两个双目标竞争选址问题模型

200711:100026788(2007)01200992081,1,2(11,100029;21,):,.,,,.:;;;:F110174:ATwoBi2objectiveOptimizationModelsforCompetitiveLocationProblemsHUAGuo2wei1,YANGFeng2mei1,LAIKinKeung2(11FacultyofScience,BeijingUniversityofChemicalTechnology,Beijing100029,China;21DepartmentofManagementSciences,CityUniversityofHongKong,HongKong,China)Abstract:Weconsidertwokindsofbi2objectivecompetitivelocationproblems.Oneistomaximizemarketshareandtominimizecost,andtheotheristomaximizeprofitandprofitmargin.Theirpropertiesandrelationsarestudied,andweshowthattheycanbesettledbysolvingasingleobjectiveparametricintegerprogrammingproblem,andthenweprovideanexactandanapproximateapproachtoobtainthesetofefficientsolutions.Finally,anumericalexampleispresentedtoilluminatethesolutiontechniques.Keywords:competitivelocation;bi2objective;weightingmethod;parametricprogramming:2005211207:(10171108):(1959-),,:,E2mail:[e-mail].1,,,[13],,.[4],,,.2080,[511].,,,[11],,.,();,,,.2,.A,,A,B,A(),.,,(),.AB,.::i,I=;j,J=;JB=B;ai=i;bi=Bi;cj=j(),;dij=ij();dibi=iB();Ni(bi)={PjJ|dijdibi};Oi(bi)={PjJ|dij=dibi,jbi};C=();0=A();k=.:xj=1Aj0:yi=1iA0zi=1i0,(BP1):(BP1)maxR(y,z)=iIaiyi+015iIaiziminC(x)=jJcjxjs.t.yijNi(bi)xj,PiI,Ni(bi),(12a)yi=0,Ni(bi)=,(12b)zijOi(bi)xj,PiI,Oi(bi),(22a)zi=0,Oi(bi)=,(22b)yi+zi1,PiI,(3)C(x)C,(4)kR(y,z)-C(x)0,(5)xj,yi,zi{0,1},PiI,PjJ.(6)A,A,AB,A..(12a)Ni(bi)A,iA,Ni(bi)=,bii,yi=0.(22a)Oi(bi)A,iA,Oi(bi)=,ibii,zi=0.(3)iA(yi=1,zi=0),A(yi=0,zi=1),B(yi=zi=0).(4),(5),,kR(y,z),(6)021.(5),,,0.aii,R(y,z).,,00120071,BP2:(BP2)maxR(y,z)-C(x)maxR(y,z)C(x)s.t.(x,y,z)FFBP1(k=1)BP1:maxR(y,z)-(1-)C(x),s.t.(x,y,z)F0,:(SP)f()=maxR(y,z)-C(x),s.t.(x,y,z)F,=1-0.BP2,,BP2SP,BP1BP2SP,.13F1,f(),0,f()=0=3.:(F1)maxR(y,z)C(x)s.t.(x,y,z)F,[12,13],.=1,f(),3,.2(x(),y(),z())SP,1)R(y(),z())C(x())0;2)R(y(),z())-C(x())[0,1],[1,+);3)R(y(),z())C(x())[0,3],R(y(),z())C(x())3,[3,+),R(y(),z())C(x())3.1)012,:R(y(1),z(1))-1C(x(1))R(y(2),z(2))-1C(x(2)),(a)R(y(2),z(2))-2C(x(2))R(y(1),z(1))-2C(x(1)).(b):(2-1)[C(x(1))-C(x(2))]0,C(x(1))C(x(2)).(a):R(y(1),z(1))-R(y(2),z(2))1[C(x(1))-C(x(2))]0,R(y(1),z(1))R(y(2),z(2)),,R(y(),z())C(x())0.2)0121,(b)R(y(1),z(1))-R(y(2),z(2))2[C(x(1))-C(x(2))]C(x(1))-C(x(2)),R(y(1),z(1))-C(x(1))R(y(2),z(2))-C(x(2)).112,(a)R(y(1),z(1))-R(y(2),z(2))1[C(x(1))-C(x(2))]C(x(1))-C(x(2)),R(y(1),z(1))-C(x(1))R(y(2),z(2))-C(x(2)).3)3,R(y(),z())C(x())3,R(y(),z())-3C(x())0,f(3)=0.1,3,f()0,R(y(),z())C(x()),R(y(),z())C(x())3.3,f()0,R(y(),z())C(x()),3,R(y(),z())C(x())3.0123,R(y(1),z(1))-R(y(2),z(2))2[C(x(1))-C(x(2))]R(y(2),z(2))C(x(2))[C(x(1))-C(x(2))],1011R(y(1),z(1))C(x(1))R(y(2),z(2))C(x(2)),R(y(),z())C(x()).312,..