Lifting Gomory Cuts With Bounded Variables

Recently, Balas and Qualizza introduced a new cut for mixed 0,1 programs, called lopsided cut. Here we present a family of cuts that comprises the Gomory mixed integer cut at one extreme and the lopsided cut at the other. We show that every inequality in this family is extreme for the appropriate infinite relaxation. We also show that these inequalities are split cuts. Finally we provide computational results

The Master Equality Polyhedron: Two-Slope Facets and Separation Algorithm

This thesis presents our findings about the Master Equality Polyhedron (MEP), an extension of Gomory's Master Group Polyhedron. We prove a theorem analogous to Gomory and Johnson's two-slope theorem for the case of the MEP. We then show how such a theorem can lead to facet defining inequalities for MEPs or extreme inequalities for an extension of the infinite group model. We finally study certain coefficient-restricted inequalities for the MEP and how to separate them