On a Generalization of the Master Cyclic Group Polyhedron

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 nontrivial facet-defining inequalities for MEP. This result generalizes similar results for the Master Cyclic Group Polyhedron by Gomory [9] and for the Master Knapsack Polyhedron by Araoz [1]. 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.

[1]  Laurence A. Wolsey,et al.  Technical Note - Facets and Strong Valid Inequalities for Integer Programs , 1976, Oper. Res..

[2]  Sanjeeb Dash,et al.  Valid inequalities based on the interpolation procedure , 2006, Math. Program..

[3]  Ellis L. Johnson,et al.  Corner Polyhedra and their connection with cutting planes , 2003, Math. Program..

[4]  Ellis L. Johnson,et al.  Cyclic group and knapsack facets , 2003, Math. Program..

[5]  Matteo Fischetti,et al.  Mixed-Integer Cuts from Cyclic Groups , 2007, Math. Program..

[6]  Sanjeeb Dash,et al.  On the strength of Gomory mixed-integer cuts as group cuts , 2008, Math. Program..

[7]  Sanjeeb Dash,et al.  Valid inequalities based on simple mixed-integer sets , 2006, Math. Program..

[8]  E. Balas,et al.  Facets of the Knapsack Polytope From Minimal Covers , 1978 .

[9]  Ellis L. Johnson,et al.  Some continuous functions related to corner polyhedra , 1972, Math. Program..

[10]  Matteo Fischetti,et al.  How tight is the corner relaxation? , 2008, Discret. Optim..

[11]  Ellis L. Johnson,et al.  T-space and cutting planes , 2003, Math. Program..

[12]  Martin W. P. Savelsbergh,et al.  Sequence Independent Lifting in Mixed Integer Programming , 2000, J. Comb. Optim..

[13]  R. Gomory.  Some polyhedra related to combinatorial problems , 1969 .

[14]  Marcus Poggi de Aragão,et al.  Robust branch-cut-and-price for the Capacitated Minimum Spanning Tree problem over a large extended formulation , 2007, Math. Program..