionprinter.ThecostsavingscanmakeitpossiblefortheFPbepricedlowerthanthesum 75

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Finally,weareinterestedintheroleoftheFP'smanufacturer.TheFP'smanufacturercanbeannewentrantoranincumbentofoneortwocurrentSPs.Intheocemachinemarket,themanufacturerofthescannerandtheprinterisalsothemanufactureroftheall-in-oneocemachine.Butinthepersonalportabledevicemarket,therstPDAphonewasintroducedbyPalm,whichisaPDAmanufacturer,whilethesuccessfuliPhonewasintroducedbyApple,whichistheleaderinthedigitalmusicplayermarket.WewillalsoanalyzetheimpactofthecompetitiveroleoftheFP'smanufacturerontheFP'slaunchdecisionandonthediusionprocesses. Innextsection,wewillreviewtheliteraturerelatedtothetopicofproductdiusionandhighlightthosemostrelatedtoourmodel. 89 ]proposesanS-shapediusionpatternasanewproductisintroducedtothemarketthendiusesgraduallytothewholemarket.TheS-shapeisdenedasthecumulativesalesoftheproduct,andthesalesrateovertimeisusuallyabellshape,whichexperiencesseveralstagesfrombirth,growth,peak,todecline.Thediusionpatternhasseveralimportantcomponents:totalmarketpotential(m),innovationcoecient()andimitationcoecient()[ 102 ].Asanewproductislaunched,itrstreachessomeinnovativeadoptersinthewholemarket.Astimegoesby,theproduct'sprevalencespreadsfromthe`neighborhood'oftheinnovativeadoptersastheneighborsimitateandbecomethefollowers.Basedonthetimeofadoption,thebuyerscanbecategorizedtooneofvegroups:innovators,earlyadopters,earlymajority,latemajority,andlaggards[ 102 ].TheBassmodelisknownforitsrobustnessincharacterizingthediusionprocesswithoutincorporatingdecisionvariables. Mahajanetal.[ 102 ]pointoutthatnewproductdiusionmodelshavetwodierentstrategicdecisions:prelaunch/launchdecisionsvs.postlaunchdecisions.Bayus[ 91 ] 76

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97 ]comparetheword-of-moutheectsondurablesandnondurablesintherstadoption. Inpostlaunchdiusionresearch,Mahajanetal.[ 102 ]illustratesixapplications:timingofsuccessivegenerations,capacitydecisionswithproductdiusion([ 97 ]and[ 96 ]),determiningthemarketvalueonanticipatedpenetration([ 99 ]),marketsaturationassessmentandexpansionopportunityfortheretailers([ 104 ]),estimationoflostsalesduetopiratedsales([ 95 ]),andlostsalesduetopatentinfringements([ 103 ]). Therearemanypapersrelatedtoproductortechnologydiusion.Forasummaryoftheexistingliterature,wereferthereadertoMajahanetal.[ 100 ]andthebookeditedbyMajahanetal.[ 102 ]. Here,wereviewseveralpapersthataremostrelevanttoourfusion-productdiusionproblemandrelatedtothediusionandsubstitutionbetweenseveralgenerationsoftechnologyorproduct.Notethatmostoftheliteratureinthisareaislimitedtoaddressingsuccessivegenerationsofproductsinaproductcategory. NortonandBass[ 105 ]constructadiusionmodelforrepeat-purchaseproductswherethenewtechnologybringssuccessivegenerationsofinnovation.Dierentfrompreviousmarket-sharesubstitutionmodels(e.g.[ 94 ]),theirdiusionmodelhastheabilitytoestimateamarketpotentialandforecastthedemandtrajectory.Assumingthatarmplansforseveralgenerationsofinnovation,whereeachinnovationincreasesthemarketpotential,theirmodelcapturesthesubstitutionofsalesfromearliertolatergenerations.ByttingtheirmodelintotheDRAM'sandSRAM'sdiusion,theyfoundthatoncethenewgenerationisintroduced,thesalesoftheoldergenerationbeginstodecline.ComparedtoFisherandPry's[ 94 ]marketsharesubstitution,NortonandBassassertthattheirmodelgeneratesmoreaccurateresultsintermsofestimationofthemarketshare. 77

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112 ]investigatetheoptimaltimetointroducenewgenerationsofadurableproduct,andtheyndthatseveralfactorsprimarilyinuencetheresult:thesubstitutioneectanddiusionbetweentwoproducts,therelativemargins,andtheplanninghorizonoftherm.Theyassumethattherstproducthashighermarginbutslowsalesgrowth,andthenewextensionhaslowermarginbutexpandsthemarketpotentials.Theresultsillustratethatthermshouldintroducethelineextensionassoonasitisavailableorshouldneverintroduceitatall.However,theypointoutatcertainvalueofparameter,astaticanalysisandadynamicanalysismaygetdierentconclusionbecausetherateofgrowthisnotconsidered. MahajanandMuller[ 101 ]extendtheBassdiusionmodelthatcapturesthesubstitutionofsuccessivegenerationsinthetechnologyinnovation 112 ]\now-or-never"rulesdonotconsiderthediscountfactor.TheyapplytheirmodelinIBM'smainframe'sdiusionprocessandndoutIBMintroducedtwosuccessivegenerationstothemarkettoolate. Putsis[ 107 ]appliesthediusionmodelintothediusionofstandaloneTVsandVCRsbyconsideringbothcross-productdemandandsupplyissues.Theirempiricaldatasupportsthehypothesisthatproductdierentiationandnewproductintroductionaremorelikelytooccurwhentheexistingproductsstarttoslowatsaturationlevels. 101 ]characterizethedemandfunctioninadierentmannerthanWilsonandNorton[ 112 ].OurmodelismoresimilartoMahajanandMuller[ 101 ]. 78

