競爭市場中產(chǎn)品組合管理博弈模型講義課件

Agametheory-basedmodelforproductportfoliomanagementinacompetitivemarket

A.Sadeghi,M.Zandieh

ExpertSystemswithApplications,2010Agametheory-basedmodelforStructureIntroductionLiteraturereviewDescriptionofthePPMproblemProblemformulationExampleConclusionsandfutureworkStructureIntroduction1.IntroductionConsumers,industrialmanagers,andsalesandmarketingpeople,alldemandproductsthatimprovetheirlifestylesortogainanedgeoverthecompetition.So,productportfolios

areinterestingformanypeople.Butunlimitedproductvarietyisnotawaytobesuccessful;therehastobeanoptimum.ItistrueformostcompaniesthattheParetoruleapplies:80%ofthesalesand/orpro?ts

comefrom20%oftheproducts.Itisevidentthatasingleproductcannot1.IntroductionConsumers,indu

ful?llthemanufacturerneedsandonthe

otherhand,fordiversitythereexistslimitation.Intoday’shighlycompetitiveenvironment,determiningan

optimalproductportfolioisveryimportantforthesurvivalofa?rm.Optimalproductportfoliohasreceivedconsiderableattention,becausetheratesoffailureofnewproductportfolioandtheirassociatedlossesareveryhigh.Thewhole

product

component

information（產(chǎn)品構建信息）,

engineeringful?llthemanufacturerne

portfoliodecision（工程組合決策）isverycrucialfortheprogressofa?rm

,becauseitisverycostlyanddifficulttochange.Thekeyquestionsare,whatthebestproductportfoliois,andhowmanufacturercan

?ndit.Productportfoliomanagement(PPM)is

ageneralbusinessconceptthatanalyzetheproductionability（生產(chǎn)能力）

andmarketpotential,simultaneously,andthendeterminethebestsetofproductsto

offer.PPMisdevelopedtodirectaproductanditsdiversityportfoliodecision（工程組合決策

includingnotonlyattributes（屬性）,levels,andprice’s,butalsoanalysisresults,environmental

requirements（環(huán)保需求）,manufacturingprocedures（生產(chǎn)流程）,productperformanceinformation（產(chǎn)品性能信息）,and

etc.ThereforePPMhasbeenclassifiedasacombinatorialoptimizationproblem.Eachcompanystrivesfortheoptimalityofitsproductofferingsthroughvariouscombinationsofproducts.ThePPMproblemmaydevelopfromtwoperspectives:(I)For

attracttheopinionofcustomersincludingnotonlyattribu

intargetmarkets.(II)Forreduce

themanufactureengineeringcosts.Firstistheproblemofmarketingmanagers,andsecondistheproblemofproducer.Whenbothofthemcomposewitheachotherasreflecttoutilityofcostumersandengineeringcosts,thisproblembecomestomisslinkbetweensaleandproductionchain.JiaoandZhang(2005)considerthecustomer–engineering

interactioninproductportfolioplanning,whichaims

tocreateproduct

familyintargetmarkets.(II)Fospeci?cations(產(chǎn)品族/系列規(guī)格)foratargetmarketsegment,andproposedamaximizingsurplussharemodel（最大剩余份額模型）.Incompetitiveenvironment,wedetermineourproductportfoliowithregardtoproductsthatofferbycompetitors,whilethecompetitorsmanagetheirproductportfoliosinregardtoourproducts.Gametheorycanbeusedtomodelthisproblem.Theproposed

modelconstructsproductportfoliospeci?cations(產(chǎn)品族/系列規(guī)格)fo

basedoncustomer–engineeringinteractionmodelinproductportfolioplanningwhichis

developedbyJiaoandZhang.PresentpaperextendspreviousworksinPPMwithregardtocustomer–engineeringconcerns

andcompetitiveenvironment.Itisnotforany

specificproduct,anditcanbeappliedtoadiversityofproductsorservices.objective:developagametheory-basedmodelasaprocedureof?ndingoptimalproductportfolio.basedoncustomer–engineer2.LiteraturereviewAPPMisde?nedasadecisionmakingthatoptimizessomecriteria,suchas

marketshare.Themaincontributionofthemostresearchesin

PPMissummarizedinfollowingissues:

1)Generatingdesign

alternativesviamulti-objective

optimization（通過多目標優(yōu)化生成設計方案）.

