Mixing MIR Inequalities with Two Divisible Coefficients - Archive ouverte HAL Access content directly
Journal Articles Mathematical Programming, Series A Year : 2010

Mixing MIR Inequalities with Two Divisible Coefficients


This paper is a polyhedral study of a generalization of the mixing set where two different, divisible coefficients are allowed for the integral variables. Our results generalize earlier work on mixed integer rounding, mixing, and extensions. They also directly apply to applications such as production planning problems involving lower bounds or start-ups on production, when these are modeled as mixed-integer linear programs. We define a new class of valid inequalities and give two proofs that they suffice to describe the convex hull of this mixed-integer set. We give a characterization of each of the maximal faces of the convex hull, as well as a closed form description of its extreme points and rays, and show how to separate over this set in O(n log n). Finally, we give several extended formulations of polynomial size, and study conditions under which adding certain simple constraints on the integer variables preserves our main result.
Fichier principal
Vignette du fichier
CMV09.pdf (260.93 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-00387098 , version 1 (24-05-2009)



Miguel Constantino, Andrew Miller, Mathieu van Vyve. Mixing MIR Inequalities with Two Divisible Coefficients. Mathematical Programming, Series A, 2010, 123, pp.451-483. ⟨10.1007/s10107-009-0266-9⟩. ⟨hal-00387098⟩


197 View
231 Download



Gmail Facebook Twitter LinkedIn More