lingo软件求解线性规划举例

 

方法一（直接解）

 代码

min=4*x11+12*x12+4*x13+11*x14
    +2*x21+10*x22+3*x23+9*x24
      +8*x31+5*x32+11*x33+6*x34;
x11+x12+x13+x14=16;
x21+x22+x23+x24=10;
x31+x32+x33+x34=22;
x11+x21+x31=8;
x12+x22+x32=14;
x13+x23+x33=12;
x14+x24+x34=14;

结果 

  Global optimal solution found.
  Objective value:                              244.0000
  Infeasibilities:                              0.000000
  Total solver iterations:                             7


                       Variable           Value        Reduced Cost
                            X11        0.000000            0.000000
                            X12        0.000000            2.000000
                            X13        12.00000            0.000000
                            X14        4.000000            0.000000
                            X21        8.000000            0.000000
                            X22        0.000000            2.000000
                            X23        0.000000            1.000000
                            X24        2.000000            0.000000
                            X31        0.000000            9.000000
                            X32        14.00000            0.000000
                            X33        0.000000            12.00000
                            X34        8.000000            0.000000

                            Row    Slack or Surplus      Dual Price
                              1        244.0000           -1.000000
                              2        0.000000           -4.000000
                              3        0.000000           -2.000000
                              4        0.000000            1.000000
                              5        0.000000            0.000000
                              6        0.000000           -6.000000
                              7        0.000000            0.000000
                              8        0.000000           -7.000000

缺点，数据多时不好找

方法二（化简）

当变量有成千上万个时，而关心的非零解只是极少数，在当前窗口读解很麻烦。下面是读取非零解的窗口操作步骤：

（1）缩小当前解的窗口（不是关闭！）；

（2）把鼠标点进模型所在窗口；

 结果

  Global optimal solution found.
  Objective value:                              244.0000
  Infeasibilities:                              0.000000
  Total solver iterations:                             7


                       Variable           Value        Reduced Cost
                            X13        12.00000            0.000000
                            X14        4.000000            0.000000
                            X21        8.000000            0.000000
                            X24        2.000000            0.000000
                            X32        14.00000            0.000000
                            X34        8.000000            0.000000

                            Row    Slack or Surplus      Dual Price
                              2        0.000000           -4.000000
                              3        0.000000           -2.000000
                              4        0.000000            1.000000
                              5        0.000000            0.000000
                              6        0.000000           -6.000000
                              7        0.000000            0.000000
                              8        0.000000           -7.000000