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I am solving a problem using benders decomposition. The master problem is solved by cplex.The subproblems are logic and can be solved without using cplex solver. The scale for subproblem is large. About 3000 cuts will add to master problem in each iteration. My problem is: after 8-9 iteration, is the final converage stage, cplex shows no solution for the master problem. I try to use conflict detection function in cplex to print the conflicted constraints. But it shows that "No conflict is available..". The master problem is LP and it's werid that it cannot be solved. The problem can be solved in many small scale.

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  • $\begingroup$ Are you saying that CPLEX reports the last master LP is infeasible? Are you adding the Benders cuts as ordinary constraints or as lazy constraints? $\endgroup$
    – prubin
    Mar 3 at 16:40
  • $\begingroup$ yes, it is the last master Lp that is reported infeasible. The benders cuts are ordinary constraints all the tme. $\endgroup$
    – XXia
    Mar 4 at 0:21

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Finding a conflict in CPLEX is a two step process. First you have to instruct CPLEX to "refine" the conflict; then you have to ask it for the results (the constraints and variable bounds that collectively make the problem infeasible). If you attempt to access the conflict before giving the "refine" instruction, CPLEX will say that there is no conflict available.

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