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200433:100026788(2004)0320069210SMCIT1,2,1,3(1.,100876;2.,710049;3.,100086):IT,,,L,SMCL:;SMC;:TP391:APositiveResearchofSMCModelsinITDistributionMarketIndustryQIJia2yin1,LIHuai2zu2,SHUHua2ying1,QINLiang2juan3(1.BeijingUniversityofPostsandTelecommunications,Beijing100876,China;2.Xi’anJiaotongUniversity,Xi’an,710049,China;3.DigitalChinaLtd,Beijing100086,China)Abstract:SMCmodelisagroupofmodelstoforecastcustomer’sbuyingbehaviorsandwasprovidedin1987.TherearefewpositiveresearchesandapplicationsofSMCmodelforshortageofcustomerdataanditscomplexity.TochooseITdistributionmarketindustryasbackground,apositiveresearchisdoneinthispaper.DigitalChinaisthebiggestcompanyinChina’sITdistributionmarket.DigitalChina’scustomerdatasampleisusedinthispaper.TheconclusionisthatSMCmodeldoesworkinITdistributionmarketindustry.Also,thereviseadviceforSMCisputforwardtomeetdifferenttypeofcustomerbehavior.Keywords:customerrelationshipmanagement;SMCmodel;customervalue:2003203205:(70371056);:(1972-),,,,,;(1933-),,,,,,;(1945-),,,,,,(CustomerRelationshipManagement,CRM),L:?,,,?L,L?LL?L,:©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.1);,,;,;2)T1;3)T2K;4)LDavidCSchmittlein,DonaldGMorrisonRichardColombo[1]DavidCSchmittleinRobertAPeterson[2],SMC,LSMC,L,,LDavidCSchmittleinRobertAPeterson,SMC;WernerJReinartzVKumar[3],,SMCLSMCLIT,IT,SMC,LIT,IT,LIT,L,SMCL,ITLSMCLSMC198715,,DavidCSchmittleinRobertAPetersonLSMC,,L,,,SMCLIT,,,SMCLITIT,ITSMCLITL,SMCITL,,L:,SMC;,,SMCIT;,,SMC,;,,SMCIT;,SMC,,L2SMCSMC:(activecustomers)(inactivecustomers).,,L,P(alive)L,LX=(x,t1,t2).t0=0,Xt0t2,x,t1L,P(aliveûX)LSMC5:1),LK0720043©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.,,tx:P[X=xûK(t),t]=e-(Kõt)xõ(Kt)xx!,x=0,1,2,3,(1)2)LL,:f(tûL)=Le-Lt(2)3)K#(),f(Kûr,A)=Ar#(r)Kr-1e-AK,K0,r,A0(3)E[K]=röG,röG2,rL4)#,:g(Lûs,B)=Bs#(s)Ls-1e-BL,s,B0(4)E[L]=söB,söB2,sL5)KLL,SMC:É)t2:AB,P[Tt2ûr,A,s,B,x,t1,t2]:AB:P[Tt2ûr,s,AB,X=x,t1,t2]=1+sr+x+sA+t2A+t1r+xB+t2A+t1sF(a1,b1;c1;z1(t1)-B+t2A+t2sF(a1,b1;c1;z1(t2))-1(5),a1=r+x+s;b1=s+1;c1=r+x+s+1;z1(y)=A-BA+y,F(a,b;c;z)(Gausshypergeometricfunction)LAB:P[Tt2ûr,s,AB,X=x,t1,t2]=1+sr+x+sA+t2B+t1r+xB+t2B+t1sF(a2,b2;c2;z2(t1))-A+t2B+t2r+xF(a2,b2;c2;z2(t2))-1(6),a2=r+x+s;b2=r+x;c2=r+x+s+1;z2(y)=B-AB+yLA=B:P[Tt2ûr,s,A=B,X=x,t1,t2]=1+sr+x+sA+t2A+t1r+x-1-1Ê)t2t3:E[x3ûr,A,s,B,X,t1,t2,t3]=P[Tt2ûr,A,s,B,x,t1,t2]õE[r3,A3,s3,B3,t3](8),r3=r+X,A3=A+T,s3=s,B3=B+T,P[Tt2ûr,A,s,B,x,t1,t2]t2L(6):E[xûr,A,s,B,t]=rBA(s-1)1-BB+ts-1(9)Ë)t2t3x3:P[X3ûr,A,s,B,x,t1,