模型的lingo語言描述如下
1）為該市設計一個從各集散點至各菜市場的定點供應方案，使用于蔬菜調運及預期的短缺損失為最小；
MODEL:
SETS:
jsd/1..3/:a;!三個集散地,收購量a(i);
csc/1..8/:b;!八個菜市場，每天需求量b(j);
dqss/1..8/:d;!各菜市場的單位短缺損失d(j);
j_c(jsd,csc):x,c,l;!i到j的距離矩陣為l(i,j),單位運費c(i,j),決策變量為 x(i,j);
ENDSETS
DATA:
a=200,170,160;
b=75,60,80,70,100,55,90,80;
d=10,8,5,10,10,8,5,8;
l=4,8,8,19,11,6,22,26,
? 14,7,7,16,12,16,23,17,
? 20,19,11,14,6,15,5,10;
c=1,1,1,1,1,1,1,1,
? 1,1,1,1,1,1,1,1,
? 1,1,1,1,1,1,1,1;
ENDDATA
@for(jsd(i):
??? [st1]@sum(csc(j):x(i,j))=a(i));!收購量限制;
@for(csc(j):
??? [st2]@sum(jsd(i):x(i,j))<=b(j));!需求量限制;
[obj]min=@sum(jsd(i):@sum(csc(j):c(i,j)*x(i,j)*l(i,j)))
+@sum(jsd(i):@sum(csc(j):d(j)*(b(j)-x(i,j))));
END
模型求解的結果如下
Global optimal solution found at iteration:??????????? 11
? Objective value:???????????????????????????????? 14330.00
?????????????????????? Variable?????????? Value??????? Reduced Cost
????????????????????????? A( 1)??????? 200.0000??????????? 0.000000
????????????????????????? A( 2)??????? 170.0000??????????? 0.000000
????????????????????????? A( 3)??????? 160.0000??????????? 0.000000
????????????????????????? B( 1)??????? 75.00000??????????? 0.000000
????????????????????????? B( 2)??????? 60.00000??????????? 0.000000
????????????????????????? B( 3)??????? 80.00000??????????? 0.000000
????????????????????????? B( 4)??????? 70.00000??????????? 0.000000
????????????????????????? B( 5)??????? 100.0000??????????? 0.000000
????????????????????????? B( 6)??????? 55.00000??????????? 0.000000