LINGO和EXCEL在数学建模中的应用

LINGO和EXCEL在数学建模中的应用

72页：最短路问题

model:

sets:

cities/A,B,C,D,E,F,G/:FL;

roads(cities,cities)/A,B A,C B,D B,E B,F C,D C,E C,F D,G E,G F,G/:W,P; endsets

data:

W=2 4 3 3 1 2 3 1 1 3 4;

enddata

N=@SIZE(CITIES); FL(N)=0;

@FOR(cities(i)|i#LT#N:FL(i)=@MIN(roads(i,j):W(i,j)+FL(j)));

@FOR(roads(i,j):p(i,j)=@IF(FL(i)#EQ#W(i,j)+FL(j),1,0));

end

运行结果：

Feasible solution found.

Total solver iterations: 0

Variable Value

N 7.000000

FL( A) 6.000000

FL( B) 4.000000

FL( C) 3.000000

FL( D) 1.000000

FL( E) 3.000000

FL( F) 4.000000

FL( G) 0.000000

W( A, B) 2.000000

W( A, C) 4.000000

W( B, D) 3.000000

W( B, E) 3.000000

W( B, F) 1.000000

W( C, D) 2.000000

W( C, E) 3.000000

W( C, F) 1.000000

W( D, G) 1.000000

W( E, G) 3.000000

W( F, G) 4.000000

P( A, B) 1.000000

P( A, C) 0.000000

P( B, D) 1.000000

P( B, E) 0.000000

P( B, F) 0.000000

P( C, D) 1.000000

P( C, E) 0.000000

P( C, F) 0.000000

P( D, G) 1.000000

P( E, G) 1.000000

P( F, G) 1.000000

Row Slack or Surplus

1 0.000000

2 0.000000

3 0.000000

4 0.000000

5 0.000000

6 0.000000

7 0.000000

8 0.000000

9 0.000000

10 0.000000

11 0.000000

12 0.000000

13 0.000000

14 0.000000

15 0.000000

16 0.000000

17 0.000000

18 0.000000

19 0.000000

85页：最小费用最大流

model:

sets:

CHSH/1..6/;

LINKS(CHSH,CHSH)/1,2 1,3 2,3 2,4 3,5 4,3 4,6 5,4 5,6 6,1/:C,U,F; ENDSETS

DATA:

U=8,7,5,9,9,2,5,6,10,15;

C=2,8,5,2,3,1,6,4,7,8;

ENDDATA

N=@SIZE(CHSH);

F(6,1)=14;

MIN=@SUM(LINKS(I,J)|I#LT#N:C(I,J)*F(I,J));

@FOR(LINKS(I,J):F(I,J)<=U(I,J));

@FOR(CHSH(I):@SUM(LINKS(J,I):F(J,I))=@SUM(LINKS(I,J):F(I,J))); END

运行结果：

Global optimal solution found.

Objective value: 205.0000

Infeasibilities: 0.000000

Total solver iterations: 0

Variable Value Reduced Cost

N 6.000000 0.000000

C( 1, 2) 2.000000 0.000000

C( 1, 3) 8.000000 0.000000

C( 2, 3) 5.000000 0.000000

C( 2, 4) 2.000000 0.000000

C( 3, 5) 3.000000 0.000000

C( 4, 3) 1.000000 0.000000

C( 4, 6) 6.000000 0.000000

C( 5, 4) 4.000000 0.000000

C( 5, 6) 7.000000 0.000000

C( 6, 1) 8.000000 0.000000

U( 1, 2) 8.000000 0.000000

U( 1, 3) 7.000000 0.000000

U( 2, 3) 5.000000 0.000000

U( 2, 4) 9.000000 0.000000

U( 3, 5) 9.000000 0.000000

U( 4, 3) 2.000000 0.000000

U( 4, 6) 5.000000 0.000000

U( 5, 4) 6.000000 0.000000

U( 5, 6) 10.00000 0.000000

U( 6, 1) 15.00000 0.000000

F( 1, 2) 8.000000 0.000000

F( 1, 3) 6.000000 0.000000

F( 2, 3) 1.000000 0.000000

F( 2, 4) 7.000000 0.000000

F( 3, 5) 9.000000 0.000000

F( 4, 3) 2.000000 0.000000

F( 4, 6) 5.000000 0.000000

F( 5, 4) 0.000000 10.00000

F( 5, 6) 9.000000 0.000000

F( 6, 1) 14.00000 0.000000