Dear all,
I am trying to solve a closed-loop supply chain network design model with Cplex, but can not get a optimal solution, the model contains 6397 constraints, 12204 variables, and some of the parameters and decision variables have 5 subscript , is it because this case is too large? Or because of the multidimensional matrix？What should I do to solve it?
Thank you in advance!
this is not too large for CPLEX to solve but it depends on a few things
1. is your formulation a tight one?
2. how long did you give CPLEX to solve?
3. do you have presolve on?
4. do you necessarily need a 0% relgap, can you make do with 5-10% relgap?
Temitayo Bankole Thank you for your reply, in my code, the flow balance constraints are tight, I have tested about 5 hours but find no optimal solution, I did not set the presolve, I read some relevent papers, they can get the best solution in their case, so I wish to realize it, too. Do you have any idea？
Bests
Five hours may not be enough time. For much smaller problems, I have waited 24+ hours for the MIP solver to finish its business. Partly, this is a result of the problem and its formulation, and partly a function of the parameters you can chance in the solver (optimality tolerance, etc.).
Zhang Xin please ensure presolve is on. then leave it overnight. at what relgap does it finish within the time limit you gave it. what is your best integer and your best bound?
Temitayo Bankole Thank you for your reply, I checked the .ops file, the presolve is automatic, I did not change the default setting of it, when I run the configuration, the gap decreases slowly from 100% to 99.8, so I wander if it is because the multidimensional matrix influence the solve efficiency of the model.
You may consider checking the constraints of your model curefully for mistakes. Also, how many continuous variables and binary in your model? One option, you can set the model to stop at the first incumbent solution at a pre-defined optimality gap (say 20%). Most solvers enable you to do so, but first, run it for 24 hours or more. Also, check in the literature if the problem is NP-Hard or not. There might be some research about the scalability of your problem.
I would suggest you compare your problem to other similar problems in the published literature from the same type, were they able to solve them using CPLEX? Did you run it for 24 hours and checked the optimality gap? Also, you may change the parameters and re-run.
Zhang Xin did you solve your problem? I face the same issue and after running the code for hours, the gap decreases very slowly.
Armaghan Bahreini as I know, the problem comes from your model having a lot of binary, integer variables. Some guidelines can be solved by applying ideas from this paper.
https://www.sciencedirect.com/science/article/abs/pii/S1876735413000020
Besides, many metaheuristics could be used to solve the problem.
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