2.某公司有6个建筑工地要开工，每个工地的位置（用平面坐标系a，b表示，距离单位：千米）及水泥日用量d(吨)由下表给出. 目前有两个临时料场位于A(5,1)，B(2,7)，日储量各有30吨.

（1）试制定每天的供应计划，即从A，B两料场分别向各工地运送多少吨水泥，使总的吨千米数最小？

（2）为了进一步减少吨千米数，打算舍弃两个临时料场，改建两个新的，日储量各为30吨，问应建在何处，节省的吨千米数会多大？

 

1

2

3

4

5

6

a

1

8

0

5

3

8

b

1

0

4

6

6

7

d

4

6

6

7

8

11

解：（1）代码：model:
sets:
    production/pr1..pr2/:d,e,f;
    position/po1..po6/:a,b,c;
   links(production,position):x;
endsets
data:
    a b=1 1
        8 0
        0 4
        5 6
        3 6
        8 7;
    c=4 6 6 7 8 11;
    f=30 30;
    d e=5 1
        2 7;
enddata
min=@sum(links(i,j):@sqrt(((a(j)-d(i))^2+(b(j)-e(i))^2))*x(i,j));
    @for(production(i):@sum(position(j):x(i,j))<f(i));
    @for(position(j):@sum(production(i):x(i,j))=c(j));
    @for(production:@free(d);@free(e););
end

（2）代码：

model:

sets:

    production/pr1..pr2/:d,e,f;

    position/po1..po6/:a,b,c;

   links(production,position):x;

endsets

data:

    a b=1 1

        8 0

        0 4

        5 6

        3 6

        8 7;

    c=4 6 6 7 8 11;

    f=30 30;

    d=,; e=,;

enddata

min=@sum(links(i,j):@sqrt(((a(j)-d(i))^2+(b(j)-e(i))^2))*x(i,j));

    @for(production(i):@sum(position(j):x(i,j))<f(i));

    @for(position(j):@sum(production(i):x(i,j))=c(j));

    @for(production:@free(d);@free(e););

end

运行结果：

Local optimal solution found.

  Objective value:                              106.8555

  Infeasibilities:                              0.000000

  Total solver iterations:                            63

 

 

                       Variable           Value        Reduced Cost

                        D( PR1)        0.000000           -2.929012

                        D( PR2)        5.210653            0.000000

                        E( PR1)        4.000000            8.685333

                        E( PR2)        5.955272            0.000000

                        F( PR1)        30.00000            0.000000

                        F( PR2)        30.00000            0.000000

                        A( PO1)        1.000000            0.000000

                        A( PO2)        8.000000            0.000000

                        A( PO3)        0.000000            0.000000

                        A( PO4)        5.000000            0.000000

                        A( PO5)        3.000000            0.000000

                        A( PO6)        8.000000            0.000000

                        B( PO1)        1.000000            0.000000

                        B( PO2)        0.000000            0.000000

                        B( PO3)        4.000000            0.000000

                        B( PO4)        6.000000            0.000000

                        B( PO5)        6.000000            0.000000

                        B( PO6)        7.000000            0.000000

                        C( PO1)        4.000000            0.000000

                        C( PO2)        6.000000            0.000000

                        C( PO3)        6.000000            0.000000

                        C( PO4)        7.000000            0.000000

                        C( PO5)        8.000000            0.000000

                        C( PO6)        11.00000            0.000000

                   X( PR1, PO1)        4.000000            0.000000

                   X( PR1, PO2)        0.000000            0.000000

                   X( PR1, PO3)        6.000000            0.000000

                   X( PR1, PO4)        0.000000            0.000000

                   X( PR1, PO5)        2.000000            0.000000

                   X( PR1, PO6)        0.000000            0.000000

                   X( PR2, PO1)        0.000000            0.000000

                   X( PR2, PO2)        6.000000            0.000000

                   X( PR2, PO3)        0.000000            0.000000

                   X( PR2, PO4)        7.000000            0.000000

                   X( PR2, PO5)        6.000000            0.000000

                   X( PR2, PO6)        11.00000            0.000000

 

                            Row    Slack or Surplus      Dual Price

                              1        106.8555           -1.000000

                              2        18.00000            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           -4.373022