基于Gumbel分布的零售产品线定价分析研究(1)

上海交通大学硕士学位论文基于Gumbel分布的零售产品线定价分析研究姓名：张宏申请学位级别：硕士专业：企业管理指导教师：李乃和2007011611.1200573618.3[1]501.1.1?()?[2]2•••[3]()•••()•:3(needsandwants)1.1.2[6]•••4[7]12561516152553070531264205[12]958675009.304508.56156915[13]61812319965002.01MorgenSteinStogin1987[16][7]91••52LattinOrtmeyer[18]1991EDLP[14]102•••()[9]••11[14]1.1.3[19][20]----••••121.2•[17]•[20]•[21]BlattergWisniewski1989[24]CarmonSimonson1998[25]13PayneBettman1999[26]BlattergWisniewski1989[24]J.MiguelVillas-Boas1998[28](BulowPfleiderer2001)[29]Katz1984[36]MussaRosen1997[34]Urban1979[32]NaertGijsbrechts1989[37]MulhernLeone1991[47]WardHansonKippMartin1996[16]14MultinomiallogitHansonMartin[16]YanoKraus1999[49]LucechoicemodelGokerAydinJenniferK.Ryan2000[52]nKyleD.ChenWarrenH.Hausman2000[55]choice-basedconjointanalysischoice-basedconjointanalysisChenHausmanGumbelMultinomiallogitGumbeln151.3Gumbel••GumbelMultinomiallogit•BlattergWisniewskiGumbeln•161.4BlattergWisniewskiGumbeln172.1αthiiA1iA−2,3,4,...,iV=V2V=1A2A2AFααAiic1iicc+Vα()1ViiiiircDFααπ==−−∑(2-1)1221DDrr∂∂=∂∂211821απiDAiirAir−11ViiirV=∑icAi_AcAiθ__1AVccVθ+=+_c11ViicV=∑FαMθimAiiirc−ir∗Ai2.21a)12210,0,(1,2)iirrriccc∗∗∗∂∂∂===∂∂∂(2-2)19b)BW**21110,0,rrcc∂∂∂∂(2-3)c)BW**12220,0,rrcc∂∂∂∂(2-4)2.31012,,1,2iiiijDrrijijβββ=−+=≠ir∗jr∗()()122211224jjiijijjircβββββββ∗−∂=∂−+22jiββ=0ijrc∗∂=∂(2-2)(2-3)(2-4)2001iiDbbr=−()()01iiircbbrπ=−−0122iiiibcrb∗=+icir∗0122iiiibcrb∗=+0ib2121Dr∂∂0122iiiiibcrcb∗−=−ic12Dr∂∂222112DDrr∂∂=∂∂123Gumbel3.13.1.124[56]()()[10]()[14]25=F()F(1)[40][11](2)()•[5]••2627•Poisson•••niri1,2,3,...in=ici1,2,3,...in=iUi1,2,3,...in=()iiFUiUcdf1,2,3,...in=()iifUiUpdf1,2,3,...in=1,2,3,...in=iirciU()iifUini1111111(,...,)()...()()...()()ininiiiiiiinniirprrFrurFrurFrurFrurfudu∞−−++=+−+−+−+−∫2n=n281)2)13)2121p11)1122UrUr2)11221122,UrUrUrUr−−21112211221122(,)(,,)pPUrUrPUrUrUrUr=+−−121p1212211111()()rpFrurfudu∞=+−∫31311n−11122111111111()...()()nnnrpFrurFrurfudu∞−−−=+−+−∫32n111221111111()...()()nnnrpFrurFrurfudu∞=+−+−∫330111111(,...,)()...()()...()nnnnnnnpPUrUrPUrPUrFrFr===34ni1111111(,...,)()...()()...()()ininiiiiiiinniirprrFrurFrurFrurFrurfudu∞−−++=+−+−+−+−∫3529()()F()()(ConjointAnalysis)3.1.2iUiUGumbeliiiUαε=+iαiεGumbel1,2,3,...in=iεGumbel()1()exp((()))xxfxeγµγµµ+=−++360.5772γ=Gumbel()()exp(())xFxeγµ−+=−3730iUiUGumbelmultinomiallogitmodelMNLMNLrandomutilitytheory[8]MNLMNLMNLutility-maximizingSJjjU1,2,3,...jJ=iiUjUjiMNLdeterministiccomponentrandomcomponentiiiiUαε=+iαiεGumbel1,2,3,...in=iεMNLiUMNLiαiMNL31iUMNLiUMNLMNLiUGumbelni()111(,...,)(,...,)(,...,)iirnnninnnrrprrerrαγµδψ−−+=3811(,...,)1exp((,...,))nnnnrrrrδψ=−−11(,...,)exp(())nniinirrrαψγµ=−=−+∑iiiUαε=+33()()11112211111112221111111()...