For an Integer Linear Programming problem (ILP), an irreducible infeasible set (IIS) is an infeasible subset of constraints, variable bounds, and integer restrictions that becomes feasible if any single constraint, variable bound, or integer restriction is removed. It is possible to have more than one IIS in an infeasible ILP. Is it possible to identify all possible Irreducible Infeasible Sets (IIS) for an infeasible Integer Linear Programming problem (ILP)? Ideally, I aim to find the MIN IIS COVER, which is the smallest cardinality subset of constraints to remove such that at least one constraint is removed from every IIS.

Thanks for your time and consideration.

Regards Ramy