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110 ]investigatesthediusionspeedof31electricalhouseholddurablesintheUnitedStatesfrom1923to1996.Theresultsshowastatisticallysignicantaccelerationonthediusionspeed.Otherfactorsaectingthediusionspeedare:economicconditions,demographicchange,whetherthereisacompetingstandardearlyinthelifecycle,andtheamountofinnovationinvestmentrequired.Theauthoremphasizesthatmanagementshouldpaycarefulconsiderationtotheprobability,timingoftakeoandspeedafterthetakeo,especiallyfortheproductwhichrequiresalargeup-frontinvestment,andhasahighuncertainpay-oandlongertake-otime. Talukdaretal.[ 108 ]investigatethediusionofsixproductsin31countries,whichcovers60%ofworldpopulation.Theyndthatthediusionofaproductintroducedearlierinonecountryisusefultoexplainthediusioncoecientsinothercountries,whilethepastexperienceofoneproductismoreusefultoestimatethepenetrationlevelofanotherproductinthesamecountry. Severalpapersaddressthetopicofparameterestimationfordiusionmodels.NortonandBass[ 105 ]assumethattheinnovationandimitationparametersovergenerationsarethesame.Theyadmitthatthisisastrongassumptionthatleadstoreasonablettotheempiricaldata.MahajanandMuller[ 101 ]assumethesameinnovativeparameterbutadierentimitationparameter.SohnandAhn[ 2 ]discussthediusionofseveralgenerationsoftechnologyfromcosttobenetanalysis.TheyuseMonteCarlosimulationtondtheinitialfactorsonthediusionfornewinformationtechnology.Also,PaeandLehmann[ 106 ]investigatethecorrelationbetweentheinter-generationtimeandthediusiondatatting.Theyreportthatthelatergenerationseemstohavesmallerinitialsales(smallerinnovationparameter)butafasterrateofgrowth(largerimitationparameter)basedontheir30pairsoftwo-generationproducts.Theyreachthisconclusionfromtheirordinaryleastsquaresregressionanalysiswhichobtainsthechangesinparametervalues(and)betweengenerations.However,VandenBulte[ 111 ]cautionsaboutthatPaeand 79

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106 ]ndingmaybeamethodsartifact.VandenBultequotesthatseveralsimulationstudies([ 109 ],[ 92 ])havethesamephenomenonobserved. Kimetal.[ 113 ]conductanempiricalmodelofthediusionoftelecommunicationproductsinHongKongandSouthKorea.Theirdynamicmarketgrowthmodelcapturesthetechnologysubstitutionaswellastheinteractionofinter-productcategoryeects.TheirdiusionttingresultsshowthattheirmodelcanmakebetterpredictionthanthegeneralBassmodel.Themarketpotentialofonecategoryoronegenerationissignicantlyaectedbyothersproductsandbytheoverallstructureofageographicmarket.However,theyalsopointoutthattheirempiricalmodelcannotanswerstrategicquestionssuchastheoptimallaunchtimeofanewproduct. Akeyquestioninuencingtherm'sdecisiontointroduceanFPconcernsitscurrentproductoeringsofSPsinthemarketplace.Earlyyearsoftheliterature,incumbentrmsarebelievedtohaveadvantageinthecompetition[ 118 ].Threeprimarysourcesofadvantagesoftheincumbentsare:(1)technologicalleadership,(2)preemptionofassets,and(3)buyerswitchingcost.However,inrecentyears,manylateentrantsleapfroggedintothemarket-leaderpositions[ 119 ].TheseleapfroggingnewentrantsincludeAmazon.com,Apple,Blackberry,andPalm.Shankaretal.[ 120 ]investigatehowlateentrantsoutsellpioneersinthepharmaceuticalindustry.Theyndthatainnovativelateentrantcancreateasustainableadvantagebyenjoyingahighermarketpotentialandhurttheproductdiusionofotherbrands.Inthischapter,wedonotinvestigatetheadvantages/disadvantagesoftheincumbentsorthenewentrant.Instead,weallowthemanufactureroftheFPtobeeitheranewentrantortheincumbentofoneortwoSPsandunderstandtheimpactofthecompetitiveroleoftheFP'smanufactureronthediusionsofallproducts. 80

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4-1 .WeassumethatthemarketcurrentlyhastwodistinctSPs,denotedas1and2,respectively.Letmibethetotaladopters(ormarketsize)forproducti(i=1;2).Weassumethat,withoutotherinterference,thedemandtrajectoryforSPiisexogenousandinuencedbytwofactors:theindependentinnovationcoecientiandtheword-of-mouth(imitative)coecienti.Notethattheproductionconstraintsanduncertaintyofdemandarenotmodeledinthispaper.Asaresult,thermalwaysproducesexactlytheamountofthedemand;thatis,thesalesrateataparticulartimeequalsthedemand.AccordingtotheBassModel[ 89 ],thesalesrate whereai=i 4{1 isknownforitsrobustnessincharacterizingthediusionprocessofanewinnovationbyassessingproperparameterswithoutincorporatingdecisionvariables.Notethattheequationassumesthecurrenttimeisatt=0.However,whenweanalyzethesalestrajectoriesfortheexistingSPs,theproductshavenormallybeeninthemarketforsometime.Weassumewhenthefusiontechnologyisachievable,theSPs1'sand2'sagesaret1andt2periodsold,respectively.Thus,weallowforthepossibilitythatthetwoSPsareatdierentstagesintheirrespectivelifecycles.Forexample,thecellularphonefortheconsumermarketintheU.S.waslaunchedintheearly80's,buttherstsuccessfulPDAfortheconsumermarketwaslaunchedin1997byPalm. 2 97 ]and[ 96 ]fordiusionmodelswhichexplicitlyconsiderproduction.3 81

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NotationandAcronyms. GiventhattheSPshavebeeninthemarketforsometime,thedemandattimetforproductishouldberevisedas: (4{2) Lett=0bethepresenttime.Fort>0,si(t)representsthesalesrateofproductiattimet.ThediusionsoftwoSPsareindependentanddeterministicwhenthereisnointerferencefromotherfactors.However,thefusiontechnologychangesthedynamicsoftheproductdiusion. Atpresenttime(t=0),themanufactureroftheFPownsthefusiontechnologyandconsidersenteringintothemarket.Fromthediscussionintheliterature,themanufactureroftheFPcaneitherbeanewentrantoranincumbent.Thismodelinvestigatestheoptimallaunchtimeofthefusionproductwhenthefusionproductmanufacturerisinone 82

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91 ].Anearly-launchednewproductwillgrabthemarketsooner,butthisstrategyalsocontainstherisksofhighdevelopmentcost,lowerqualityfrompoordesign,andfailureofproducttransition.AU-shapeddevelopmentcostfunctionisproposedbySmithandReinertsen[ 115 ],Guptaetal.[ 116 ],Murmann[ 117 ]andBayus[ 91 ].IfthermwantstolaunchtheFPimmediately,thermneedstoinvestmoreinproductdevelopment.Ifanewproductdevelopmentprojectisdelayed,thenthedevelopmentcostcanbetrimmedbyreducingthedevelopmenttime.Lettmtobethetimewithminimaldevelopmentcostofthisfusiontechnology;hence,tmrepresentthetechnologycostmatu-rity.SimilartoBayus[ 91 ],weassumethedevelopmentcostvoftheFPlaunchedattimefollowsaU-shapeasdescribedbelow. dt=(ttm)fort< ThedevelopmentcostcurveandtherstderivativeofdevelopmentcostwithrespecttotimeareshowninFigure4-1.Therstderivativeofthedevelopmentcostisdecreasing(increasing)iftheFPislaunchedbefore(after)tm,andtheminimaltotaldevelopment 83

