基于区间数的应急物资储备库最小费用选址模型

191Vo.l19,No.120102OPERATIONSRESEARCHANDMANAGEMENTSCIENCEFeb.2010:2008212208:(NO:70471063,70771010);985(NO:107008200400024):(19642),,,,,:郭子雪1,2,齐美然1,张强2(1.,071002;2.,100081):,,,:;;;:O224:A:100723221(2010)0120015206MinmiumCostModelofEmergencyMaterialStorage`LocationBasedonIntervalNumberGUOZi2xue1,2,QIMei2ran1,ZHANGQiang2(1.SchoolofManagement,HebeiUniversity,Baoding071002,China;2.SchoolofManagementandEconom2ics,BeijingInstituteofTechnology,Beijing100081,China)Abstrac:tInthispaper,aminimumcostmodelofemergencymaterialstoragelocationbasedonintervalnumberisstudied.Firs,ttheconceptandoperationsofintervalnumberaregiven.Second,themodelofemergencyma2terialstoragelocationbasedonintervalnumberissetup,andthesolutionalgorithmforthismodelispresented.Finally,anumericalexampleshowsthatthemethodisvalid.Keywords:managementengineering;locationmode;lintervalnumber;emergencymaterialstorage0Hakimi[1]1964,[2~11],,;2080,,,,,,,,,,,,11[a,b],,a,bIR,a[b,a,bI(R)={[a,b]|a,bIR,a[b},,RI(R),,2[a,b],[c,d]II(R),:1)[a,b]+[c,d]=[a+c,b+d]2)[a,b]-[c,d]=[a-d,b-c]3)r[a,b]=[ra,rb],r\0[rb,ra],r0,rIR3[a,b][c,d],[a,b][[c,d]a[c;b[d;[a,b][c,d][a,b][[c,d][a,b]X[c,d]4rIR,a[r[b,r[[a,b]5A=[a-,a+],B=[b-,b+],len(A)=a+-a-,len(B)=b+-b-,P(A[B)=max(0,len(A)+len(B)-max(0,a+-b-))len(A)+len(B)A[B,ab,,P(a[B)=max(0,len(B)-max(0,a-b-))len(B)P(A[b)=max(0,len(A)-max(0,a+-b))len(A)12,P(A[B):1)P(A[B)=P(B[A),P(A[B)=P(B[A)=1,A=B2)a+[b-,P(A[B)=13)a-\b+,P(A[B)=04)A,B,C,A[B,P(A[C)\P(B[C)1)~4),,2)AB,3AB22.1S1,S2,,,Snn,D1,D2,,,Dmmcij=[c-ij,c+ij]SjDi(i=1,2,,,16201019n;j=1,2,,,m),fj=[f-j,f+j]Sj(),,cijfj,ajSj,bi=[b-j,b+j]Di,,2.20-1xij,0-1xij=1,DijSj0,DijSj,0-1yj=1,j,0,j,minEmi=1Enj=1[c-j,c+j]xij+Enj=1[f-j,f+j]yj(1)s.t.Enj=1xij=1(i=1,2,,,m)(2)xij-yj[0(i=1,2,,,m;j=1,2,,,n)(3)Emi=1[b-j,b+j]xij-ajyj[0(j=1,2,,,n)(4)xij,yjI{0,1}(i=1,2,,,m;j=1,2,,,n)(5),(1);(2);(3);(4),:Enj=1ajyj\Emi=1[b-j,b+j];(5)xjyi0-1,minEmi=1Enj=1[c-ij,c+j]xij+Enj=1[f-j,f+j]yjs.t.Enj=1xij=1(i=1,2,,,m)xij-yj[0(i=1,2,,,m;j=1,2,,,n)xij,yjI{0,1}(i=1,2,,,m;j=1,2,,,n)36X(1)~(5),X*Z(X*)Z(X)1minZ1=Emi=1Enj=1c-jxij+Enj=1f-jyjs.t.Enj=1xij=1(i=1,2,,,m)xij-yj[0(i=1,2,,,m;j=1,2,,,n),(6)Emi=1[b-j,b+j]xij-ajyj[0(j=1,2,,,n)xij,yjI{0,1}(i=1,2,,,m;j=1,2,,,n)minZ2=Emi=1Enj=1c+jxij+Enj=1f+jyj171,:s.t.Enj=1xij=1(i=1,2,,,m)xij-yj[0(i=1,2,,,m;j=1,2,,,n),(7)Emi=1[b-j,b+j]xij-ajyj[0(j=1,2,,,n),xij,yjI{0,1}(i=1,2,,,m;j=1,2,,,n).