Title: Cutting planes based on simple mixed-integer programs

An important approach to solving practical integer programimng problems is to use cutting planes (inequalities satisfied by all integer solutions) such as the Gomory mixed-integer cut. We show how to derive cutting planes for general integer programs from a very simple mixed-integer program with one constraint and three variables. We call these cutting planes two-step MIR inequalities, as we can derive them by applying the mixed integer rounding (MIR) principle twice. We dicuss computational results which relate to the effectiveness of these cutting planes when applied to practical problems.