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101 ].Theydonotconsidertheimpactofdevelopmentcost,whichmayvarywiththelaunchtimeofthenewgeneration. Figure4-1. DevelopmentCostatDierentLaunchtimeofFP. ThesubstitutionbetweentheFPandtheSPsissimilartothesubstitutionbetweenproductsofdierentgenerations.Tomakethemodeltractable,weassumethatthereisonlyonegenerationofFPconsidered.TheFPmadeavailablebythefusiontechnologyisindexedasproduct3andisassociatedwithadditionaladoptersofpopulationsizem3.Thecompositionofm3includes(1)theconsumerswhoarenotincludedinm1orm2,and(2)theconsumerswhohadpurchasedoneortwoSPsbeforethelaunchoftheFPandwill`upgrade'topurchasetheFP.VandenBulteandLilien[ 109 ]pointoutthem3cancomefrompopulationgrowth. LetbeadecisionvariablewhichisthelaunchtimeoftheFP.Thelaunchtimeiscriticaltothermbecauseitoftenimpactsonmanyaspectsofdiusion.First,toachieveanearlierlaunchtime,thermoftenneedstoallocatemoreinvestmentinproductdevelopment.Second,theearlierthelaunchofthenewproduct,themorepotential 84

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Manyfactorsmayhaveanimpactonthelaunchtimingdecision:therelativeprotabilityofallproducts,thediusionspeed,thedevelopmentcostofanewproduct,thenumberofnewadopters,andtheswitchingrateofthefuturebuyersfromtheoldproductstothenewproduct.Intherealworld,aconversecausalrelationshipmayexistwherethelaunchtimeinuencesthesefactors.Tosimplifythemodel'scomplexity,weassumeonlythedevelopmentcostofproductintroductionisaectedbythelaunchtimedecision.Thetotaladoptersm3,theprotmarginofFP,theswitchingrate,andthediusionparametersareindependentofthelaunchtime.Similartoexistingliteratureonmulti-generationdiusionmodels,weassumethatthelaunchtimeoftheFPwillnotimpactthevaluesofotherparameters. However,thelaunchofFP3providesthefutureadoptersinm1andm2anoption.NortonandBass[ 105 ]andMahajanandMuller[ 101 ]bothassumeanewgenerationproductexpandsthemarketandthesubstitutioneectbetweenthenewandoldgenerationsoftheproductiscapturedbysomeproportionofconsumersfortheoldgenerationproductthatwillswitchtoanewversionoftheproduct.WehaveasimilarassumptionandweallowdierentswitchingratesforthetwoSPs.Normally,theSPwithahigherswitchingratehasahighersimilaritytotheFPandwecallitthebaseSPoftheFP,andtheSPwithsmallersubstitutioniscalledthenon-baseSP.Forexample,anall-in-oneprinterworksprettywellasaprinter(baseSP)andlesswellasascanner(non-baseSP).Forthefuturebuyersofthethesingle-functionprinter,theconsumersnormallybuyeitherasingle-functionprinteroramulti-functionprinter.Specically,itismorelikelythatconsumersfortheprinterwillswitchtothefusionproduct.Conversely,thefuturebuyersofasingle-functionscannerarelesslikelytopurchasethefusionproductsincethescanninginthefusionproductisthesecondaryfeature. 85

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NowweconstructthesalestrajectoriesafterthelaunchoftheFP.Tosimplifythenotation,wedropthetimeargumentinrelatedvariableswhenpossible.LetsnibethesalesofproducticonsideringtheconsumerswitchafterthelaunchoftheFP,then (4{5) where0Ri<1(i=1;2)representstheswitchingrateofthedemandofSPiswitchingtotheFP,andsm33=m3(1+a3)b3eb3(t) 89 ].NotethatMahajanandMuller[ 101 ]useasimilarformtocapturetheswitchingfromtheoldtothenewgeneration.TheexpressionRisi(i=1;2)representsthefutureadoptersthatswitchfromSPi.However,duetooverlappingcustomerneeds,onlyw(s1R1+s2R2)willpurchasetheFP. Letd1,d2andd3betheunitprotofproducts1,2,and3,respectively.Wedonotconsiderthediscountfactorinourobjectivefunctionfortworeasons.First,itisdiculttoidentifywhenandhowmuchthedevelopmentcostoccursatanypointoftimesincethiscostoccursbeforethelaunchtime.Second,omittingthediscountfactorallowsustoidentifyotherfactorsinuencingtheoptimalsolution.Therm'sgoalistondtheoptimallaunchtimewhichmaximizestheirprot. 86

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Theobjectivefunctionsofthermunderthethreescenariosareasfollows. maxI=ZT3[d3sn3]dtv()maxII=Z0[d1s1]dt+ZT3[d1sn1+d3sn3]dtv()maxIII=Z0[d1s1+d2s2]dt+ZT3[d1sn1+d2sn2+d3sn3]dtv() TherminscenarioIisanewentrantandisconcernedchieywiththeprotoftheFPafterthelaunch.TherminscenarioIIneedstoevaluatethetotalprotfromSP1beforetheFP'slaunchandthetotalprotofSP1andFP3afterthelaunch.TheobjectivefunctionoftherminscenarioIIIincludestheprotofSPs1and2beforetheFP'slaunchandthetotalprotofallproductsaftertheFP'slaunch.Taketherstderivativeoftheprotfunctionswithrespectto,weobtaindI 87

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(4{6) (4{7) (4{8) Unfortunately,theoptimallaunchtimessolvedbytherstorderconditionsaboveareinacomplicatedform 112 ]mentiontheoptimallaunchtimesolutioncanbefoundbytakingthederivativeoftheprotfunctionwithrespecttothelaunchtimedecisionandndthevalueofthelaunchtimewhenthederivativevanishes.However,theyalsopointoutthatthevalueoftheoptimallaunchtimeis\sucientlycomplicatedthatitischallengingtogetinsightaboutitsimplication."MahajanandMuller[ 101 ]useoptimalcontroltheorytoinvestigatetheoptimalitycondition,butdonotobtainaclosedformsolution. 88

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Thesecondderivativesoftheprotfunctionswithrespecttoarepresentedbelow.Since_s1,_s2,and_sm33canbeeitherpositiveornegativedependingontheincreasingordecreasingsalesrates,theglobalconcavityoftheprotfunctioncannotbeguaranteed.d2I EventhoughtheFOCisincomplicatedformandtheprotfunctioncanbeneitherconvexorconcave,wecanstillobtainthecandidatesoftheoptimallaunchtimebysettingtheFOCzero.NotethattheFOC'sbeingzeroisjustanecessaryconditionoftheoptimalsolution. FromthecompositionofdI 89

