Intersection Cuts with Infinite Split Rank

Authors:
Amitabh Basu;Gé/rard Cornué/jols;Franç/ois Margot
Affiliations:
Department of Mathematics, University of California, Davis, Davis, California 95616;Tepper School of Business, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213/ and LIF, Faculté/ des Sciences de Luminy, Université/ de Marseille, 13288 Marseille, France;Tepper School of Business, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213
Venue:
Mathematics of Operations Research
Year:
2012

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Abstract

We consider mixed-integer linear programs where free integer variables are expressed in terms of nonnegative continuous variables. When this model only has two integer variables, Dey and Louveaux characterized the intersection cuts that have infinite split rank. We show that, for any number of integer variables, the split rank of an intersection cut generated from a rational lattice-free polytope L is finite if and only if the integer points on the boundary of L satisfy a certain “2-hyperplane property.” The Dey--Louveaux characterization is a consequence of this more general result.