2)Accountingforuncertaintyandcompetitionwhenestimatingtheachievementofbusinessgoals.

3)Applyingmeta-heuristicalgorithms（元啟發(fā)式算法）

2.LiteraturereviewAPPMisd

tosolveacombinatorial

problemduringtheproductlinedesign.ThedevelopmentofalgorithmsHeuristic(identifyproductpro?leproductlinedesign)

algorithms

improvedheuristicalgorithms

geneticalgorithms.Thedevelopmentofmodels1)JiaoandZhangproposedamodelto

addresstheproductportfolioplanningproblem,itconsiderscustomerpreferences,choiceprobabilitiesandtosolveacombinatorialp

platformbasedproductcosting.Also,ageneticalgorithmprocedureisapplied.

2)AiyoshiandMaki

proposedagameproblemundertheconstraintsofallocationofproductandmarketsharesimultaneously.Theirresearchisconsideredseveralmanufacturersinoligopolymarket（寡頭壟斷市場）.Thisproposedmodel,ontheonehandhadthecompetitivecircumstance,butontheotherhand,didnothas

detailssuchaslargevarietyofcustomers'preferences,customer–engineeringconcerns,etc.platformbasedproductcos

3)modelinthispaper

considersbothdetailsandcompetitivecircumstance.3)modelinthispapercon3.DescriptionofthePPMproblemConsideringthe?rmcapabilitiestoproduceproducts,asetofproductportfolioshavebeenidenti?ed.Eachproducthascertaindesirabilitybetweencustomers.Morespeci?cally,weconsiderascenarioinwhichasetofproducts,havebeenidenti?ed,giventhatthemanufacturer(m)hasthecapabilities(bothdesignandproduction)toproducealltheseproducts,..Aproductportfolio,,isasetconsistingofsomeselectedproduct.Combined

withtheproducts,asetofproductportfoliosarecreated,.

相關參數(shù)3.DescriptionofthePPMprobForexample,ifmanufacturermcanproduce3product,7productportfolioareavailable:（=7）

Everyproduct,

,isassociatedwithcertainengineeringcosts,denotedas.Therearemultiplemarketsegments,S={s1,...,sg,...,sG},eachcontaininghomogeneouscustomers,withade?nitesize,Qg.Thecustomer–engineeringinteractionisForexample,ifmanufacturermembodiedinthedecisionsassociatedwithcustomers’choicesofdifferentproducts.Variouscustomerpreferencesondiverseproductsarerepresentedbyrespectiveutilities,(utilityofthegthsegmentforthenthproductofmthmanufacturer).Productdemandsormarketshares,(marketshareofthegthsegment

forthenthproductofmthmanufacturer),aredescribedbytheprobabilitiesofcustomers’choosingproducts.Customerschooseaproductbasedonthesurplusembodiedinthedecisions

buyerrule.Theyhave

theoptionofnotbuyinganyproductsorbuyingcompetitors’products.Weassumethatcompetitorsrespondtothemanufacturer’smoves,meaningthat,thecompetitionreactbyintroducingnewproducts.buyerrule.Theyhavetheo4.ProblemformulationThepresentpaperconsidersamarketwithGsegments,

