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The convex hull of the all-different system with the inclusion property: a simple proof

Marco Di Summa ()
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Marco Di Summa: Dipartimento di Matematica, Università degli Studi di Padova, Italy

No 2013069, CORE Discussion Papers from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

Abstract: An all-different constraint for a given family of discrete variables imposes the condition that no two variables in the family are allowed to take the same value. Magos et al. [Mathematical Programming, 132 (2012), pp. 209–260] gave a linear-inequality description of the convex hull of solutions to a system of all-different constraints, under a special assumption called inclusion property. The convex hull of solutions is in this case the intersection of the convex hulls of each of the all-different constraints of the system. We give a short and simple proof of this result, that in addition shows the total dual integrality of the linear system.

Keywords: all-different constraint; convex hull; integral polyhedron; total dual integrality (search for similar items in EconPapers)
JEL-codes: C10 (search for similar items in EconPapers)
Date: 2013-12-31
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