sequence by sequence constraints怎么写来调度

Question

现在，我尝试添加 EQ7: 一个新约束，使每个 start_pour[k][j] 不同于其他 start_pour[k][j] 等于 site_process_time[c] 的可运行模型。它显示了一个宽松的解决方案 = 没有可行的解决方案。我该如何写这个约束？谢谢。

 EQ7 :
 forall(c in customer)
   sum(k in truck, j in job)
      (start_pour[k][j] + site_process_time[c] + (M*(1-x[c][k][j]))) <= 
   sum(k in truck, j in job)
      (start_pour[k][j] + (M*(1-x[c][k][j])));

.MOD

 int c =...;
 int k =...;
 int j =...;

 range customer     =   1..c;
 range truck        =   1..k;
 range job          =   1..j;


 float demand[customer]=...;
 float travel[customer]=...;
 float plant_process_time[customer]=...; 
 float site_process_time[customer]=...; 

 float capacity[truck]=...;

 int M=...;


 dvar int+ start_load[truck][job];
 dvar int+ start_pour[truck][job];

 dvar boolean x[customer][truck][job];
 dvar boolean y[customer];

 /***************************************/

 dexpr float Travel_Cost =  sum(c in customer, k in truck, j in job)
                              x[c][k][j];

 dexpr float Penalty_Cost = sum(c in customer)
                              M*y[c];

 minimize   Travel_Cost  + Penalty_Cost;

 /***************************************/

 subject to { 

 EQ2 : //Assignment
 forall(k in truck, j in job)
   sum(c in customer)
     x[c][k][j] <= 1 ;


 EQ3 : //Precedence
 forall(k in truck, j in job : j > 1)
   sum(c in customer)
     x[c][k][j] <=
   sum(c in customer)
     x[c][k][j-1];

 EQ4 : //Demand <= Supply
 forall(c in customer)
   sum(k in truck, j in job)
     x[c][k][j] * capacity[k] >= demand[c] * (1-y[c]);


 EQ5 : //Job-Time Sequencing;
 forall(c in customer, k in truck, j in job)
   start_load[k][j] + plant_process_time[c] + travel[c] <= start_pour[k][j] + (M*(1-x[c][k][j-1]));


 EQ6 : //Job-Time Sequencing;
 forall(c in customer, k in truck, j in job: (j-1) in job)
   start_pour[k][j-1] + site_process_time[c] + travel[c] <= start_load[k][j]+ (M*(1-x[c][k][j-1]));

 }

.DAT

 c = 2;
 k = 2;
 j = 5;

 demand = [10 30];
 travel = [5 10];
 plant_process_time = [1 1];
 site_process_time = [2 2];

 capacity = [4 5];

 M= 100000;

Answer 1

要使 sur 模型正常工作，您至少需要更改

EQ5 : //Job-Time Sequencing;
 forall(c in customer, k in truck, j in job)
   start_load[k][j] + plant_process_time[c] + travel[c] <= start_pour[k][j] + (M*(1-x[c][k][j-1]));

进入

EQ5 : //Job-Time Sequencing;
 forall(c in customer, k in truck, j in job:(j-1) in job)
   start_load[k][j] + plant_process_time[c] + travel[c] <= start_pour[k][j] + (M*(1-x[c][k][j-1]));

那么你可以使用逻辑约束而不是大 M

EQ5 : //Job-Time Sequencing;
 forall(c in customer, k in truck, j in job:(j-1) in job)
(1==x[c][k][j-1] ) => (start_load[k][j] + plant_process_time[c] + travel[c] <= start_pour[k][j]);

对于 EQ7，您可以从

开始

EQ7 :
 forall(c in customer)
   forall(ordered k,k2 in truck, ordered  j,j2 in job)

      start_pour[k][j] != start_pour[k2][j2];

甚至

    EQ7 :
 forall(c in customer)
   forall(ordered k,k2 in truck, ordered  j,j2 in job)

     ((1==x[c][k][j] ) && (1==x[c][k2][j2]))=> (abs(start_pour[k][j] -start_pour[k2][j2]) >=plant_process_time[c]);

如果您想考虑处理时间

我建议您在 CPLEX 中查看 CPOptimizer，因为这对调度非常有用。

sequence by sequence constraints怎么写来调度

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