S={s1,...,sg,...,sG},and2manufacturersthateachofthemcan

offerNmproducts,

andJmproductportfolios,

.Thisgivesthebimatrix-game（雙矩陣對策）

problemwith2playersandJmstrategyforeach,(m=1or2).Thepayoffforeachplayerwillofcoursedependonthecombinedactionsofbothplayers.Apayoffmatrixshowswhatpayoff

eachplayerwillreceiveat4.ProblemformulationThepres

theoutcomeofthegame.Forplayer

m(m=1or2),thepayoffmatrix,Fm,isasfollows:theoutcomeofthegame.FInsummary,aJ1

×J2–bimatrixgameisplayedbytwoplayers,player1andplayer2.Player1hasafinitesetandplayer2hasa?nite

set

of

purestrategies.Thepayoffmatrixes[f1(

)],

ofplayer1

and

ofplayer2aredenotedbyF1andF2respectively.Thisgameisdenotedby(F1,F2).Nowthegame(F1,F2)isplayedasfollows.Players1and2choose,independentofeachother,astrategyInsummary,aJ1×J2–bimatr

andrespectively.Here

canbeseenastheprobabilitythatplayer1(2)chooseshis–throw(–thcolumn).The(expected)payoffforplayer1isx1F1x2andtheexpectedpayofftoplayer2isx1F2x2.Astrategypair()isanequilibriumforthegame(F1,F2)ifandThesetofallequilibriaforthegame(F1,F2)isdenotedbyE(F1,F2).ByatheoremofNashthissetisnon-emptyforallbimatrix-games(Nash,1950).Somemethodsforcalculatingpayoffmatrixarrays,,arethere(seeSection2).WeusedthefunctionthatproposedbyJiaoandZhang(2005).Thisfunctionisbasedoncustomer-engineeringinteractionmodelinPPM.Thisisasfollows:ThesetofallequilibriaforEq.(3)istheexpectedsharedsurplusbyofferingaproductportfolio,consistingofproducts,tocustomersegments,sg,eachwithsizeQg.Themarketpotentials,Qg,canbegivenexogenouslyattheoutsetorestimatedthroughavarietyoftechniquesbasedonhistoricaldataortestmarkets.Theutilityofthegthsegmentforthenthproductofmthmanufacturerisdenotedas.ThismodelassumesthatcustomersonlychooseaEq.(3)istheexpectedshared

productwithapositivesurplus.Thechoiceprobability,,

thatacustomerorasegment,sg,choosesaproduct,,withNcomcompetingproducts,isdefinedasfollows:whereuisascalingparameter（尺度參數(shù)）.Accordingtomatrix(1)andEq.(3),letthefunctionbedefinedbyproductwithapositivesu競爭市場中產(chǎn)品組合管理博弈模型講義5.ExampleInthissection,asimpleexampletousetheproposedmodelispresented.Forsimplicity,weconsideramarketwithtwocompetitor(M=2),andfourdifferentproducts(Nm=4)foreach.Feasiblestrategies,isdefinedasfollows:5.ExampleInthissection,as產(chǎn)品組合數(shù)=24-1=15???產(chǎn)品組合數(shù)=24-1=15???Threesegmentsareidentified,i.e.,s1,s2,ands3.Q1,Q2,andQ3areassumed0.2,0.3and0.5,respectively.Table1showstheutilitiesofthreesegmentstoeveryproduct()andcostofeach().Also,scalingparameter(u)issupposed0.8.Therefore,2payoffmatrixesF1andF2formedformanufacturer1and2,separately.Thisgameandobtaineddatafromexpectedsharedsurplusvalues(Eq.(5))aresummarizedinFig.1.Threesegmentsareidentified,返回返回競爭市場中產(chǎn)品組合管理博弈模型講義TheoptimalresultforeachmanufacturerisderivedfromtheNashequilibriumpointofthegame.Astrategypairisanaloneequilibriumforthegame.Therelatedpayoffpairis(0.74,0.83).Theoptimalresultforeachma6.ConclusionsandfutureworkThispaperproposedagametheory-basedmodelthatisusedtomaximizetheexpectedsharedsurplusforaproductportfoliomanaged.Theproductportfoliomanagement(PPM)isanimportantoptimizationproblemthatincludesthelargesetofconstraintsandcharacteristics.Therefore,itisveryhelpfulforamanagertouseamarketingdecisionsupportsystemwhichprovideshimtheacceptablesolutionswithconsideringmoreterms.Accordingtothisgoal,a6.Conclusionsandfutureworkgametheory-basedmodelisproposedandappliedtosolvetheproblemsinvolvedinPPM.TherearepotentiallyunlimitedopportunitiesforresearchinPPM.Futurestudiescanfocusonothercharacteristicstoachievemoreidealresults.Othernotabledirectionsforfutureresearchesincludeallowingforsequentialentrystrategies,timevaryingutilitiesandchangingcustomerbehaviors.gametheory-basedmodelisTheEnd!TheEnd!返回返回相關概念納什定理：在一個有n個博弈方的博弈G=﹛S1,…,Sn：u1,…,un}中，如果n是有限的，且Si都是有限集（對i=1，…，n），則該博弈至少存在一個納什均衡，但可能包含混合策略。

