Originally posted by: bornee

hello, in order to caclulate the lower bound for the distance for each vehicul : 

R[i][v] represents either if the city i is visited by the vehicle v or not (c1 and c2)

c1 : forall (v in V, i in I )
  ( sum (j in J: j!=i) Xijv[i][j][v] >=1 ) => (R[i][v]==1);
 
 c2 : forall (v in V, i in I )
  ( sum (j in J: j!=i) Xijv[i][j][v] ==0 ) => (R[i][v]==0);
 
 Wi = the distance between citie i and the  dépôt (c3)

  c3 : forall (v in V, i in I, j in ID2:i!=j)
   (R[i][v]==1) => ( W[i]==  item(DIJ,<i.i,j.j>).valeur) ;
lets D[v] is the cost of routing a vehicle, it must be larger than the sum of the radial distances of the furthest two customers from the depot visitided by the same vehicule v. i difine this constraint like (c4) :

dvar boolean y;

 c4 : forall (v in V, i in I, j in J: i!=j)
    ( W[i] - W[j] * y >= 0 && W[i]- W[j]*(1-y) <= 0 ) => ( D[v] == 2*( y *( W[i]*R[i][v]) + (1-y)*(W[j]*R[j][v])));
 

i dont know if with this constraint true or not (if this constraint calculate the sum of the distance of the 2 furthest  customers from the depot visitided by the same vehicule v ). in cplex i have 2 errors :

1) CPLEX(default) ne peut pas extraire le modèle : IloAlgorithm cannot extract extractable.    Modèle1PDPT        Inconnu    Problème OPL
 2) CPLEX(default) ne peut pas extraire lexpression : {1}.    Modèle1PDPT.mod    /Modèle1PDPT    203:16-204:115 C:\Users\HENI\Desktop\Modèle1PDPT\Modèle1PDPT.mod    Problème OPL

i try with this second methode :

c4 : forall (v in V, i in I, j in J: i!=j)
    (  R[i][v] == 1 && R[j][v]==1 && W[i]- W[j] * y >= 0 && W[i]- W[j](1-y) <= 0 ) => ( D[v] == 2*( y * W[i] + (1-y)*W[j]));

or this methode

c4: forall (v in V, i in I, j in J: i!=j)
    (  R[i][v] == 1 && R[j][v]==1 && W[i]- W[j] * y >= 0 && W[i]- W[j](1-y) <= 0 ) => ( D[v] == 2 *( W[i] + W[j]));

i have an error :
Le type dvar int+ ne peut pas être utilisé pour userFunction.    Modèle1PDPT.mod    /Modèle1PDPT    204:8-81 C:\Users\HENI\Desktop\Modèle1PDPT\Modèle1PDPT.mod    Problème OPL

???????
 

Best regards