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Whendi Fromtheanalysisabove,weknowthatnoclosed-formanalyticalsolutioncanbeobtained.Duetothisconstraint,wealsocannotobtainthesensitivityanalysisontheoptimalsolution.Inthenextsection,weexemplifymanysetsofnumericalexamplestostudytheoptimalFPlaunchtime. 90

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Intherealworld,theSPsmayhavedierentmarketsizesandprotmargins.Toreectthissituation,inournumericalexamples,weletSP2havealargermarketsize(m2>m1)andahigherunitprot(d2>d1) 1.5 ).Forexample,aPDAphonewhichiscategorizedinthePDAshipmentbyamarketresearchrmcanbeincludedincellphonesalesinanotherrm.Thesetworeasonsmaketheindustrialdataunreliableforttingtheproductdiusions.9 91

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90 ].Notethat,indicatesthediusionspeedmultiplieroftheFPwithrespecttothediusionspeedoftheSPs1and2.Whenisgreaterthanone,theFPhasafasterdiusionspeedthantheSPs.Inthebasecase,weassumethatthediusionspeedoftheFPisthesameasthediusionspeedoftheSPs. Basedonthescenarioswedescribeabove,thefusionproductmanufacturercanbeoneoffourdierentroles(I)atotalnewentrant,(II.1)amanufacturerofSP1,(II.2)amanufacturerofSP2,and(III)amanufactureroftwoSPs.Table 4-2 liststheoptimalsolutionsfromallcasesandallfourscenariosconductedinthispaper.Insection 4.5.1 wecontrasttheimpactofdierentlaunchtimesonthediusionprocesses.Insection 4.5.2 ,wecomparetheresultsamongfourscenarios.Theimpactsofparameterchangeswillbediscussedinsections 4.5.3 to 4.5.8 92

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OptimallaunchtimeofFPandtheprotunderfourscenariosand31cases. 1=2=0:0049;1=2=0:644;3=1;3=1;=1;t1=2;t2=4;T3=20; 93

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Figure4-2. ExamplesofCumulativeSales. Figures4-2.1and4-2.2areintendedtoillustratetheimpactofalternatefusionproductlaunchtimesonthediusionforallproducts.Figure4-2.1showsthemarketpenetrationiftheFPislaunchedat=1.AstheFPislaunched,thecumulativesalesforSPs1and2increasebysmallerratesassomepotentialadoptersswitchtobuytheFP.Eventually,thecumulativesalesofSPs1and2dropsfrom100to52.1,andfrom200to149.4afterthelaunchofthefusionproduct.Conversely,thecumulativesalesofFP3increasesfrom200to241.4.ThetotalunitsofSPsdrop98.5butitonlygets41.1unitsofFPincreases.Thedierenceisduetotheoverlapofconsumers.SomeconsumerswhohaveneedsintwoSPseventuallyswitchtotheFPandjustbuyoneFPinsteadoftwo. Figure4-2.2showsthemarketpenetrationiftheFPislaunchedat=3.IftheFPislaunchedlater,suchasinFigure4-2.2=3,thentheimpactsoftheFPtotheSPsaremoderated.ThecumulativesalesofSPsremainintactbeforetheFPislaunched.The 94

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Next,weinvestigatethefactorswhichinuencetherm'soptimallaunchtimedecisionforthefusionproduct. 4-2 andtensub-guresinFigure4-3showthatthemoresubstitutionthattheFPhaswithitscurrentSP(s),thegreaterthecannibalizationconcernsfortherm,andthelaterthermshouldintroducetheFP.ThecannibalizationeectishighestinScenarioIII,thenScenarioII.2,thenScenarioII.1,thenScenarioI,whichhasnoconcernofcannibalization. TheresultsarenotsurprisingbecauseanewentranthasnothingtoloseandarmwhooersSPsandFPmustbeconcernedwith(1)theincreasedsalesoftheFPwhichcomeswiththedecreasedsalesofSPs;(2)somefutureadopterschooseto\buyoneFPinsteadoftwoSPs,"whichisreectedbyparameterw.Weshouldnotethatthecannibalizationiscapturedbymanyfactors,includingtherelativemagnitudesoftotalfutureadopters,unitprots,theswitchingrate,andthedegreeoftheoverlap.Dierentscenariosalsoreectdierentcannibalizationeectsdependingontherm'smixofcurrentproductoerings.Forexample,inFigure4-3.8,therminscenarioII.1actsmorecloselytotherminscenarioIwhenthetotalmarketisrelativelylower(m1=50).Whenm1=200,therminscenarioII.1hasmorecannibalizationconcernsincem1islarger;asaresult,thegapintheoptimallaunchtimebetweenscenariosII.1andIislarger.Thesameparameterchangemayhavedierentdegreesofimpactonthermsindierentscenarios.InFigure4-3.9,thegapofoptimallaunchtimesbetweenscenariosII.1andII.2iswiderwhenthepotentialcannibalizationislarger.AlargerR2fortherminscenarioII.1isbenecialsincemoreconsumersfromm2willswitchtobuytheFP;however,tothe 95

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1.5 ,wementionthatthesynergyoftheFPmayincludespacesaving,lowertotalpurchasingcost,andfunctionsynchronization.ThereareseveralwaysthatthesynergyoftheFPisreectedinthemodel.First,whentwofunctionshavegreatersynergy,thediusionoftheFPmaybefaster.Second,whentheFPhasgreatersynergytointegratetwofunctionstogether,itnormallyhasahigherunitprot.Third,theFPmighthasalargernumberoffutureadopterswhenithasgreatersynergy. NortonandBass[ 105 ]usethesameinnovationandimitationparameterstotthediusiondataofdierentgenerationsofDRAM.However,vandenBulteandLilien[ 109 ]pointoutthatBassmodelsdoesnotaccountthedeclinesofrealprices,improvingperformancesandincreasingdistributionpenetration.Thesefactorsincreasethetotaladoptersandresultinadownwardpressureontheestimates(i.e.,and).VandenBulte[ 110 ]investigatesthechangesofthediusionspeedof31electricaldurablesintheUnitedStatesfrom1923to1996.Hedenesdiusionspeedasthetimetoreachacertainmarketpenetrationlevelandmeasuresitbytheslopecoecientofthelogisticdiusionmodel.Thevarianceofdiusionspeedisprimarilyexplainedbythepurchasingpower,thedemographics,andthematurityoftheproducts.Excludingthevariance,thisstudyndsthatthediusionspeedisincreasingwithstatisticalsignicance. Basedontheaboveresearch,weuseamultipliertorepresentwhethertheFPhasanequalorlargerdiusionspeedthanitscomponentSPs.Inthebasecasewesetthefusionproduct'sinnovationandimitationparametersoftheFPatthesamelevelastheSPs(=1).Incases1to3,wesetat1.1,1.2,and1.3,respectively.Table 4-2 showsthat,inallscenarios,thediusionspeedhasnosignicantimpactontheoptimallaunchtimeandthetotalprotwhenotherparametersremainunchanged.Eventhoughthe 96