產(chǎn)品組合：由不同的產(chǎn)品線構成，而產(chǎn)品線又是由不同的產(chǎn)品項目構成。產(chǎn)品組合策略：在產(chǎn)品組合的深度、廣度和相關性方面做的籌劃和安排。產(chǎn)品組合的廣度：產(chǎn)品線的數(shù)量。產(chǎn)品組合的廣度：產(chǎn)品項目（規(guī)格或品種）的數(shù)量相關概念納什定理：在一個有n個博弈方的博弈G=﹛S1,…,S遺傳算法（GeneticAlgorithm）是一類借鑒生物界的進化規(guī)律（適者生存，優(yōu)勝劣汰遺傳機制）演化而來的隨機化搜索方法。其主要特點是直接對結構對象進行操作，不存在求導和函數(shù)連續(xù)性的限定；具有內在的隱并行性和更好的全局尋優(yōu)能力；采用概率化的尋優(yōu)方法，能自動獲取和指導優(yōu)化的搜索空間，自適應地調整搜索方向，不需要確定的規(guī)則。遺傳算法（GeneticAlgorithm）是一類借鑒生物

單一產(chǎn)品策劃

單一產(chǎn)品策劃程序策劃目標環(huán)境分析市場細分目標市場市場定位概念產(chǎn)品營銷組合返回

單一產(chǎn)品策劃

單一產(chǎn)品策劃程序策劃目標環(huán)境分析市場細分目標Agametheory-basedmodelforproductportfoliomanagementinacompetitivemarket

A.Sadeghi,M.Zandieh

ExpertSystemswithApplications,2010Agametheory-basedmodelforStructureIntroductionLiteraturereviewDescriptionofthePPMproblemProblemformulationExampleConclusionsandfutureworkStructureIntroduction1.IntroductionConsumers,industrialmanagers,andsalesandmarketingpeople,alldemandproductsthatimprovetheirlifestylesortogainanedgeoverthecompetition.So,productportfolios

areinterestingformanypeople.Butunlimitedproductvarietyisnotawaytobesuccessful;therehastobeanoptimum.ItistrueformostcompaniesthattheParetoruleapplies:80%ofthesalesand/orpro?ts

comefrom20%oftheproducts.Itisevidentthatasingleproductcannot1.IntroductionConsumers,indu

ful?llthemanufacturerneedsandonthe

otherhand,fordiversitythereexistslimitation.Intoday’shighlycompetitiveenvironment,determiningan

optimalproductportfolioisveryimportantforthesurvivalofa?rm.Optimalproductportfoliohasreceivedconsiderableattention,becausetheratesoffailureofnewproductportfolioandtheirassociatedlossesareveryhigh.Thewhole

product

component

information（產(chǎn)品構建信息）,

engineeringful?llthemanufacturerne

portfoliodecision（工程組合決策）isverycrucialfortheprogressofa?rm

,becauseitisverycostlyanddifficulttochange.Thekeyquestionsare,whatthebestproductportfoliois,andhowmanufacturercan