()()...nnnrnnnrpFrurFrurfuduprrprrdααεαεαεαεε∞∞−=+−+−=+++−+++−∫∫39()()11,2,...,iiirrinβαα=−−−=Gumbel36373932112111111111()exp(())11...1exp(())nniiinrrrniiipexpeexpeexpedeerεβεβεγγγµµµααγαµγµεγεµµαγµ=++−+−+−+∞−−−+−−−+==−−−+−∑=−−−+∫∑310383.21()0ifu()0iu∞iiri35ir()()()(),111111()...()()...()()0inijjikkiikijriiiiinniipfrurFrurfudurFrFrFrFrfr∞≠−−++∂=−+−+−∂−∑∏∫0niipr∂∂(),1,...,ijin≠=311ii11(,...,)(,...,)nnnnrrrrδψiir33()iireαγµ−−+iiri2()0ifu()0iu∞jjrijr111111()...()...()()...()()0iniijjiiiiiiinniirjpFrurfrurFrurFrurFrurfudur∞−−++∂=+−+−+−+−+−∂∫(),1,...,ijin≠=312()0ifu()0iu∞j1n−n1()1122111111()...()()1()nnnnrpFrurFrurFrurfudu∞−−∆=+−+−+−−∫1()10nnFrur+−−10p∆34,1,2ii=312332312312123221212212(,,)(,,)(,)(,,)1(,)(,)(,)iiirrrprrrprrrrrrrprrrrδψδψ−=−31233123212212(,,)(,,)1(,)(,)rrrrrrrrrrδψδψ−iiUGumbeliUGumbelcannibalization353.3λnn+1n350np11np22npinipλinipλiinipλi,1,2,...niiDpinλ==3133836()111(,...,)(,...,)(,...,)iirnnniinnnrrDprrerrαγµδλλψ−−+==31411(,...,)1exp((,...,))nnnnrrrrδψ=−−11(,...,)exp(())nniinirrrαψγµ=−=−+∑314iα0iiDα∂∂315iiαi37n4.1BW41iDVithi1,2,....iV=()()()()1100iiiiiVVVVMrMrrDMrMrααα++−−=−=−1,,,,iiVVforiVrrforiVrα+≤=41irithi1iα+ithiithi1iα+1i+1ir+ithi1iα+1i+1ir+i1i+VMα38VαM232441BWBlattberg-WisniewskiithiiD1iir+r1ir−_11ViiccV==∑__1VAVccVα+=+VαiD1iirr+1iirr+__1VAVccVα+=+_Ajcc1,2,...,jV=00c=()1ViiiircDFααπ==−−∑4221n4.2BW_Ajcc2a)iAir∗391111122iiiiiiiircmrrccr∗∗∗∗∗∗∗∗+−+−−++++−==00mc=1VVrα+=43b)iAim∗iA_0()iiAkkmcc∗==−∑44c)_12VVAVrrccα∗∗−=−+45d)(1)iA2Vi2iA2Vi1111122VViViiiircVVα∗===+−∑∑464.34142()()()11ViiiiircMrrFαπ+==−−−∑4747ir000rc==1VVrα+=11120iiiiircrrc−−+−+−+=1,2,...,,...,ikV=48491_0()iiAkkrcc−∗==−∑4944401__00()()iiiiiAkiAkkkmrcccccc−∗∗===−=−−=−∑∑Vr∗1r∗43451___10()2VVAkAVAVkrrcccccα−∗∗=−=−−=−+∑461_11011111()22VViViAkViiikiircccVVVα−∗=====−=+−∑∑∑∑48431111122iiiiiiiircrcmrcr∗∗∗∗∗−−+−+−++++==225V=_123456VAccccccα+++++=_1Arc=_212Arcc=−_3123Arccc=−−_41234Arcccc=−−−_512345Arccccc=−−−−1c4A41()_451234123224333VAcccccrccccα++−=−−−=−+5A_Ac12345,,,AAAAA1A4A()()4512323ccccc+++_ATotalVDMcα=−,iiir21iimm∗∗+_1Aicc+VsA_Ac()()1111011VVViVSiViVSiiiccccVcVVVVααα===+−++−+−=++∑∑∑_Ajcc42iA1_0()iiAkkrcc−∗==−∑_Ac,ir∗_Ac,ir∗422421Vrr−2a1111122iiiiiiiirmcrrccr+−+−−++++−==4341iciAiRciA_11VcVrVα∗+=+10irc∗∂∂i10rR∗∂∂_AVVVrccα∗=−+0,,0VVi