数学建模,线性规划,运输为问题

有限制的运输问题：6个发点6个收点，其供应量、接收量和运费如下表1（”-”表示某个

设：发点i 向收点j 的货物供应量为xij.

目标函数：

MinZ=20x11+15x12+16x13+5x14+4x15+7x16+17x21+15x22+33x23+12x24+8x25+6x26+9x31+12x32+18x33+16x34+30x35+13x36+12x41+8x42+11x43+27x44+19x45+14x46+7x52+10x53+21x54+10x55+32x56+6x64+11x65+13x66

供应限制：x11+x12+x13+x14+x15+x16=20

x21+x22+x23+x24+x25x+26=30

x31+x32+x33+x34+x35+x36=50

x41+x42+x43+x44+x45+x46=40

x52+x53+x54+x55+x56=30

x64+x65+x66=30

需求限制：x11+x21+x31+x41=30

x12+x22+x32+x42+x52=50

x13+x23+x33+x43+x53=40

x14+x24+x34+x44+x54+x64=30

x15+x25+x35+x45+x55+x65=30

x16+x26+x36+x46+x56+x66=20

LINGO 代码:

min =20*x11+15*x12+16*x13+5*x14+4*x15+7*x16+17*x21+15*x22+33*x23+12*x24+8*x25+6*x26+9*x31+12*x32+18*x33+16*x34+30*x35+13*x36+12*x41+8*x42+11*x43+27*x44+19*x45+14*x46+7*x52+10*x53+21*x54+10*x55+32*x56+6*x64+11*x65+13*x66;

x11+x12+x13+x14+x15+x16=20;

x21+x22+x23+x24+x25+x26=30;

x31+x32+x33+x34+x35+x36=50;

x41+x42+x43+x44+x45+x46=40;

x52+x53+x54+x55+x56=30;

x64+x65+x66=30;

x11+x21+x31+x41=30;

x12+x22+x32+x42+x52=50;

x13+x23+x33+x43+x53=40;

x14+x24+x34+x44+x54+x64=30;

x15+x25+x35+x45+x55+x65=30;

x16+x26+x36+x46+x56+x66=20;

LINGO 求解结果：

Global optimal solution found.

Objective value: 1620.000

Infeasibilities: 0.000000

Total solver iterations: 9

Variable Value Reduced Cost X11 0.000000 14.00000 X12 0.000000 6.000000 X13 0.000000 4.000000 X14 0.000000 3.000000 X15 20.00000 0.000000 X16 0.000000 5.000000 X21 0.000000 7.000000 X22 0.000000 2.000000 X23 0.000000 17.00000 X24 0.000000 6.000000 X25 10.00000 0.000000 X26 20.00000 0.000000 X31 30.00000 0.000000 X32 20.00000 0.000000 X33 0.000000 3.000000 X34 0.000000 11.00000 X35 0.000000 23.00000 X36 0.000000 8.000000 X41 0.000000 7.000000 X42 0.000000 0.000000 X43 40.00000 0.000000 X44 0.000000 26.00000 X45 0.000000 16.00000 X46 0.000000 13.00000 X52 30.00000 0.000000 X53 0.000000 0.000000 X54 0.000000 21.00000 X55 0.000000 8.000000 X56 0.000000 32.00000 X64 30.00000 0.000000

X65 0.000000 3.000000 X66 0.000000 7.000000

Row Slack or Surplus Dual Price 1 1620.000 -1.000000 2 0.000000 -2.000000 3 0.000000 -6.000000 4 0.000000 -5.000000 5 0.000000 -1.000000 6 0.000000 0.000000 7 0.000000 -6.000000 8 0.000000 -4.000000 9 0.000000 -7.000000 10 0.000000 -10.00000 11 0.000000 0.000000 12 0.000000 -2.000000 13 0.000000 0.000000

所以运输方案为：

运输点接收点1

运输点2 30 20 接收点2

运输点3 30 40 接收点3

运输点 10 20 4

运输点 20 接收点5

运输点6 接收点6

这样的方案费用最小为1620.