基于模糊机会约束规划的最优产量决策

186Vol.18,No.6200912OPERATIONSRESEARCHANDMANAGEMENTSCIENCEDec.2009:2008211202:(70471063;70771010);985(107008200400024):(19822),,,:,;(19552),,,,:,,(,100081):,,CournotStackelberg,,,:;;;;:C934:A:100723221(2009)0620089208TheOptimumOutputQuantityDecisionBasedonFuzzyChanceConstrainedProgrammingZHANGHui2juan,ZHANGQiang(SchoolofManagementandEconomics,BeijingInstituteofTechnology,Beijing100081,China)Abstract:Theoptimumoutputquantitydecisionofaduopolymarketisinvestigatedunderafuzzyenvironment.CombingtheCournotmodel,Stackelbergmodelandthefuzzypossibilitytheory,afuzzychanceconstrainedpro2grammingmodelisdevelopedtodeterminetheoptimumoutputquantityunderfourgamepatterns.Finally,anu2mericalexampleisgivenwhichsuggeststhatthebestdecisionisbothofthecompaniesarefollowersbasedonai2mingforthemaximumprofitofaduopolymarket.Keywords:managementscience;cournotmodel;stackelbergmodel;chanceconstrainedprogramming;outputquantitydecision0,.,,AB,,.,:.,,,;,,AlepuzUrbano[1],Lavigne[2],,,[3],,,,,,,,,1Pos{A}APos{A},Nahmias[4]:,P(),1Pos{}=12Pos{}=03P(){Ai},Pos{mi=1Ai}=sup1imPos{Ai},Liu[5]4i,Posi{},i=1,2,,n,,=ni=1i,AP(),Pos{A}=sup(1,2,,n)APos{1}Pos{2}Pos{n},Pos=ni=1Posi1[4](,P(),Pos)R,2[5]Pos{0}=0(Pos{0}=0),()3[5]f:RnR,i(i,P(i),Posi),i=1,2,,n,=f(1,2,,n)(ni=1i,P(ni=1i),ni=1Posi),(1,2,,n)=f(1(1),2(2),,n(n)),P(1,2,,n)ni=1i4[6]1,2,,n,RB1,B2,,Bn,Pos{iBi,i=1,2,,n}=min1inPos{iBi},1,2,,n1[7]1,2,,n,fi:RR,i=1,2,,n.f1(1),f2(2),,fn(n),5[8](,P(),Pos),(0,1],L=inf{r|Pos{r}},U=sup{r|Pos{r}},L(U)()1=(a,b,c)L=b+a(1-),U=b+c(1-).2[9]ù,(0,1],(+ù)L=L+ùL,(+ù)U=U+ùU3[10](,P(),Pos),f:RR,(0,1],(1)f(x)x,(f())L=f(L)(f())U=f(U);(2)f(x)x,(f())L=f(U)(f())U=f(L)2,:qiiQ=qA+qBp(Q)09200918cfiiciiikikqFiki(follower)kqLiki(leader)k:,,AB,,P(Q)=A-Q=A-(qA+qB),A(1,P(1),Pos1),()(2,P(2),Pos2),A.3P(Q)12,P(12),Pos1Pos2,Pos{A-Q0}=0cfAcfBcAcB(3,P(3),Pos3)(4,P(4),pos4)(5,P(5),pos5)(6,P(6),Pos6),A.A=(A-Q-cA)qA-cfAB=(A-Q-cB)qB-cfB3,AB(1235,P(1235),Pos1Pos2Pos3Pos5)(1246,P(1246),Pos1Pos2Pos4Pos6)3LiuIwamura[11,12],,,:(1);(2)A,B;(3)B,A;(4).(1),;(2)(3),:,.(4),,1(),,,maximaxmaxqFA1A1(qFA1)s.t.Pos{A-(qFA1+qFB1)-cA)qFA1-cfAA1(qFB1)}Pos{A-(qFA1+qFB1)-cA)0}=0(1)maxqFB1B1(qFB1)s.t.Pos{A-(qFA1+qFB1)-cB)qFB1-cfBB1(qFB1)}Pos{A-(qFA1+qFB1)-cB)0}=0(2),qFA1qFB1,A1(qFA1)B1(qFB1)ABmaximaxmaxqFA1(A1(qFA1))U=((A-(qFA1+qFB1)-cA)qFA1-cfA)Us.t.Pos{A-(qFA1+qFB1)-cA0}=0(3)maxqFB1(B1(qFB1))U=((A-(qFA1+qFB1)-cB)qFB1-cfB)Us.t.Pos{A-(qFA1+qFB1)-cB0}=0(4)196,:1(A1(qFA1))U(B1(qFB1))UAB,pos{A-(qFA1+qFB1)-cA0}=0Pos{A-(qFA1+qFB1)-cB0}=0,(1)A,q3FA1=AU-2cLA+cLB3L,,(A1(q3FA1))U=(AU+cLB-2cLA)29L-cLfA(2)B,q3FB1=AU-2cLB+cLA3L,,(B1(q3FB1))U=(AU+cLA-2cLB)29L-cLfBAcfAcA,1-3A(A1(qFA1))U=(A-(qFA1+qFB1)-cA)qFA1-cfA)U=AU-L(qFA1+qFB1)-cLA)qFA1-cLfA=-Lq2FA1+(AU-LqFB1-cLA)qFA1-cLfAAd(A1(qFA1))UdqFA1=AU-2LqFB1-cLA,d2(A1(qFA1))Udq2FA1=-2L,d2(A1(qFA1))Udq2FA1=-2L0,(A1(qFA1))U,q3FA1(qFB1)=AU-LqFB1-cLA2L(5),(B1(qFB1))Uq3FB1(qFA1)=AU-LqFA1-cLB2L(6)(5)(6),ABq3FA1=AU-2cLA+cLB3L,q3FB1=AU-2cLB+cLA3LAB(A1(q3FA1))U=(AU+cLB-2cLA)29L-cLfA,(B1(q3FB1))U=(AU+cLA-2cLB)29L-cLfBLiu[11]minimax,,maxqFA1(A1(qFA1))L=((A-(qFA1+qFB1)-cA)qFA1-cfA)Ls.t.Pos{A-(qFA1+qFB1)-cA0}=0(7)maxqFA1(B1(qFB1))L=((A-(qFA1+qFB1)-cB)qFB1-cfB)Ls.t.Pos{A-(qFA1+qFB1)-cB0}=0(8)2(A1(qFA1))L,(B1(qFB1))LAB,pos{A-(qFA1+qFB1)-cA)}=0pos{A-(qFA1+qFB1)-cB0}=0,(1)A,q3FA1=AL-2cUA+cUB3U,,(A1(q3FA1))L=(AL+cUB-2cUA)29U-cUfA;(2)B,q3FB1=AL-2cUB+cUA3U,,29200918(B1(q3FB1))L=(AL+cUA-2cUB)29U-cUfB1,2A,B():AB,BAmaximaxmaxqLA2A2,(qLA2,q3FB2(qLA2)s.t.Pos{A-(qLA2+q3FB2(qLA2))-cA)qLA2-cfAA2(qLA2)}Pos{A-(qLA2+q3FB2(qLA2))-cA0}=0q3FB2maxqFB2B2(qFB2)s.t.Pos{A-(qLA2+qFB2)-cB)qLB2-cfBB2(qLB2)}Pos{A-(qLA2+qFB2)-cB0}=0(9),AqLA2,B2(qFB2)B,A2(qLA2,q3FB2(qLA2))A,(9)maxqLA2(A2(qLA2,q3FB2(qLA2)))U=((A-(qLA2+q3FB2(qLA2))-cA)qLA2-cfA)Us.t.Pos{A-(qLA2+q3FB2(qLA2))-cA)0}=0q3FB2maxqFB2B2((qFB2))U=((A-(qLA2+qFB2)-cA)qFB2-cfB)Us.t.Pos{A-(qLA2+qFB2)-cB)0}=0(10)3A2(qLA2,q3FB2(qLA2))U(B2(qFB2))UAB,pos{A-(qLA2+q3FB2(qLA2))-cA0}=0pos{A-(qLA2+qFB2)-cB0}=0(10)(cLB-2cLA+AU2L,2cLA-3cLB+AU4L)2-31,Bq3FB2(qLA2)=AU-LqLA2-cBL2L(A2(qLA2,q3FB2(qLA2)))U=-Lq2LA2+(AU-Lq3FB2(qLA2)-cLA)qLA2-cLfA=-12Lq2LA2+12(AU+cLB-2cLA)qLA2-cLfA(A2(qLA2))Ud(A2(qLA2))UdqLA2=-LqLA2+AU+cLB2-cLA,d2(A2(qLA2))Udq2LA2=-L0(A2(qLA2))UqLA2,q3LA2=cLB-2cLA+AU2L(11)(A2(q3LA2))U=(AU+cLB-2cLA)28L-cLfA(12)Bq3FB2=2cLA-3cLB+AU4L(13)396,:(B2(q3FB2))U=(AU+2cLA-3cLB)216L-cLfB(14)minimaxmaxqLA2(A2(qLA2,q3FB2(qLA2)))L=((A-(qLA2+q3FB2(qLA2))-cA)qLA2-cfA)Ls.t.Pos{A-(qLA2+q3FB2(qLA2))-cA0}=0q3FB2maxqLA2(B2(qLB2))L=((A-(qLA2+qFB2)-cB)qFB2-cfB)Ls.t.Pos{A-(qLA2+qFB2))-cB0}=0(15)4(A2(qLA2,q3FB2(qLA2)))L(B2(qFB2))LdAB,Pos{A-(qLA2+q3FB2(qLA2))-cA0}=0Pos{A-(qLA2+qFB2)-cB0}=0(15)(cUB-2cUA+AL2U,2cUA-3cUB+AL4U)3,3B,A()2,:(1)maximax(q3FA3,q3LB3)=(2cLB-3cLA+AU4L,cLA-2cLB+AU2L)AB(A3(q3FA3))U=(AU+2cLB-3cLA)216L-cLfA,(B3(q3LB3))U=(AU+cLA-2cLB)28L-cLfA(2)minimax(q3FA3,q3LB3)=(2cUB-3cUA+AL4U,cUA-2cUB+AL2U)AB(A3(q3FA3))L=(AL+2cUB-3cUA)216U-cUfA,(B3(q3LB3))L=(AL+cUA-2cUB)28U-cUfB4,,23q3LA4=q3LA2=cLB-2cLA+AU2L,q3LB4=q3LB3=cLA-2cLB+AU2LAB(A4(q3LA4))U=(cLB-cLA)(AU-2cLA+cLB)4L-cLfA,(B4(q3LB4)