?ndit.Productportfoliomanagement(PPM)is

ageneralbusinessconceptthatanalyzetheproductionability（生產(chǎn)能力）

andmarketpotential,simultaneously,andthendeterminethebestsetofproductsto

offer.PPMisdevelopedtodirectaproductanditsdiversityportfoliodecision（工程組合決策

includingnotonlyattributes（屬性）,levels,andprice’s,butalsoanalysisresults,environmental

requirements（環(huán)保需求）,manufacturingprocedures（生產(chǎn)流程）,productperformanceinformation（產(chǎn)品性能信息）,and

etc.ThereforePPMhasbeenclassifiedasacombinatorialoptimizationproblem.Eachcompanystrivesfortheoptimalityofitsproductofferingsthroughvariouscombinationsofproducts.ThePPMproblemmaydevelopfromtwoperspectives:(I)For

attracttheopinionofcustomersincludingnotonlyattribu

intargetmarkets.(II)Forreduce

themanufactureengineeringcosts.Firstistheproblemofmarketingmanagers,andsecondistheproblemofproducer.Whenbothofthemcomposewitheachotherasreflecttoutilityofcostumersandengineeringcosts,thisproblembecomestomisslinkbetweensaleandproductionchain.JiaoandZhang(2005)considerthecustomer–engineering

interactioninproductportfolioplanning,whichaims

tocreateproduct

familyintargetmarkets.(II)Fospeci?cations(產(chǎn)品族/系列規(guī)格)foratargetmarketsegment,andproposedamaximizingsurplussharemodel（最大剩余份額模型）.Incompetitiveenvironment,wedetermineourproductportfoliowithregardtoproductsthatofferbycompetitors,whilethecompetitorsmanagetheirproductportfoliosinregardtoourproducts.Gametheorycanbeusedtomodelthisproblem.Theproposed

modelconstructsproductportfoliospeci?cations(產(chǎn)品族/系列規(guī)格)fo

basedoncustomer–engineeringinteractionmodelinproductportfolioplanningwhichis

developedbyJiaoandZhang.PresentpaperextendspreviousworksinPPMwithregardtocustomer–engineeringconcerns

andcompetitiveenvironment.Itisnotforany

specificproduct,anditcanbeappliedtoadiversityofproductsorservices.objective:developagametheory-basedmodelasaprocedureof?ndingoptimalproductportfolio.basedoncustomer–engineer2.LiteraturereviewAPPMisde?nedasadecisionmakingthatoptimizessomecriteria,suchas

marketshare.Themaincontributionofthemostresearchesin

PPMissummarizedinfollowingissues:

1)Generatingdesign

alternativesviamulti-objective

optimization（通過多目標優(yōu)化生成設計方案）.

2)Accountingforuncertaintyandcompetitionwhenestimatingtheachievementofbusinessgoals.

3)Applyingmeta-heuristicalgorithms（元啟發(fā)式算法）

2.LiteraturereviewAPPMisd

tosolveacombinatorial

problemduringtheproductlinedesign.ThedevelopmentofalgorithmsHeuristic(identifyproductpro?leproductlinedesign)

algorithms

improvedheuristicalgorithms

geneticalgorithms.Thedevelopmentofmodels1)JiaoandZhangproposedamodelto

addresstheproductportfolioplanningproblem,itconsiderscustomerpreferences,choiceprobabilitiesandtosolveacombinatorialp

platformbasedproductcosting.Also,ageneticalgorithmprocedureisapplied.

2)AiyoshiandMaki

proposedagameproblemundertheconstraintsofallocationofproductandmarketsharesimultaneously.Theirresearchisconsideredseveralmanufacturersinoligopolymarket（寡頭壟斷市場）.Thisproposedmodel,ontheonehandhadthecompetitivecircumstance,butontheotherhand,didnothas

detailssuchaslargevarietyofcustomers'preferences,customer–engineeringconcerns,etc.platformbasedproductcos

3)modelinthispaper

considersbothdetailsandcompetitivecircumstance.3)modelinthispapercon3.DescriptionofthePPMproblemConsideringthe?rmcapabilitiestoproduceproducts,asetofproductportfolioshavebeenidenti?ed.Eachproducthascertaindesirabilitybetweencustomers.Morespeci?cally,weconsiderascenarioinwhichasetofproducts,havebeenidenti?ed,giventhatthemanufacturer(m)hasthecapabilities(bothdesignandproduction)toproducealltheseproducts,..Aproductportfolio,,isasetconsistingofsomeselectedproduct.Combined

withtheproducts,asetofproductportfoliosarecreated,.

