Originally posted by: yokito

Hello,

I would like to ask you about giving cplex a bound in a contraint way. I have a problem where the objective value  (obj=A+B+C)  is the sum of objective values of each vehicle . I solve a problem instance to optimality in 5 seconds. Nervertheless, when I include a constraint based on that value in the way that

vehicle1 >= A

vehicle2 >=B

vehicle3 >= C

it requires a lot of time to solve the problem. This also happened to me in a different variation when I give cplex an bound and introduced it as a constraint. 

Any help and advice is very good welcome!

You did not indicate the type of model, but I suspect it is a MILP (or ILP). If so, the time increase is not entirely surprising. Assuming you ran CPLEX on the original problem with default parameter settings, it is possible that CPLEX found a feasible but suboptimal solution quickly, then used heuristics to refine that solution to a better (possibly optimal) solution. With the added constraints, the suboptimal solutions CPLEX found along the way are now infeasible, so the heuristics have no opportunity to improve them.

Even if the heuristics are not an issue, the search trajectory changes when you make previously feasible branches infeasible. That could make the problem solve faster, but it also could (and apparently does) make it slower.

You could try relaxing the added constraints a bit (e.g., vehicle1 >= A - epsilon for a not terribly small choice of epsilon), but even then there is no guarantee how this affects solution time.