t2,t3]=P[X3ûr+x,A+t2,s,B+t2,t3]õP[Tt2ûr,A,s,B,x,t1,t2](10)173SMCIT©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.,(10):P[Xûr,A,s,B,t]=x+r-1xAA+trtA+txBB+ts+x+r-1xsArBsV3(11)V3=t0Hx(A+H)-(r+x)(B+H)-(s+1)dH(12)A,B,r,s,DavidC.Schmittlein&RobertA.PetersonDavidCSchmittlein,DonaldGMorrisonRichardColombo3(32step),(22step),L1)2)3)DavidCSchmittlein,DonaldGMorrisonRichardColomboSMC,DavidC.Schmittlein&RobertA.Peterson,,L3SMCITSMCSMC5LITIT,,,,L,IT,SMC:PoissonL,,Ehrenberg[4],Uncle&Ehrenberg[5],L,ITLPoisson,##L,,L,SMCIT,:1SMCIT;2SMCIT;3SMC;1(%)2000104914.82000115416.32000125316.020011288.520012185.4200134513.6200144814.5200153610.93311004200010,200111()L552(200010),,7,331,5,SMC,,I200110,SMC,11,200111,;II200111,L2720043©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.5SMCITI,DavidC.Schmittlein&RobertA.Peterson22step,r=1.66,A=3.58,s=0.33,B=0.5,Maple-v7.0SMC(5)-(12)(),200111LIII200111,SMCIT,LSMCITAB,(5)LX=(x,t1,t2),(5)t2L200010t0=1,I,t2200111,t2=13,,2.2t2X=(x,t1,t2)t2=13135(1,1,13)0.070792(3,3,13)0.076311(8,10,13)0.788153(3,10,13)0.874694(2,13,13)1.0001154(14,13,13)1.0001122(23,13,13)1.000P[Tt2ûr,A,s,B,x,t1,t2],r=1.66,A=3.58,s=0.33,B=0.5,t2=13,DavidCSchmittlein,DonaldGMor2risonRichardColombo,:,,,792153;,,,311153;,792153311153LSMCIT,L331200111,0.600,11,0;,1112;111,11,2L3.3200111200111012[0.000,0.600)15215199.34%10.66%00%[0.600,1.000)756181.33%1317.33%11.33%1.0001035553.40%4240.78%65.83%33026780.91%5616.97%72.12%,0.600L,,,;0.600,,,L373SMCIT©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.,,,,,,L,SMCIT,1LSMCITLSMCr=1.66,A=3.58,s=0.33,B=0.5SMC(8),,,L4t2X=(x,t1,t2)200111135(1,1,13)0.011792(3,3,13)0.022311(8,10,13)0.454153(3,10,13)0.243694(2,13,13)0.2181154(14,13,13)0.9331122(23,13,13)1.470E[x3ûr,A,s,B,X,t1,t2,t3],r=1.66,A=3.58,s=0.33,B=0.5,t2=13,t3=1I,200111L33111,ITSMC(2,4),:,,,311153;,,,792153200111;,11541122792153L,IT,LI331200111II200111,SMCL,0.300,1.000,2;,,12;0.800,;1.000,2L5.5200111200111012[0.000,0.300)16916798.82%21.18%00%[0.300,0.500)524178.85%1121.15%00%[0.500,0.800)856576.47%1821.18%22.35%[0.800,1.000)351337.14%2263.86%00%[1.000,1.700)13538.46%323.08%538.46%33026780.91%5616.97%72.12%4720043©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.5,,,L,L,,,,,,L,LSMCITLr=1.66,A=3.58,s=0.33,B=0.5(9)I200110t3x3P[X3ûr,A,s,B,x,t1,t2,t3],30,2Lx3,L,200111,3,30;27,2.12%;156,16.97%;,80.81%Lt3,,L,SMCITL(9),P[X3ûr,A,s,B,x,t1,t2,t3]01,,LI,L,IT,3L,,,L6SMCITSMC,:L(Customer2base)L,,,L,,LSMC,,,,,LL,L,L,L,L,,L,,;,,,,,L,L,,L:rA=0.46,5.56Lr=1.66,,LsB=0.66Ls=0.33,,