The n-step mixed integer rounding (MIR) functions are used to generate n-step MIR inequalities for (mixed) integer programming problems (Kianfar and Fathi, 2006). We show that these functions are sources for generating extreme valid inequalities (facets) for group problems. We first prove the n-step MIR function, for any positive integer n, generates two-slope facets for the infinite group problem, and then show under appropriate conditions on parameters, these functions also generate facets for the finite master cyclic group problem. We discuss that similar results are true for the group problems with continuous variables.
Operations Research Technical Report 2006-2, North Carolina State University