(6)(7)Pareto(1)~(5)2minZ3=(1-A)(Emi=1Enj=1c-jxij+Enj=1f-jyj)+A(Emi=1Enj=1c-jxij+Enj=1f+jyj)s.t.Enj=1xij=1(i=1,2,,,m)xij-yj[0(i=1,2,,,m;j=1,2,,,n)Emi=1[b-j,b+j]xij-ajyj[0(j=1,2,,,n)xij,yjI{0,1}(i=1,2,,,m;j=1,2,,,n)(6)(7)Pareto,(1)~(5)7(1)~(5)X,P(Emi=1[b-j,b+j]xij-ajyj[0)=KXEmi=1[b-j,b+j]xij-ajyj[03K,Emi=1[b-j,b+j]xij-ajyj[0(1-K)Emi=1b-jxij+KEmi=1b+jxij-ajyj[0,len([b-j,b+j]xij)=b+jxij-b-jxij,len(ajyj)=0len(Emi=1[b-j,b+j]xij)-(Emi=1b+jxij-ajyj)len(Emi=1[b-j,b+j]xij)\K5:Emi=1b-jxij-ajyj\0,P(Emi=1[b-j,b+j]xij-ajyj[0)\K;Emi=1b-jxij-ajyj0,P(Emi=1[b-j,b+j]xij-ajyj[0)=1\KP(Emi=1[b-j,b+j]xij-ajyj[0)\K,P(Emi=1[b-j,b+j]xij-ajyj[0)\K,(1-K)Emi=1b-jxij+KEmi=1b+jxij-ajyj[08AK(1)~(5)A-K,XKA,AK,(1)~(5)minZ3=(1-A)(Emi=1Enj=1c-jxij+Enj=1f-jyj)+A(Emi=1Enj=1c+jxij+Enj=1f+jyj)s.t.Enj=1xij=1(i=1,2,,,m)xij-yj[0(i=1,2,,,m;j=1,2,,,n)(1-K)Emi=1b-jxij+KEmi=1b+jxij-ajyj[0(j=1,2,,,n)xij,yjI{0,1}(i=1,2,,,m;j=1,2,,,n)18201019,(1)~(5),AK,46D1,D2,,,D6,4S1,S2,S3,S4Sjbj,cij=[c-ij,c+ij]ai=[a-i,a+i]()fj=[f-j,f+j](1),1(:)(:)DjSi123456fjbjS1[3,4][5.5,6.4][2.5,3][9,10][6.5,7][8,8.5][700,800]25S2[6,6.5][4.5,5.5][7,7.5][5,5.5][8,9][3,3.5][900,950]20S3[7,8][6,6.5][4,4.5][5,6][2,2.5][8,9][1050,1100]30S4[10,11][8,9][8,8.5][3,4][9,9.5][4,4.5][750,820]26ai[5,6][6.5,7][8,9][4,5][9,10][6,6.5]--0-1yj=1,j,0,j(j=1,2,,3,4),0-1xij=1,Disj0,Disj(i=1,2,3,4,5,6;j=1,2,3,4),minZ=E6i=1E4j=1[c-ij,c+ij]xij+E4j=1[f-j,f+j]yjs.t.E4j=1xij=1xij-yj[0(i=1,2,4,5,6j=1,2,3,4)E6i=1[a-i,a+i]xij-bjyj[0(j=1,2,3,4)xij,yjI{0,1}(i=1,2,3,4,5,6j=1,2,3,4)AK,minZ=(1-A)(E6i=1E4j=1c-ijxij+E4j=1f-jyj)+A(E6i=1E4j=1c+ijxij+E4j=1f+jyj)s.t.E4j=1xij=1xij-yj[0(i=1,2,4,5,6j=1,2,3,4)E6i=1[a-i,a+i]xij-bjyj[0(j=1,2,3,4)xij,yjI{0,1}(i=1,2,3,4,5,6j=1,2,3,4)A-1,K=1,minZ1=4x11+6.4x21+3x31+10x41+7x51+8.5x61+6.5x12+5.5x22+7.5x32+5.5x42+9x52+3.5x62+8x13+6.5x23+4.5x33+6x43+2.5x53+9x63+11x14+9x24+8.5x34+4x44+9.5x54+4.5x64+800y1+950y2+1100y3+820y4191,:s.t.x11+x12+x13+x14=1,x21+x22+x23+x24=1,x31+x32+x33+x34=1x41+x42+x43+x44=1,x51+x52+x53+x54=1,x61+x62+x63+x64=1x11[y1,x21[y1,x31[y1,x41[y1,x51[y1,x61[y1x12[y2,x22[y2,x32[y2,x42[y2,x52[y2,x62[y2x13[y3,x23[y3,x33[y3,x43[y3,x53[y3,x63[y3x14[y4,x24[y4,x34[y4,x44[y4,x54[y4,x64[y46x11+7x21+9x31+5x41+10x51+6.5x61[25y16x12+7x22+9x32+5x42+10x52+6.5x62[20y26x13+7x23+9x33+5x43+10x53+6.5x63[30y36x14+7x24+9x34+5x44+10x54+6.5x64[26y4xij,yjI{0,1}(i=1,2,3,4,5,6j=1,2,3,4):x11=1,x21=1,x31=1,x44=1,x54=1,x64=1,y1=1,y4=1,0,Z01=1651.4,A=0,K=1,:x11=1,x31=1,x51=1,x24=1,x44=1,x64=1,y1=1,y4=1,0,1477;A=1,K=0,:x11=1,x21=1,x31=1,x44=1,x54=1,x64=1,y1=1,y4=1,0,1651.4;A=0.8,K=0.7,:x11=1,x21=1,x31=1,x44=1,x54=1,x64=1,y1=1,y4=1,0,1616.525,,,:[1]HakimiSL.Optimallocationofswitchingcentersandtheabsolutecentersand