选课策略LINGO

选课策略

max z=5x 1+4x 2+4x 3+3x 4+4x 5+3x 6+2x 7+2x 8+3x 9；

123452x x x x x ++++≥

356893x x x x x ++++≥

46792x x x x +++≥ 32120x x x --≤ 740x x -≥ 52120x x x --≤

760x x -≥

580x x -≥

92120x x x --≤

916i i x

==∑；

LINGO 出程序：

model :

max =5*x1+4*x2+4*x3+3*x4+4*x5+3*x6+2*x7+2*x8+3*x9; x1+x2+x3+x4+x5>=2;

x3+x5+x6+x8+x9>=3;

x4+x6+x7+x9>=2;

2*x3-x1-x2<=0;

x4-x7<=0;

2*x5-x1-x2<=0;

x6-x7<=0;

x8-x5<=0;

2*x9-x1-x2<=0;

x1+x2+x3+x4+x5+x6+x7+x8+x9=6;

@bin (x1);@bin (x2);@bin (x3);@bin (x4);@bin (x5);@bin (x6); @bin (x7);@bin (x8);@bin (x9);

@gin(x1);@gin(x2);@gin(x3);@gin(x4);@gin(x5);@gin(x6);

@gin(x7);@gin(x8);@gin(x9);

end

运行结果

Global optimal solution found.

Objective value: 22.00000

Objective bound: 22.00000

Infeasibilities: 0.000000

Extended solver steps: 0

Total solver iterations: 0

Model Class: PILP

Total variables: 9

Nonlinear variables: 0

Integer variables: 9

Total constraints: 11

Nonlinear constraints: 0

Total nonzeros: 47

Nonlinear nonzeros: 0

Variable Value Reduced Cost X1 1.000000 -5.000000 X2 1.000000 -4.000000 X3 1.000000 -4.000000 X4 0.000000 -3.000000 X5 1.000000 -4.000000 X6 0.000000 -3.000000 X7 1.000000 -2.000000 X8 0.000000 -2.000000 X9 1.000000 -3.000000 Row Slack or Surplus Dual Price

1 22.00000 1.000000

2 2.000000 0.000000

3 0.000000 0.000000

4 0.000000 0.000000

5 0.000000 0.000000

6 1.000000 0.000000

7 0.000000 0.000000

8 1.000000 0.000000

9 1.000000 0.000000

10 0.000000 0.000000

11 0.000000 0.000000