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Optimallaunchtimeofthefusionproductversusvariousfactors. 97

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IfthesynergyofthetwofunctionsisreectedontheFP'sunitprot,thentheFP'soptimallaunchtimeisstronglyinuenced.Cases4,5,and6arecomparablesituationstothebasecasewithalternatevaluesfortheFP'sunitprot.TheresultsinFigure4-3.2showthatwhentheFPislessprotable,thelaunchtimeshouldbepostponedtomorecloselymatchthetimeoftechnologymaturity.ThedevelopmentcoststructureinourmodelmakesouroptimallaunchtimedierentfromWilsonandNorton's[ 112 ]\nowornever"andfromMahajanandMuller's[ 101 ]\noworat-peak"conclusions.WhenthereisahigherunitprotfortheFP,thelaunchtimeshouldbeearlierinordertocapturemoredemandfromtheSPs.ItshouldbenotedthattheFP'soptimallaunchtimeshouldbenolaterthanthetechnologycostmaturity,whichoccurswhentheFPhasarelativelyhighunitprotcomparedwiththetwoSPstogether.IftheFPislessprotable,itispossiblethattheoptimallaunchtimecanbepostponedaftertmunderacertaincircumstance.WhentheFP'sprotisonlyslightlylargerthanSP2,thelowd3willcausesomeprotlossduetotheswitching\fromtwoSPstooneFP"thusdeterringthelaunchoftheFP. KurawarwalaandMatsuo[ 98 ]ndtheinnovativeandimitativeparametersareeasytoassess,butthemagnitudeofthetotaladoptershashighuncertainty.Cases7,8,9andthebasecaseshowthattheFP'soptimallaunchtimeisveryinsensitivetovariousmarketsizesoftheFP(Figure4-3.3)whenthecannibalizationisstrong.TheresultsmeanthatifthehighersynergyoftheFPisrepresentedbymorefutureadopterswhileotherconditionsremainthesame,thentheFP'soptimallaunchtimeisnotmuchdierentfromthecasewithalowersynergyFPforrmswithexistingproducts.ForthermsinscenariosIandII.1,FP'smarketsizehasstrongerinuencetotheoptimallaunchtime. 98

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Cases10,11,12andthebasecasecomparedierentslopesofthedevelopmentcostcurves,whichisrepresentedby.Figure4-3.4showsthatadevelopmentcostcurvewithasteepslope,whichhasalarger,leadstoalateroptimallaunchtimeoftheFP.Furthermore,theimpactontheoptimaltimetomarketissizable.Astime-to-marketbecomesmorecostly,thermshouldwaittillthefusiontechnologyismoremature. Cases13,14,15andthebasecasecomparevariousvaluesforthetechnologycostmaturity.WendthattheFP'soptimallaunchtimeshouldbeearlywhenthefusiontechnology'smaturityisearly.Whenafusiontechnologywillbematureimmediately,itimpliestheintegrationoffunctionisnotdicult.Thetechnologybreak-throughofchipdesigninrecentyearsshowsthesignofamaturefusiontechnology,thereforemanyfusionproductsareavailablesoonafteranewfunction(e.g.,MP3player,digitalcamera)isinventedandoeredinthemarket.Ifthefusiontechnology'smaturityislate,theconvexcostcurvehindersthermfromanearlylaunchoftheFP. 99

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Inthissection,weinvestigatetheimpactoftheagesoftheSPs.SincethefusiontechnologyappearsverysoonafterthelaunchofthelaterlaunchedSP,weinvestigatetheimpactofvariousvaluesfort2 13 EvaluatingtheimpactofSPageonoptimallaunchtime,wendthatthecannibalizationisapossibleexplanationforthedierence.Whenthecannibalizationisweak,asaresult,asSP2agesanditsdemandisclosertopeak,thermshouldlaunchtheFPsoonertocapturethedemandswitch.Butifthermhasstrongdegreeofcannibalizationconcern,thermpostponesthelaunchofFPwhenSP2isyoungsincetheswitchfromSP2isalsosmallatthismoment.Ift=0isabouttheexionpointofSP2'ssalesrate,thenthesalesrateofSP2isatitsmaximumincreasingrate.Inthiscase,duetoalargerswitchoffromSP2totheFP,thermshouldlaunchtheFPearlier.Thedecreasingthenincreasingoptimallaunchtimealongwitht2onlyoccurswhenthecannibalizationisstrong(i.e.,scenariosII.2andIII).EventhoughtheimpactsontheoptimaltimeinscenariosII.2andIIIarenotinuential,insomesettingstheimpactcanbestronger. Cases19,20,21andthebasecasecomparetheoptimallaunchtimeoftheFPfordierentvaluesofthelengthoftheplanninghorizon.SimilartoWilsonandNorton[ 112 ],wendthattheplanninghorizonisadecisivefactorfortheoptimallaunchtimewhen 100

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Toaddressthesubstitutioneects,weinvestigatetheimpactofdierentdegreesofswitchingrateR2.AlargervalueofR2meansthatahigherproportionoffutureadoptersmayswitchtotheFP.ThehighertheR2is,thehigherproportionindemandofSP2willbesubstitutedfortheFP.Cases22,23,24andthebasecasecomparetheimpactofdierentdegreesofR2.TheresultsinFigure4-3.9showsthatwhentheFP'ssubstitutionrateishigher,thermshouldlaunchtheFPearly.NotethattheimpactofR1issymmetrictoR2. 101

