On a Generalization of the Master Cyclic Group Polyhedron

Sanjeeb Dash IBM Research Ricardo Fukasawa Georgia Inst. Tech. Oktay G unl uk IBM Research March 6, 2008 Abstract 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-de ning inequalities for MEP. This result generalizes similar results for the Master Cyclic Group Polyhedron by Gomory [9] and for the Master Knapsack Polyhedron by Ara oz [1]. Furthermore, this characterization also gives a polynomial time algorithm for separating an arbitrary point from MEP. We describe how facet-de ning inequalities for the Master Cyclic Group Polyhedron can be lifted to obtain facet-de ning inequalities for the MEP, and also present facet-de ning inequalities for MEP that cannot be obtained in such a way. Finally, we study the mixed-integer extension of MEP and present an interpolation theorem that produces valid inequalities for general mixed integer programming problems using facets of MEP.