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What should you do when you face an infeasible solution? I have implemented the model with the dataset from the paper but found infeasible solution.

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You could try the following approaches:

  • Find the Irreducible Infeasible Set (most solvers can do this for you). This will give you an infeasible subset of constraints and variable bounds that will become feasible if any single constraint or variable bound is removed and can thus help you identify what is going on.
  • Iteratively relax groups of constraints, and check which one is making the problem infeasible. Once you have identified which constraint is causing infeasibility, you could penalize its violation in the objective function.

You could also share your model and your code for external help. And last but not least, you could contact the authors of the paper (last resort) if the problem proves to be indeed infeasible with the published data set.

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Infeasibility in many cases comes from two things. First, the issues in the relationship between the defined variables and corresponding constraints (buggy model), and the second, the RHS values. Besides what mentioned by Kuifje, the answers of Matteo Fischetti and other community members in this link would be very interested.

Adding slack variables (with a high penalty in the objective function) converts hard constraints into soft ones, and can also be useful to locate the source of infeasibility. This approach can be very useful for feasible problems for which finding a heuristic feasible solution is hard/very time-consuming.

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Does the paper you mention contain the optimal solution? If so, just substitute it into each of your constraints and look for one that is violated. That constraint presumably contains an error.

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  • $\begingroup$ Unfortunately, the model is so complex with lots of decision variables. The paper too doesn't provide the full solution, just the z value which is the objective function. $\endgroup$
    – overboxed
    Commented Oct 19, 2022 at 7:35

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