Purchasing Constraint in CPLEX using binary constraints

Question

I have been trying to develop a constraint which says B[i][t]= 1 then Pur[i][t]==Q[i] and when B[i][t]==0 then Pur[i][t]==0

Please guide. Thanks

Answer 1

In OPL and all CPLEX APIs you can use logical constraints.

In OPL for instance,

int nbKids=300;
float costBus40=500;
float costBus30=400;
 
dvar int+ nbBus40;
dvar int+ nbBus30;
minimize
 costBus40*nbBus40  +nbBus30*costBus30;
 
subject to
{
 40*nbBus40+nbBus30*30>=nbKids;
 
 // with if nb buses 40 more than 3  then nb buses30 more than 7
 
 (nbBus40>=3)=>(nbBus30>=7);
 //(nbBus40>=3)<=(nbBus30>=7); //equivalent
}

In your example

(B[i][t]== 1) => (Pur[i][t]==Q[i]) ;
(B[i][t]==0) => ( Pur[i][t]==0);