Split rank of triangle and quadrilateral inequalities

Santanu S. Dey () and Quentin Louveaux ()
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Santanu S. Dey: Université catholique de Louvain (UCL). Center for Operations Research and Econometrics (CORE)
Quentin Louveaux: Montefiore Institute, Université de Liège, Belgium

No 2009055, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

Abstract: A simple relaxation of two rows of a simplex tableau is a mixed integer set consisting of two equations with two free integer variables and non-negative continuous variables. Recently Andersen et al. [2] and Cornu´ejols and Margot [13] showed that the facet-defining inequalities of this set are either split cuts or intersection cuts obtained from lattice-free triangles and quadrilaterals. Through a result by Cook et al. [12], it is known that one particular class of facet- defining triangle inequality does not have a finite split rank. In this paper, we show that all other facet-defining triangle and quadrilateral inequalities have finite split rank. The proof is constructive and given a facet-defining triangle or quadrilateral inequality we present an explicit sequence of split inequalities that can be used to generate it.

Keywords: mixed integer programs; split rank; group relaxations (search for similar items in EconPapers)
Date: 2009-09-01
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