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Finallywechangethevalueofwto0.6,0.8,and0.9incases28,29,and30,respectively,incontrasttothebasecasewithw=0:7.Figure4-3.10showsthatwhenthereismoreoverlapbetweenthetwoSPs'futureadopters,thermshouldintroducetheFPlaterbecausethebuyersfromtheSPswilleventuallypurchasejustoneFPratherthantwoSPs.ThisresultimpliesthatwhenthermintendstolaunchtheFPto\hittwobirdswithonestone,"theyneedtocarefullyestimatehowmanyfuturebuyersforthemarketsofthetwoSPswilleventuallybuyjustoneFP. 112 ]ndthatthesubstitutioneects,thediusionbetweentwogenerationsofsimilarproducts,andtherelativeprotabilityaremajorfactorsinuencingtheoptimallaunchtimeofthenewproduct.Ournumericalexamplessupporttheirconclusion.MahajanandMuller[ 101 ]demonstratethattherelativemarketsizesbetweengenerationsarealsoinuentialtotheintroductiontime.Inourproductdiusionmodels,thenumericalanalysesshowthatthemarketsizeoftheFPmattersforthermwithlesscannibalizationconcern.Besides,thereareadditionalfactorsimpactingthelaunchdecisionofthefusionproduct:(1)theshapeofthedevelopmentcostcurveforaearlylaunchofFP,(2)thetechnologycostmaturity,(3)theageoftheearlierlaunchSP(4)theoverlapdegreefromtwoSPmarkets,andthemostimportant(5)thecompetitiveroleofthefusionproductsupplier.TheinuenceoftheFP'smarketsize,thediusionspeedoftheFP,andtheplanninghorizonontheoptimallaunchtimearenotnotableforthesenumericalstudies. Intermsofthedemandmodelstructure,ourmodelissimilarto[ 101 ].However,whilethermalsoconsiderstheconvexdevelopmentcost,theoptimallaunchtimeisoftenbetween`now'andthetechnologycostmaturitywhentheFPisrelativelylucrative.In 102

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Herewesummarizetheinsightsfromthenumericalexamples. 1.Thegreaterthecannibalizationconcernoftherm,thelatertheFPshouldbelaunched. 2.Theoptimallaunchtimeispushedbackasthefollowingfactorsincrease:thesteepnessofthedevelopmentcostcurveforanearlylaunchoftheFP,thetechnologycostmaturity,theplanninghorizon,andtheoverlapdegreefromtwoSPmarkets. 3.Theoptimallaunchtimeshouldbesetearlierasthefollowingfactorsincrease:theFP'sprotmarginsandtheswitchingratefromtwoSPstoasingleFP. 4.IftheFPisprotableenoughtoosetthelostsalesofSPs,theFP'soptimallaunchtimewillbebetween`now'andthetechnologycostmaturity.WhentheFPismoreprotableortheearly-launchislesscostly,thermshouldintroducetheFPearlier. 5.Whentheplanninghorizonisrelativelylong,themarketsizeandthediusionspeedoftheFPdonothaveinuentialimpactontheoptimallaunchtimeoftheFP. 6.TheagesoftheSPsshowstrongnon-linearityontheoptimallaunchtimewhenthermhasincreasedcannibalizationconcerns.TheoptimallaunchtimeisconvexdecreasingthenincreasingastheagesoftheSPsincreasesfromyoungtomature. Wendthatthediusionspeedisnotinuentialtothetotalprot.Wecaneasilytellthatthediusionspeed(Figure4-4.1)givenarelativelylongplanninghorizon 103

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Thisgureshowstheimpactofparameterchangeontheprot.Theprotofthebasecaseisstandardizedas1andcontrastedbytheprotsofothercases. 104

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Wendthattheinteractionsbetweensomefactorsandtherm'scompetitiverolehasajointimpactonthetotalprot.Forexample,inFigure4-4.2theprotmarginoftheFPhasstrongimpactontheprotofthermwithlesscannibalizationconcern.InFigure4-4.3,alargermarketsizeoftheFPhaslargerimpactontheprotofthermwithmorecannibalizationconcern.But,ifthemarketsizeoftheFPissmall,thenithaslargerimpactontheprottothermwithlesscannibalizationconcern.Thedevelopmentcost(Figure4-4.4)andthetechnologycostmaturity(Figure4-4.5)havemoderateimpacttothetotalprot,whichvarieslessthanvepercentoftheprotofthebasecase.EventhoughwendashortplanninghorizonwillinducethermtolaunchtheFPmuchearlier,itsimpactonthetotalprotisminor.ThisisbecausethatlaunchingtheFPmuchearlierwillmakethediusionoftheFPnishasmuchasitcaninashortplanninghorizon,asaresult,theoveralllossintotalprotismoderated. FromFigure4-4,wecanobtainthefollowinginsights. 1.IfthesynergyoftheFPisreectedbyahigherprotmarginoralargermarketsize,thesynergyhasastrongimpactsonthetotalprotinallscenarios. 2.Thediusionspeedhasnoinuentialimpactonthetotalprotwhentheplanninghorizonislongenough. 3.AshortplanninghorizonandtheswitchingratesoftwoSPstoFPhavemoderateimpactonthetotalprot,especiallywhenthermoersthreeproductsandhasagreatercannibalizationconcern. 4.WhenthermhasthemaximumcannibalizationconcernasinscenarioIII,theimpactonthetotalprotfromthefactors(exceptthemarketsizesandprotmargins)ismoremoderatedthaninotherscenarios. 5.WhenthermhasaminimumcannibalizationconcernasinscenarioI,theoptimallaunchdecisionhasagreaterimpactonthetotalprotthanarmwhichhashighercannibalization.ThisresultimpliesthatanewentrantshouldbemorecarefulwhenitdecidesthelaunchtimeoftheFP. 105

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WendthatthecompetitiveroleoftheFP'smanufacturerisinuentialtothelaunchdecisionoftheFP.WhenthesupplieroftheFPisalsothesupplieroftheSP(s),thehighercannibalizationresultsinalaterlaunchtimeoftheFP.ThisndingsuggeststhermsinvolvedshouldevaluatewhoownsthefusiontechnologyandassessthepossibleactionsoftheFPintroduction. AsthelaunchtimeoftheFPisthedecisionvariable,ournumericalexamplesdemonstratethatseveralfactorsareinuentialtotheoptimallaunchtimeoftheFP.WhentheFPhasahigherprotmargin,thermshouldlaunchtheFPearlier.ThediusionspeedorthemarketsizeoftheFPmattersonlywhentheplanninghorizonisshort.Aatterdevelopmentcostcurve,earlymaturityofthefusiontechnology,andahigherswitchingratefromSPtoFPalsoimplyanearlierlaunch.However,iftherearemoreconsumersswitching\fromtwoSPtooneFP,"thenthermshouldlaunchtheFPlater.TheageoftheSPhasamorecomplexinuenceontheoptimallaunchtimedecision.Forthermwithmorecannibalizationconcern,thermshouldlaunchtheFPlaterwhentheSPis`young'or`old,'andlaunchtheFPearlierwhentheSPisat 106