[14][1,3].22),0121,R(y(1),z(1))-R(y(2),z(2))C(x(1))-C(x(2)),R(y,z),R(y,z)C(x).,112,R(y,z),R(y,z)C(x).23),3,,3.3,3,.3(1,3),SP(x(),y(),z())BP2,,BP2[1,3]SP.1,2(1,3),12.22)3),R(y(),z())-C(x())R(y,z)C(x)(1,3),BP2,(x(1),y(1),z(1))(x(2),y(2),z(2)),,(x(),y(),z()),(1,3)BP2.[14]..4BP2BP1.(x0,y0,z0)BP2,(x,y,z)F,R(y0,z0)-C(x0)R(y,z)-C(x)R(y0,z0)C(x0)R(y,z)C(x)(x0,y0,z0)BP1,(x,y,z)F,R(y0,z0)R(y,z)C(x0)C(x)R(y0,z0)R(y,z)C(x0)C(x),R(y0,z0)-C(x0)R(y,z)-C(x)R(y0,z0)C(x0)R(y,z)C(x),..3BP2SP,13,4BP1BP2,BP1BP2,,BP1BP2.500,0,1)R(y(),z())=R(y(0),z(0)),C(x())=C(x(0));2)SPSP0,.1).00,C(x())=C(x(0)),00,10C(x(0))C(x(1)),21)C(x(0))C(x(1)),,1,21C(x(1))C(x(2)),x(n),n=0,1,2,C(x(n)),C(x(n)),C(x(n))C(x(n-1))-1C(x(0))-n,,C(x(n))-,C(x(n))0,(a)(b)R(y(0),z(0))=R(y(),z()).2)1),0,R(y(),z())-C(x())=R(y(0),z(0))-C(x(0)),,SP0SP,,,SPSP0..5,0,C(x())=C(x(0)),21),C(x()),C(x(0)),23),[0,+).C(x(0))F2:20120071(F2)minC(x)s.t.(x,y,z)F.[0,+),3.,BP1SP,[0,+),5[0,+),,SP,[0,3],[3,23],,[(n-1)3,n3],n,C(x)F2.,BP1BP2SP,,BP2,[1,3],3F1.BP1,[0,n3],nF2.3311BP1BP2,F2F1,F2,F1[12,13],,:1)(x0,y0,z0)F,1=R(y0,z0)C(x0),i=1;2)(xi,yi,zi)=argf(i);3)f(i)=0,,i,(xi,yi,zi).,i+1=R(yi,zi)C(xi),i=i+1,2).BP1BP2,[15,16],.,LB(),UB().LB()=UB(),f().,f(),[a,b][a,c]b[c,b]a,acb,[a,b].1ABQAPAB,PQ,ABQAP.V={|(,f())LB(),,f()LB()}.([1,3]):1)SP1,SP3;2)LB()V;3)V=,.,SP,V,,2)..f()[1,3]ABCDE,1.1f()[1,3]2SP,[1,3]SP1,SP3,,LB()APPE,UB()AE,P,f(P)LB(P),V={P}.SPP,Q,LB()(ABBRRE),BR,2,f(B)=LB(B),f(R)LB(R),V={R},f()[1,Q].[Q,3],SPR,,S,LB()(QCCDDE),CD,f3011(C)=LB(C),f(D)=LB(D),V=,,f()[Q,S][S,3],4,[1,B][B,C][C,D][D,3]ABBCCDDE.312,,,,311.,R(y,z)-C(x),[17](Addalgorithm),[17](Exchangealgorithm),,,.,,,,(4)(5).:1)();2),.,,,1).BP2,F13,,,3,f(3)=0,f(),,3.3,123,ii+1BP2,i+015,SPi+015,,.BP1,F2C(x),[0,1][3,n3],ii+1BP1,.[1,3]BP2.4.,,,.0=280,C=800,BEFK.1.3,,,A,D,I,J,,25,.401200711R(y,z)C(x)R(y,z)-C(x)R(y,z)PC(x)[0,12P13]A,C,D,I,J12107754351156[12P13,22P23]A,D,I,J10906454451169[22P23,1]A,D,I8704154552110[1,1.2]A,D,I8704154552110[1.2,10]A,I69026542521603[10,+)A,D54025029021160A,I,J,D,C121077543511560.5A,I,D,J,C121077543511561A,I,D87041545521101180A,I690265425216032.63A,I69026542521605.2A,I690265425216010.4A,D5402502902116:BP2A,BP1A.3=2160,3,1160,.5,.,,.,,,,,,.,.,(),,,.,.,,,,,,,...:[1]CurrenJ,MinH,SchillingD.Multiobjectiveanalysisoffacilitylocationdecisions[J].EuropeanJournalofOperationalResearch,1990,49:295-307.[2]FernandezE,PuertoJ.Multiobjec