Abstract
The n-step mixed integer rounding (MIR) functions generate n-step MIR inequalities for MIP problems and are facets for the infinite group problems. We show that the n-step MIR functions also directly generate facets for the finite master cyclic group polyhedra especially in many cases where the breakpoints of the n-step MIR function are not necessarily at the elements of the group (hence the linear interpolation of the facet coefficients obtained has more than two slopes).
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