We study the Master Equality Polyhedron (MEP) which generalizes the Master Cyclic Group Polyhedron and the Master Knapsack Polyhedron. We present an explicit characterization of the polar of the nontrivial facet-defining inequalities for the MEP. This result generalizes similar results for the Master Cyclic Group Polyhedron by Gomory (1969) and for the Master Knapsack Polyhedron by Araoz (1974). Furthermore, this characterization also gives a polynomial time algorithm for separating an arbitrary point from the MEP. We describe how facet defining inequalities for the Master Cyclic Group Polyhedron can be lifted to obtain facet defining inequalities for the MEP, and also present facet defining inequalities for the MEP that cannot be obtained in such a way. Finally, we study the mixed-integer extension of the MEP and present an interpolation theorem that produces valid inequalities for general mixed integer programming problems using facets of the MEP.
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