相關參數(shù)3.DescriptionofthePPMprobForexample,ifmanufacturermcanproduce3product,7productportfolioareavailable:（=7）

Everyproduct,

,isassociatedwithcertainengineeringcosts,denotedas.Therearemultiplemarketsegments,S={s1,...,sg,...,sG},eachcontaininghomogeneouscustomers,withade?nitesize,Qg.Thecustomer–engineeringinteractionisForexample,ifmanufacturermembodiedinthedecisionsassociatedwithcustomers’choicesofdifferentproducts.Variouscustomerpreferencesondiverseproductsarerepresentedbyrespectiveutilities,(utilityofthegthsegmentforthenthproductofmthmanufacturer).Productdemandsormarketshares,(marketshareofthegthsegment

forthenthproductofmthmanufacturer),aredescribedbytheprobabilitiesofcustomers’choosingproducts.Customerschooseaproductbasedonthesurplusembodiedinthedecisions

buyerrule.Theyhave

theoptionofnotbuyinganyproductsorbuyingcompetitors’products.Weassumethatcompetitorsrespondtothemanufacturer’smoves,meaningthat,thecompetitionreactbyintroducingnewproducts.buyerrule.Theyhavetheo4.ProblemformulationThepresentpaperconsidersamarketwithGsegments,

S={s1,...,sg,...,sG},and2manufacturersthateachofthemcan

offerNmproducts,

andJmproductportfolios,

.Thisgivesthebimatrix-game（雙矩陣對策）

problemwith2playersandJmstrategyforeach,(m=1or2).Thepayoffforeachplayerwillofcoursedependonthecombinedactionsofbothplayers.Apayoffmatrixshowswhatpayoff

eachplayerwillreceiveat4.ProblemformulationThepres

theoutcomeofthegame.Forplayer

m(m=1or2),thepayoffmatrix,Fm,isasfollows:theoutcomeofthegame.FInsummary,aJ1

×J2–bimatrixgameisplayedbytwoplayers,player1andplayer2.Player1hasafinitesetandplayer2hasa?nite

set

of

purestrategies.Thepayoffmatrixes[f1(

)],

ofplayer1

and

ofplayer2aredenotedbyF1andF2respectively.Thisgameisdenotedby(F1,F2).Nowthegame(F1,F2)isplayedasfollows.Players1and2choose,independentofeachother,astrategyInsummary,aJ1×J2–bimatr

andrespectively.Here

canbeseenastheprobabilitythatplayer1(2)chooseshis–throw(–thcolumn).The(expected)payoffforplayer1isx1F1x2andtheexpectedpayofftoplayer2isx1F2x2.Astrategypair()isanequilibriumforthegame(F1,F2)ifandThesetofallequilibriaforthegame(F1,F2)isdenotedbyE(F1,F2).ByatheoremofNashthissetisnon-emptyforallbimatrix-games(Nash,1950).Somemethodsforcalculatingpayoffmatrixarrays,,arethere(seeSection2).WeusedthefunctionthatproposedbyJiaoandZhang(2005).Thisfunctionisbasedoncustomer-engineeringinteractionmodelinPPM.Thisisasfollows:ThesetofallequilibriaforEq.(3)istheexpectedsharedsurplusbyofferingaproductportfolio,consistingofproducts,tocustomersegments,sg,eachwithsizeQg.Themarketpotentials,Qg,canbegivenexogenouslyattheoutsetorestimatedthroughavarietyoftechniquesbasedonhistoricaldataortestmarkets.Theutilityofthegthsegmentforthenthproductofmthmanufacturerisdenotedas.ThismodelassumesthatcustomersonlychooseaEq.(3)istheexpectedshared

productwithapositivesurplus.Thechoiceprobability,,

thatacustomerorasegment,sg,choosesaproduct,,withNcomcompetingproducts,isdefinedasfollows:whereuisascalingparameter（尺度參數(shù)）.Accordingtomatrix(1)andEq.(3),letthefunctionbedefined