Finding the minimum weight IIS cover of an infeasible system of linear inequalities

Given an inconsistent set of inequalities Ax less than or equal to b, the irreducible inconsistent subsystems (IISs) designate subsets of the inequalities such that at least one member of each subset must be deleted in order to achieve a feasible system. By solving a set covering problem over the IISs, one can determine a minimum weight set of inequalities that must be deleted in order to achieve feasibility. Since the number of IISs is generally exponential in the size of the original subsystem, we generate the IISs only when they are violated by a trial solution. Computational results on the NETLIB infeasible LP library are given.