A fuzzy method to repair infeasibility in linearly constrained problems

In this paper we introduce a fuzzy method to deal with infeasibility in linearly constrained programs. Given an infeasible instance, we determine how much we should perturb the right-hand side coefficients in order to attain feasibility and propose a 'feasible reformulation' of the problem. Although we prove that our algorithm always finds such a reformulation the convenience of using it can be decided by the analyst. By this, we mean that the method also provides a simple way to compute lower bounds on the changes on every right-hand side coefficient, and if the decision maker considers that some of the magnitudes are unacceptable, he or she simply stops at this step. We think that it will be specially useful for those situations in which the cause of the infeasibility is in the requirement of specifying exact values for the parameters in the mathematical programs formulation. (C) 2001 Elsevier Science B.V. All rights reserved.