运输问题的产销平衡表与单位运价

TPMKstandardizationoffice【TPMK5AB-TPMK08-TPMK2C-TPMK18】运输问题的产销平衡与单位运价下表给出某运输问题的产销平衡表与单位运价表。将此问题转化为最小费用最大流问题，画出网络图并求数值解。产量销地123产量2030242252087销量456网络图如下，弧旁数字为.设为边(i,j)上的数量，为边(i,j)上的单位运费，则最小费用最大流的数学为边(i,j)上的额定容量，规划表达sets:points/s,v1,v2,v3,v4,v5,t/;edge(points,points)/s,v1s,v2v1,v3v1,v4v1,v5V2,v3v2,v4v2,v5v3,tv4,tV5,t/:c,u,f;endsetsdata:c=0020245302220000;u=87888777456;vf=15;enddatamin=@sum(edge(i,j):c(i,j)*f(i,j));@for(points(i)|i#ne#@index(s)#and#i#ne#@index(t):@sum(edge(i,j):f(i,j))-@sum(edge(j,i):f(j,i))=0;);@sum(edge(i,j)|i#eq#@index(s):f(i,j))=vf;@sum(edge(j,i)|i#eq#@index(t):f(j,i))=vf;@for(edge(i,j):@bnd(0,f(i,j),u(i,j)));endGlobaloptimalsolutionfound.Objectivevalue:240.0000Totalsolveriterations:1VariableValueReducedCostVF15.000000.000000C(S,V1)0.0000000.000000C(S,V2)0.0000000.000000C(V1,V3)20.000000.000000C(V1,V4)24.000000.000000C(V1,V5)5.0000000.000000C(V2,V3)30.000000.000000C(V2,V4)22.000000.000000C(V2,V5)20.000000.000000C(V3,T)0.0000000.000000C(V4,T)0.0000000.000000C(V5,T)0.0000000.000000U(S,V1)8.0000000.000000U(S,V2)7.0000000.000000U(V1,V3)8.0000000.000000U(V1,V4)8.0000000.000000U(V1,V5)8.0000000.000000U(V2,V3)7.0000000.000000U(V2,V4)7.0000000.000000U(V2,V5)7.0000000.000000U(V3,T)4.0000000.000000U(V4,T)5.0000000.000000U(V5,T)6.0000000.000000F(S,V1)8.000000-10.00000F(S,V2)7.0000000.000000F(V1,V3)2.0000000.000000F(V1,V4)0.00000012.00000F(V1,V5)6.0000000.000000F(V2,V3)2.0000000.000000F(V2,V4)5.0000000.000000F(V2,V5)0.0000005.000000F(V3,T)4.0000000.000000F(V4,T)5.000000-8.000000F(V5,T)6.000000-15.00000RowSlackorSurplusDualPrice1240.0000-1.00000020.0000000.00000030.000000-10.0000040.00000020.0000050.00000012.0000060.0000005.00000070.000000-10.0000080.000000-20.00000结果其最小总费用为240。