Originally posted by: Rym

I want to improve the performance of my model by combing two constraints ( in yellow) in one ony if possible

dvar boolean lumda[V][P];
dvar boolean phy[P];
dexpr int O = sum( i in V, j in P) lumda[i][j];
dexpr int ODPVMType[vtype in VMTypes]=sum( i in V, j in P:vms[i]==vtype) lumda[i][j];
dexpr int OP = sum( j in P) phy[j];
minimize OP;

//constraints

subject to{ 
//une machine virtuelle est hébergée par au plus une seule pm
  limit:
   forall( i in V)
     sum( j in P ) lumda[i][j] <= 1;
    

//la quantité de cpu consommée par les vms ne depasse la la quantité de cpu de la pm j
   cpur:
    forall( j in P)
      sum( i in V) cpui[i]*lumda[i][j] <= cpuj[j];
        

//la quantité de ram consommée par les vms ne depasse la la quantité de ram de la pm j
    ramr:
     forall( j in P)
       sum( i in V) rami[i]*lumda[i][j] <= ramj[j];

//la quantité de disk consommée par les vms ne depasse la la quantité de disk de la pm 

    diskr: 
     forall( j in P)
       sum( i in V) diski[i]*lumda[i][j] <= diskj[j];
       
       
//la somme des vms hebergèes ne depasse pas le nombre des demandes satisfaites

       
              glob:
 v <= sum (i in V, j in P) lumda[i][j];
//quand est ce que phyprends un

     phyone:
       forall ( i in V, j in P)
      lumda[i][j]<= phy[j] ;

//quand est ce que phy prends zero

   phynull:
      forall (j in P)
        phy[j]<= sum (i in V) lumda[i][j];

}

Thanks
 

The second constraint (phynull) looks redundant to me and could just be dropped.

phy[j] has positive coefficient in the objective, hence it will be set to 0 whenever possible and for phy[j]=0 constraint phynull is always satisfied. phy[j] will only be set to 1 if there is an i such that lumda[i][j]==1. This very lumda[i][j] will also appear in the right side of the respective phynull constraint. Hence that constraint will trivially be satisfied: the left side is 1 while the right side is at least 1.

Originally posted by: Rym

I agree with you.  Thanks