Two-Step MIR Inequalities for Mixed Integer Programs

Two-step MIR inequalities are valid inequalities derived from a facet of a simple mixedinteger set with three variables and one constraint. In this paper we investigate how to effectively use these inequalities as cutting planes for general mixed-integer problems. We study the separation problem for single constraint sets and show that it can be solved in polynomial time when the resulting inequality is required to be sufficiently different from the associated MIR inequality. We discuss computational issues and present numerical results based on a number of data sets.