Infeasibility and Unboundedness

Infeasibility and unboundedness are closely related topics in optimization theory, and therefore certain of the concepts for one will have direct relation to the other. This part contains:

As you know, ILOG CPLEX can provide solution information about the models that it optimizes. For infeasible outcomes, it reports values that you can analyze to detect what in your problem formulation caused this result. In certain situations, you can then alter your problem formulation or change ILOG CPLEX parameters to achieve a satisfactory solution.

Infeasibility can arise from various causes, and it is not possible to automate procedures to deal with those causes entirely without input or intervention from the user. For example, in a shipment model, infeasibility could be caused by insufficient supply, or by an error in demand, and it is likely that the optimizer will tell the user only that the mismatch exists. The formulator of the model has to make the ultimate judgment of what the actual error is. However, there are ways to try to narrow down the investigation or even provide some degree of automatic repair.

ILOG CPLEX provides tools to help you analyze the source of the infeasibility in a model. Those tools include the conflict refiner for detecting minimal sets of mutually contradictory bounds and constraints, and FeasOpt for repairing infeasibilities.