Originally posted by: Hello76483

Hey, I have a Problem. I want to model a tour starting at the Depot with 0, and ending the tour at 5 (also the Depot).

My notations are this (programmed a little different)

D={3,4,6}

Depot={0,5}

P={1,2}

E[P] is depending on P

AllN= D union P union Depot

AllS= All E[P]

All_ = AllS union AllN

NoP= D union Depot

{string} L = {"L1"};

int cardofL=card(L);

 

minimize sum(j,i in NoP) costsD[i][j]*x[i][j] + sum(i in P, k in E[i]) costsPD[i][k] *x[i][k];

 

subject to {

    forall(i in D)        
       sum(j in All_ diff P) x[i][j] == 1; 
     
    forall(j in D)     
       sum(i in All_ diff P) x[i][j] == 1;    
          
    forall(i in P) ct3[i]:                    
      sum(k in E[i]) x[i][k] == 1;                
      
    forall(i in AllS)                     
      sum(j in All_) x[j][i] == sum(j in All_) x[i][j]; 
      
    forall(i in P, k in E[i]) ct4[i][k]:
      sum(j in E[i]) x[i][j] >= x[i][k];       
     
    forall(i in Depot: i == 0)
      sum(j in All_) x[i][j] == cardofL;
    
    forall(i in Depot: i == 5)
       sum(j in All_) x[i][j] == 0;
       
    forall(j in Depot: j == 5) ct7[j]:
      sum(i in All_) x[i][j] == cardofL;
      
    forall(j in Depot: j == 0)
      sum(i in All_) x[i][j] == 0;
      
    forall(i,j in Depot)
      x[i][j] == 0;
         

     forall(i,j in All_ : i== j)
        x[i][j] == 0;                            
            
     forall(i in P,j in All_ diff E[i])
       x[j][i] == 0;
       
     forall(i in P,j in All_ diff E[i])
       x[i][j] == 0;
            
     forall(i in P,k in E[i])
       x[i][k] == sum(j in All_ diff P) x[j][k];          

      

    forall(i in All_ diff P,j in All_ diff P) ctTravel[i][j]:
      Traveltime[i][j] == Distance[i][j]*sT;
      
    forall(i in P, k in E[i]) ctTravel2[i][k]:
      Traveltime[i][k] == Distance[i][k] *(sW + sP);
      
    forall(i in D)
      Servicetime[i] == Tu*(-Demand[i]);
    
    forall(i in P)
      Servicetime[i] == Tl*Demand[i];
    
    forall(i in Depot union AllS)
      Servicetime[i] == 0;
 

    forall(i,j in All_) ctKosten1[i][j]:
      costsD[i][j] == cA*Servicetime[i] + cA*Traveltime[i][j]*cT; //17
        
    forall(i in P,k in E[i]) ctKosten4[i][k]:
      costsPD[i][k] == cA*Servicetime[i] + Traveltime[i][k]*cA + Distance[k][i]*sP*cP ; //18
      
}

 

I hope it is clear what I'm trying to do. The Problem is, Cplex is doing a lot of subtours now, and I'm not able to avoid them. 

Maybe someone could help me? That would be awesome!

#DecisionOptimization
#OPLusingCPLEXOptimizer

Hi

you could have a look at

https://www.ibm.com/developerworks/community/forums/html/topic?id=f58daf79-f752-48e4-8f25-54b2f6f71b40&ps=25

regards

#DecisionOptimization
#OPLusingCPLEXOptimizer