CPLEX：CP Optimizer 用 0 解决方案运行很长时间

Question

我使用约束编程在 CPLEX 中运行我的模型，我的模型设法在 8 个工人的情况下运行。但是 3 小时后，它仍然没有解决方案，所以我不得不停止模型。

我的模型有问题吗？我尝试在 Excel 文件中仅使用几个样本来运行模型，但在运行数小时后仍然无法为我提供解决方案。提前非常感谢您！

我的模组。文件：

using CP;
int scale=10;

int NumbDay =...;
int NumbTask =...;

range Day = 1 .. NumbDay;
range Task = 1 .. NumbTask;

int maxRepetition = NumbDay;
dvar int F [Task] in 1..maxRepetition;
range Repetition = 0 .. maxRepetition;

int h [Day]=...;
int R [Task]=...;
int c [Day]=...;
int E [Task]=...;
int d [Day]=...;
int O [Task]=...;
int P [Task] =...;
float t [Task]=...;

dvar int+ r [i in Task][j in Repetition];
dvar int+ e [i in Task][j in Repetition];
dvar int+ o [i in Task][j in Repetition];
dvar int+ n [i in Task][j in Repetition];

dvar int scalenW[Day] in 0..100;
dexpr float W [k in Day]=scalenW[k]/scale;

dvar boolean X [Day][Task][Repetition];

dexpr float e1 = sum(k in Day)(((sum(k in Day, i in Task, j in Repetition) t [i]*X[k][i][j])/365) - W [k])^2;

dexpr float e2 = sum(i in Task, j in Repetition) n [i][j];

minimize staticLex(e1, e2);
subject to 
{
    constraint_1:
        forall (i in Task){
            F [i] >= P [i];
    }
    constraint_2:
        forall (k in Day){
            sum(i in Task) (sum(j in Repetition)(t [i]*X [k][i][j]*(j<=F[i]-1))) == W [k];
    }  
    constraint_3:
        forall (i in Task, j in Repetition){
            sum(k in Day) X [k][i][j] == 1 * (j<=F[i]-1);
    }   
    constraint_4:
        forall (k in Day, i in Task, j in Repetition){
            X [k][i][j] == 0 || X [k][i][j] == 1;
    }
     constraint_5:
        forall (i in Task, j in Repetition){
          (r[i][j]!=0) => sum(k in Day)(X [k][i][j] * h [k]) <= r [i][j];
    }
    constraint_6:
        forall (i in Task, j in Repetition){
           r [i][j] <= 10 * NumbDay;
    }
    constraint_7:
        forall (i in Task){
            r [i][0] == R [i];
    }
    constraint_8:
        forall (i in Task, j in 1..NumbDay){
          r [i][j] == (R [i] + sum(k in Day) (X [k][i][j-1] * h [k])) * (j<=F[i]-1);
    }
    constraint_9:
        forall (i in Task, j in Repetition){
           (e[i][j]!=0) => sum(k in Day)(X [k][i][j] * c [k]) <= e [i][j];
    }
    constraint_10:
        forall (i in Task, j in Repetition){
           n [i][j] == e [i][j] - sum(k in Day)( X [k][i][j] * c [k]);
    }
    constraint_11:
        forall (i in Task, j in Repetition){
           e [i][j] <= 10 * NumbDay;
    }
    constraint_12:
        forall (i in Task){
            e [i][0] == E [i];
    }
    constraint_13:
        forall (i in Task, j in 1..NumbDay){
            e [i][j] == (E [i] + sum(k in Day) (X [k][i][j-1] * c [k])) * (j<=F[i]-1);
    }
     constraint_14:
        forall (i in Task, j in Repetition){
           (o[i][j]!=0) => sum(k in Day)(X [k][i][j] * d [k]) <= o [i][j];
    }
    constraint_15:
        forall (i in Task, j in Repetition){
           o [i][j] <= 10 * NumbDay;
    }
    constraint_16:
        forall (i in Task){
            o [i][0] == O [i];
    }
    constraint_17:
        forall (i in Task, j in 1..NumbDay){
            o [i][j] == (O [i] + sum(k in Day) (X [k][i][j-1] * d [k])) * (j<=F[i]-1);
    }
}

我的数据。文件：

SheetConnection ModelData("ModelData.xlsx");

NumbDay from SheetRead(ModelData,"1mosize!B1");
NumbTask from SheetRead(ModelData,"1mosize!B2");

h from SheetRead(ModelData,"1mo1D2!B2:B31");
R from SheetRead(ModelData,"1mo1D1!B2:B20");
c from SheetRead(ModelData,"1mo1D2!C2:C31");
E from SheetRead(ModelData,"1mo1D1!C2:C20");
d from SheetRead(ModelData,"1mo1D2!D2:D31");
O from SheetRead(ModelData,"1mo1D1!D2:D20");
t from SheetRead(ModelData,"1mo1D1!E2:E20");
P from SheetRead(ModelData,"1mo1D1!I2:I20");

My Excel Data file

Answer 1

如果你把比例变成

int scale=1000;

和

//    constraint_2:
//        forall (k in Day){
//            sum(i in Task) (sum(j in Repetition)(t [i]*X [k][i][j]*(j<=F[i]-1))) == W [k];
//    }  

进入

constraint_2:
    forall (k in Day){
        abs(sum(i in Task) (sum(j in Repetition)(t [i]*X [k][i][j]*(j<=F[i]-1))) - W [k])<=1;
}  

你会得到解决方案