Lingo 指派问题

lingo解决指派问题~

sets:
event /1..4/:;
athlete /1..5/:;
link(athlete,event):chji,x;
endsets
data:
chji = 8.69.78.99.4
9.28.38.58.1
8.88.79.39.6
8.57.89.57.9
8.09.48.27.7;
enddata
max = @sum(link:chji * x);

@sum(link:x) = 10;

@for(athlete(I):@sum(event(J):x(I,J)) >= 1);

@for(athlete(I):@sum(event(J):x(I,J)) <= 3);

@for(event(J):@sum(athlete(I):x(I,J)) >= 1);

@for (link:@bin(x));

其实题目是不够全的 需要指出是否四个人必须要分别翻译四种语言 还有指派时间指的是加起来还是最长的那个 这里按照每人必须对应一个语言 指派时间是加起来算
model:
sets:
person/1..4/;
language/1..4/;
translate(person,language):time,x;
endsets
data:
time=
2 15 13 4
10 4 14 15
9 14 16 13
7 8 11 9;
enddata
min=@sum(translate:time*x);
@for(person(i):@sum(language(j):x)=1);
@for(language(j):@sum(person(i):x)=1);
@for(translate:@bin(x));
end

model:
sets:
a/1..5/;
time(a,a):t,n;!n(i,j)=1则意味i去做j任务;
endsets
data:
t=8 6 10 9 12
9 12 7 11 9
7 4 3 5 8
9 5 8 11 8
4 6 7 5 11;
enddata
[OBJ]min=@sum(time:t*n);
@for(a(i):@sum(a(j):n(i,j))=1);!每个任务只给一个人做;
@for(a(j):@sum(a(i):n(i,j))=1);!每个人只能做一件任务;
end
运行结果：
Global optimal solution found.
Objective value: 30.00000
Total solver iterations: 6

Variable Value Reduced Cost
T( 1, 1) 8.000000 0.000000
T( 1, 2) 6.000000 0.000000
T( 1, 3) 10.00000 0.000000
T( 1, 4) 9.000000 0.000000
T( 1, 5) 12.00000 0.000000
T( 2, 1) 9.000000 0.000000
T( 2, 2) 12.00000 0.000000
T( 2, 3) 7.000000 0.000000
T( 2, 4) 11.00000 0.000000
T( 2, 5) 9.000000 0.000000
T( 3, 1) 7.000000 0.000000
T( 3, 2) 4.000000 0.000000
T( 3, 3) 3.000000 0.000000
T( 3, 4) 5.000000 0.000000
T( 3, 5) 8.000000 0.000000
T( 4, 1) 9.000000 0.000000
T( 4, 2) 5.000000 0.000000
T( 4, 3) 8.000000 0.000000
T( 4, 4) 11.00000 0.000000
T( 4, 5) 8.000000 0.000000
T( 5, 1) 4.000000 0.000000
T( 5, 2) 6.000000 0.000000
T( 5, 3) 7.000000 0.000000
T( 5, 4) 5.000000 0.000000
T( 5, 5) 11.00000 0.000000
N( 1, 1) 0.000000 0.000000
N( 1, 2) 0.000000 0.000000
N( 1, 3) 0.000000 3.000000
N( 1, 4) 1.000000 0.000000
N( 1, 5) 0.000000 3.000000
N( 2, 1) 0.000000 1.000000
N( 2, 2) 0.000000 6.000000
N( 2, 3) 0.000000 0.000000
N( 2, 4) 0.000000 2.000000
N( 2, 5) 1.000000 0.000000
N( 3, 1) 0.000000 3.000000
N( 3, 2) 0.000000 2.000000
N( 3, 3) 1.000000 0.000000
N( 3, 4) 0.000000 0.000000
N( 3, 5) 0.000000 3.000000
N( 4, 1) 0.000000 2.000000
N( 4, 2) 1.000000 0.000000
N( 4, 3) 0.000000 2.000000
N( 4, 4) 0.000000 3.000000
N( 4, 5) 0.000000 0.000000
N( 5, 1) 1.000000 0.000000
N( 5, 2) 0.000000 4.000000
N( 5, 3) 0.000000 4.000000
N( 5, 4) 0.000000 0.000000
N( 5, 5) 0.000000 6.000000
N(i,j)=1的地方就是安排i去干j任务。

model:
sets:
r/1..5/:;
c/1..5/:;
link(r,c):time,x;
endsets
data:
time= 8 6 10 9 2
9 12 7 11 9
7 4 3 5 8
9 5 8 11 8
4 6 7 5 11;
enddata
min=@sum(link:x*time);
@for(link:@bin(x));
@for(r(i):@sum(c(j):x(i,j))=1);
@for(c(j):@sum(r(i):x(i,j))=1);
end

Global optimal solution found.
Objective value: 23.00000
Objective bound: 23.00000
Infeasibilities: 0.000000
Extended solver steps: 0
Total solver iterations: 0

Variable Value Reduced Cost
TIME( 1, 1) 8.000000 0.000000
TIME( 1, 2) 6.000000 0.000000
TIME( 1, 3) 10.00000 0.000000
TIME( 1, 4) 9.000000 0.000000
TIME( 1, 5) 2.000000 0.000000
TIME( 2, 1) 9.000000 0.000000
TIME( 2, 2) 12.00000 0.000000
TIME( 2, 3) 7.000000 0.000000
TIME( 2, 4) 11.00000 0.000000
TIME( 2, 5) 9.000000 0.000000
TIME( 3, 1) 7.000000 0.000000
TIME( 3, 2) 4.000000 0.000000
TIME( 3, 3) 3.000000 0.000000
TIME( 3, 4) 5.000000 0.000000
TIME( 3, 5) 8.000000 0.000000
TIME( 4, 1) 9.000000 0.000000
TIME( 4, 2) 5.000000 0.000000
TIME( 4, 3) 8.000000 0.000000
TIME( 4, 4) 11.00000 0.000000
TIME( 4, 5) 8.000000 0.000000
TIME( 5, 1) 4.000000 0.000000
TIME( 5, 2) 6.000000 0.000000
TIME( 5, 3) 7.000000 0.000000
TIME( 5, 4) 5.000000 0.000000
TIME( 5, 5) 11.00000 0.000000
X( 1, 1) 0.000000 8.000000
X( 1, 2) 0.000000 6.000000
X( 1, 3) 0.000000 10.00000
X( 1, 4) 0.000000 9.000000
X( 1, 5) 1.000000 2.000000
X( 2, 1) 0.000000 9.000000
X( 2, 2) 0.000000 12.00000
X( 2, 3) 1.000000 7.000000
X( 2, 4) 0.000000 11.00000
X( 2, 5) 0.000000 9.000000
X( 3, 1) 0.000000 7.000000
X( 3, 2) 0.000000 4.000000
X( 3, 3) 0.000000 3.000000
X( 3, 4) 1.000000 5.000000
X( 3, 5) 0.000000 8.000000
X( 4, 1) 0.000000 9.000000
X( 4, 2) 1.000000 5.000000
X( 4, 3) 0.000000 8.000000
X( 4, 4) 0.000000 11.00000
X( 4, 5) 0.000000 8.000000
X( 5, 1) 1.000000 4.000000
X( 5, 2) 0.000000 6.000000
X( 5, 3) 0.000000 7.000000
X( 5, 4) 0.000000 5.000000
X( 5, 5) 0.000000 11.00000

---

Lingo 指派问题视频