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Becauseweincorporatemanyrealisticfunctionsforthedevelopmentcostandthematuritytimeofthefusiontechnology,theoptimallaunchtimepolicyisdierentfromtheconclusionsofWilsonandNorton's[ 112 ]\nowornever"andfromMahajanandMuller's[ 101 ]\noworat-peak."WhentheFPisrelativelyprotable(normallyitis),theoptimallaunchtimeoftheFPisbetween`now'andthematurityofthefusiontechnology.Ingeneral,themoreprotabletheFPis,theearliertheFPshouldbelaunched. Thenumericalexamplesdemonstratetheimpactofparameterchangesontheoptimallaunchtimeandthetotalprot.Thediusionspeedisnotinuentialtotheoptimallaunchtimeaswellasthetotalprotwhentheplanninghorizonisrelativelylong.TheunitprotoftheFParebothinuentialtothetotalprotandtheoptimallaunchtime.Otherparametervaluesaremoreinuentialtotheoptimallaunchtime,buttheirimpactsonthetotalprotismoderated,whichdependsontheroleofthermandthecannibalizationeect.Theresultsprovideguidelinestormswhentheyassessthevaluesofthediusionparameters. However,ourmodelconstructsavalidskeletonforempiricalandnumericalapplications.Manyimportantvariablesaresimpliedinourmodel.Whileapplyingtonumericaldatattingandforecasting,moredetailofthecorrelationbetweenmanyvariablescanbeconstructedinthedatatting.Forexample,thediusionspeedsandsubstitutioneectsmightdependonthelaunchtime,andtheproductpricemaydecreaseovertime.Numericaldatattinghasmoreexibilitytoincorporatethedynamicsamongmanyfactors. Wewanttomentionthat,toanalyzethediusionoftheFP,acompleteandreliableindustrialsurveyisstronglyneeded,especiallyinthemarketofthepersonalmobiledevice,thePC,homeentertainmentdevices,andocemachines.Aswediscussabove,awell-categorizedstatisticsforthesalesofrelatedproductsistherststepforthis 107

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108

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ThermshouldunderstandandparameterizethedemandsubstitutioneectbetweeneachsinglefunctionproductandtheMFP.Assumingthisinformationisavailable,wedemonstratethatthemaximumprotmarginassociatedwiththeMFPandthedegreeofthesubstitutioneectsarekeyfactorstotherm'soptimalchoice.TooertheMFP,theMFP'sprotmarginshouldbenolessthantheweightedaverageprotmarginforthetwosinglefunctionproducts,whichisthelowerboundofoeringtheMFP.AstheMFPbecomesmoreprotable,thermshouldrstdiscontinuethesingle-functionproductwhichhasloweradjustedprotmargin.OeringonlytheMFPisoptimalwhentheMFPisveryprotableanditindicatesthermshouldusetheMFPtoreplacetwodistinctsingle-functionproducts. Theseresultsalsoprovidesomeinsightsintohowthermcouldpotentiallyinuencethechoiceofaportfoliostrategy.SincethemaximumprotmarginfortheMFPisafunctionofthecostassociatedwiththeMFP(lowerthecost,higherthemaximumprotmargin),thiscouldbeviewedasanincentivetolowerthemanufacturingcostsassociatedwiththeMFPsothatitcouldbeincludedinitsoptimalproductportfoliochoice. Ananalysisofthedemandsubstitutioneectsalsoleadstosomeinterestinginsights.WhentheMFPhasstrongsubstitutioneectswithitsbaseandnon-baseproduct,oeringtheMFPisonlyjustiedbyahigherprotmarginoftheMFP.Inessence,smaller 109

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Thereareseveralmanagerialinsightsgeneratedfromtheanalysisofthemodel.Ingeneral,theoptimalportfoliocanbeeasilyfound,butitscompositiondependsontwomajorparameters:protmarginsandsubstitutionmatrix.Anoptimalportfoliooftencontainsjustasmallsubsetofallproductvariants,especiallywhenthesubstitutioneectsarestrong.Incontrast,theproductportfolioismorediculttodeterminewhencannibalizationeectsaresmallbutexistentbetweenthedierentproductvariants.Thissituationcanoccurwhenthesetofsingle-functionproducts(SPs)underconsiderationissomewhatincongruent,orwhenthefusionproducts(FPs)createasignicantlydierentmarketthantheoriginalSPs. Second,all-in-onefusionproductisnotalwaysincludedintheoptimalportfolio.Thiscasemayoccurduetohighvariablecostoftheall-in-one,designconictbetweensomeof 110

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Finally,numericalresultsshowthattheoptimalportfoliointhissituationgenerallycontainsawidervarietyofproductsandismoresensitivetochangesintheprotandcannibalizationparameters.Notethattheobjectiveofarmshouldbemaximizingitsprotratherthanprovideanyproductthatistechnologicallyachievable. WendthatthecompetitiveroleoftheFPmanufacturerisimportanttothelaunchdecisionoftheFP.AnFPmanufacturerwhichisanewentrantshouldintroducetheFPtothemarketearlierthantheFPmanufacturerwhoisalsothemanufacturerofoneortwoSPs.ThehighercannibalizationconcernofthermresultsinalaterlaunchtimeoftheFP.ThisndingsuggeststhermsinvolvedshouldevaluatewhoownsthefusiontechnologyandassessthepossibleactionsoftheFPintroduction. OurnumericalexamplesdemonstrateseveralfactorsareinuentialtotheoptimallaunchtimeoftheFP.WhentheFPhasahigherprotmargin,thermshouldlaunchtheFPearlier.ThediusionspeedorthemarketsizeoftheFPmattersonlywhentheplanninghorizonisshort.Aatterthedevelopmentcost,earlymaturityofthefusion 111

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NotethatthefactorswhichareinuentialtotheoptimallaunchtimeoftheFPdonotalwayshavestrongimpactonthetotalprot,andtheimpactsonthetotalprotalsodiersacrossscenarios.Theresultsprovideguidelinestormswhentheyassessthevaluesofthediusionparameters. AsecondavenueoffutureresearchistofocusondevelopingadynamicmodelincorporatinglearningeectsandmarketgrowthintotheMFPproblem.Astechnologyadvancesandprocessimprovement,theMFPsbecomemoreacceptableintermsofthepriceandthequality.MahajanandMuller[ 101 ]investigateseveralgenerationsofIBM'smainframeserverandndtwogenerationsofIBMserversarelaunchedtolate.IntheMFPproblem,thejointconsiderationofqualityimprovement,unitcostdownandthe 112

