An effective polynomial-time heuristic for the minimum-cardinality IIS set-covering problem

The state-of-the-art methods for analyzing infeasible linear programs concentrate on isolating Irreducible Infeasible Sets (IISs) of constraints. However, when there are numerous infeasibilities in the model, it is also useful to identify a minimum-cardinality set of constraints which, if removed from the LP, renders it feasible. This set of constraints covers the IISs. This paper presents a heuristic algorithm for finding a small-cardinality set of constraints which covers the IISs in an infeasible LP. Empirical tests show that it finds a true minimum-cardinality cover over all of the examples in a test set, though this performance cannot be guaranteed in general.