（二十三）lingo 指派優化

CODE

model:
    sets:
        !人數;
        var/1..6/;
        link(var,var):c,x;
    endsets
    data:
        !收益矩陣;
        c=20 15 16 5 4 7
        17 15 33 12 8 6
        9 12 18 16 30 13
        12 8 11 27 19 14
        0 7 10 21 10 32
        0 0 0 6 11 13; 
    enddata
    min=@sum(link:c*x);
    @for(var(i):@sum(var(j):x(i,j))=1);
    @for(var(j):@sum(var(i):x(i,j))=1);
    @for(link:@bin(x));
End

RESULT

  Global optimal solution found.
  Objective value:                              34.00000
  Objective bound:                              34.00000
  Infeasibilities:                              0.000000
  Extended solver steps:                               0
  Total solver iterations:                             0


                       Variable           Value        Reduced Cost
                       C( 1, 1)        20.00000            0.000000
                       C( 1, 2)        15.00000            0.000000
                       C( 1, 3)        16.00000            0.000000
                       C( 1, 4)        5.000000            0.000000
                       C( 1, 5)        4.000000            0.000000
                       C( 1, 6)        7.000000            0.000000
                       C( 2, 1)        17.00000            0.000000
                       C( 2, 2)        15.00000            0.000000
                       C( 2, 3)        33.00000            0.000000
                       C( 2, 4)        12.00000            0.000000
                       C( 2, 5)        8.000000            0.000000
                       C( 2, 6)        6.000000            0.000000
                       C( 3, 1)        9.000000            0.000000
                       C( 3, 2)        12.00000            0.000000
                       C( 3, 3)        18.00000            0.000000
                       C( 3, 4)        16.00000            0.000000
                       C( 3, 5)        30.00000            0.000000
                       C( 3, 6)        13.00000            0.000000
                       C( 4, 1)        12.00000            0.000000
                       C( 4, 2)        8.000000            0.000000
                       C( 4, 3)        11.00000            0.000000
                       C( 4, 4)        27.00000            0.000000
                       C( 4, 5)        19.00000            0.000000
                       C( 4, 6)        14.00000            0.000000
                       C( 5, 1)        0.000000            0.000000
                       C( 5, 2)        7.000000            0.000000
                       C( 5, 3)        10.00000            0.000000
                       C( 5, 4)        21.00000            0.000000
                       C( 5, 5)        10.00000            0.000000
                       C( 5, 6)        32.00000            0.000000
                       C( 6, 1)        0.000000            0.000000
                       C( 6, 2)        0.000000            0.000000
                       C( 6, 3)        0.000000            0.000000
                       C( 6, 4)        6.000000            0.000000
                       C( 6, 5)        11.00000            0.000000
                       C( 6, 6)        13.00000            0.000000
                       X( 1, 1)        0.000000            20.00000
                       X( 1, 2)        0.000000            15.00000
                       X( 1, 3)        0.000000            16.00000
                       X( 1, 4)        0.000000            5.000000
                       X( 1, 5)        1.000000            4.000000
                       X( 1, 6)        0.000000            7.000000
                       X( 2, 1)        0.000000            17.00000
                       X( 2, 2)        0.000000            15.00000
                       X( 2, 3)        0.000000            33.00000
                       X( 2, 4)        0.000000            12.00000
                       X( 2, 5)        0.000000            8.000000
                       X( 2, 6)        1.000000            6.000000
                       X( 3, 1)        0.000000            9.000000
                       X( 3, 2)        0.000000            12.00000
                       X( 3, 3)        0.000000            18.00000
                       X( 3, 4)        1.000000            16.00000
                       X( 3, 5)        0.000000            30.00000
                       X( 3, 6)        0.000000            13.00000
                       X( 4, 1)        0.000000            12.00000
                       X( 4, 2)        1.000000            8.000000
                       X( 4, 3)        0.000000            11.00000
                       X( 4, 4)        0.000000            27.00000
                       X( 4, 5)        0.000000            19.00000
                       X( 4, 6)        0.000000            14.00000
                       X( 5, 1)        1.000000            0.000000
                       X( 5, 2)        0.000000            7.000000
                       X( 5, 3)        0.000000            10.00000
                       X( 5, 4)        0.000000            21.00000
                       X( 5, 5)        0.000000            10.00000
                       X( 5, 6)        0.000000            32.00000
                       X( 6, 1)        0.000000            0.000000
                       X( 6, 2)        0.000000            0.000000
                       X( 6, 3)        1.000000            0.000000
                       X( 6, 4)        0.000000            6.000000
                       X( 6, 5)        0.000000            11.00000
                       X( 6, 6)        0.000000            13.00000

                            Row    Slack or Surplus      Dual Price
                              1        34.00000           -1.000000
                              2        0.000000            0.000000
                              3        0.000000            0.000000
                              4        0.000000            0.000000
                              5        0.000000            0.000000
                              6        0.000000            0.000000
                              7        0.000000            0.000000
                              8        0.000000            0.000000
                              9        0.000000            0.000000
                             10        0.000000            0.000000
                             11        0.000000            0.000000
                             12        0.000000            0.000000
                             13        0.000000            0.000000