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Third,whenthemanufacturertriestofusemanyfunctionsintoanall-in-onedevice,theproductspace,platformandhumaninterfaceareconnedinalimitedscale.Howshouldthemanufacturerdesignthefusionproduct?Fromtheoutsidetheproductdimensions,whatisthebesthumaninterfacedesign?Whichfunctionshouldthefusionfunctionusedastheplatformbase?Whentheproductdimensionsistoosmalltoputalltogether,howshouldarmtosegmentdierentFPs? Fourth,anempiricalttingforthediusionoftheFPisstronglyneededinmanyproductmarkets,especiallyinpersonalmobiledevice,PC,homeentertainingandocemachines.Aspreviouslymentioned,awell-categorizedstatisticsforthesalesofrelatedproductsarethesteppingstonesforthisresearch.Withoutreasonablecategorization,anyFPdiusionttingwouldbebiased.ThisisespeciallychallengingbecausemanyFPintegratemorethanfourorvefunctionsinonedevice.Chapter3showsthecomplexityofproductportfoliowithcorrelatednfunctions.WithdierentfunctioncombinationsofFP,theinteractionsamongallcorrelatedproductsarediculttocapture.Thecurrentmarketresearchshowsdeciencyofcategorizationintheirmarketreports.WesuggestthecategorizationoftheFPshouldbeascompleteaspossible.Astheresult,thisstatisticscanbeeasilyre-categorizedtoapplytodierentproductdiusionanalysiswhenitisneeded.Severalquestionsareneededtobeanswered:WhetherthediusionspeedoftheFPissignicantlydierentfromitscomponentSPs?Dotwoproductshavesimilardiusionpatternwhentheyhashighersimilarityandsubstitutioneects?WhetheranewFPislaunchedatarighttime?DoesanewFPcapturemostofitsdemandfromotherSPsorFPs?OranewFPgeneratesasignicantamountofnewpotentialadopters?Anempiricalresearchtoanswerthesequestionswouldhavemuchcontributiontothebusinesswhentheychoosetointroducenewproductorenteramarket. 113

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114

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thehessiananditsdeterminantsare:H=266664@2 Sincethedeterminantsofthehessianalternateinsign,weconcludethatisstrictlyandjointlyconcaveinq1;q2;q3. 115

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OnexaminingTable2.1,wenotethateachstrategyprovidesafeasiblesolution(i.e.,qi0)intermsoftheparameterd3when: Theremainderofthisproofisprovideddependingupontherangeofvaluesfortheparameterd3intheTheorem. Thislaststatementistruesince:(a)d3d1r130whichisafeasibilityconditionforPMFPS1;and(b)d2r23+d1r13d30whichistherangefortheparameterd3weareinvestigating.Hence,wecanconcludethatNMFPSispreferredoverPMFPS1.Ina 116

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Nowintherange0
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ThisimpliesthattherangespeciedinCase3,canberestatedasr113d1(1r223)+d2r230 NowitiseasytoshowthatPMFPS2ismonotonicallyincreasingintherangeford3givenbyCase3A.Thus,theprotsunderPMFPS2areminimumwhend3=r113d1(1r223)+d2r23+whereissettobesucientlysmall.Say0,thenconsider:PMFPS2(d3=r113d1(1r223)+d2r23)NMFPS=d22+(1r223)1(d3r23d2)2(d21+d22)=(1r223)1(r113d1(1r223))2d21=r213d21(1r223)d21>0since1r223>r213)r213(1r223)>1 Giventheseresults,wecanconcludethatPMFPS2isthedominantstrategyforCase3A. Case3B:r113d1>r123d2 ThisimpliesthattherangespeciedinCase3,canberestatedasr123d2(1r213)+d1r13
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NowitiseasytoshowthatPMFPS1ismonotonicallyincreasingintherangeford3givenbyCase3B.Thus,theprotsunderPMFPS1areminimumwhend3=r123d2(1r213)+d1r13+whereissettobesucientlysmall.Say0,thenaswithCase3A,itcanbeshownthat:PMFPS1(d3=r123d2(1r213)+d1r13)NMFPS>0 Giventheseresults,wecanconcludethatPMFPS1isthedominantstrategyforCase3B.Case4:d32[3;1)ormaxfr113d1;r123d2gd3 119

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Takingtherstandsecondderivativesoftheobjectivefunctionforproblem(GP),weobtain 2(rk;j+rj;k)(k;j2f1;2;:::;ngandk6=j)representstheaveragesubstitutioneectbetweenproductskandj. 120

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TheequationsystemfortheFOCsisshownbelow.SolvingtheoptimalquantityvectorbyCramer'srule,weobtainthefollowing: 2)=[]1(d+1 2)0qkk=0;8k:

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LetSbeanyportfoliowithallpositive-quantityproducts,thatisqk>0;8k2S,thentheoptimalquantitiesandtheprotareshownin E{1 and E{2 ,respectively. S=qST(pScS)=qST(2dSrSqS)=2qSTdSqSTrSqS=2dSTAdj[S]dS 122

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TheprotdierencebetweentheparentS0andthechildSportfoliosisS0S=jSjdS0TAdj[S0]dS0jS0jdSTAdj[S]dS jSj(qS0j)2;

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LetAbean(nn)matrixandletBbethe(n1)(n1)submatrixobtainedbydeletingthelastrowandlastcolumnofA.LetAdj(A)andAdj(B)betheadjugatematricesofAandB.Letx0=(x1;:::;xn)T,x=(x1;:::;xn1)T,y0=(y1;:::;yn)Tandy=(x1;:::;yn1)T. Thenequation( G{1 )isequivalentto Letrbethecolumnvectorwhosei-thentryisthe(n;i)cofactor(1)i+njAn;ijofA.Similarly,letcbethecolumnvectorwhosei-thentryisthe(i;n)cofactorofA.(Thusr=cifA=AT.)Thenbythecofactorexpansionofdeterminants,wehave sowecanrewrite( G{2 )as

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For1i;jn,letfijdenotethe(i;j)entryofF.Then( G{4 )isequivalenttotheequations Toprove( G{5 )wenowexamineeachentryofF,usingthedenition( G{1 ).Ifeithertherowindexorthecolumnindexisequalton,thentheentryissimplythatofjBjAdj(A).Thus, G{5 )holdswheneveriorjisequalton. Itremainstocheckfijfor1i;jn1.From( G{1 ),weseethat Forthesevaluesofiandjtheequation( G{5 )followsimmediatelybyapplyingLemma 1 belowto( G{6 ).Thiscompletestheproofofthetheorem. 1 isaclassicalformulaofJacobi(1833),sometimescalledtheDodgsonCondensationFormula. 125

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jS0j.Thereforeweobtainthefollowing. S0S=jSjdS0TAdj[S0]dS0jS0jdSTAdj[S]dS jSj(qS0j)2:

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YuwenChenisadoctoralcandidateinOperationsManagementattheUniversityofFlorida.Hisresearchfocusesonnewproductstrategyrelatedtomulti-functionproducts.Yuwenisalsointerestedinproblemsontechnologymanagement,operationsandsupplychainmanagement.YuwenreceivedhisbachelordegreesinAccountingfromNationalTaiwanUniversityinTaipei,Taiwanin1993.Yuwenhadthreeyearsofworkingexperiencesinhigh-techindustryinTaiwanandCalifornia.YuwenplanstograduateinMay2008andpursueacareerinanacademiaenvironmentthathasabalanceofteaching,researchandtheconnectionwithrealbusiness. 135