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Facets for Continuous Multi-Mixing Set with General Coefficients and Bounded Integer Variables

Manish Bansal (bansal***at***vt.edu)
Kiavash Kianfar (kianfar***at***tamu.edu)

Abstract: Bansal and Kianfar introduced continuous multi-mixing set where the coefficients satisfy the so-called n-step MIR conditions and developed facet-defining inequalities for this set. In this paper, we first generalize their inequalities for the continuous multi-mixing set with general coefficients (where no conditions are imposed on the coefficients) and show that they are facet-defining in many cases. Next, we further generalize the continuous multi-mixing set with general coefficients by incorporating upper bounds on the integer variables. We introduce a family of valid inequalities for this set through a unified generalization of the n-step cycle inequalities and the mingled n-step MIR inequalities. We indicate how to separate over these inequalities in polynomial time and present the conditions under which a subset of these inequalities are facet-defining.

Keywords: n-step cycle inequalities, n-step mingling, n-step MIR, continuous mixing, mixed integer programming, cutting planes

Category 1: Integer Programming

Category 2: Integer Programming ((Mixed) Integer Linear Programming )

Category 3: Integer Programming (Cutting Plane Approaches )

Citation: M. Bansal, K. Kianfar, "Facets for the continuous multi-mixing set with general coefficients and bounded integer variables," Discrete Optimization, 2017; Available at http://www.sciencedirect.com/science/article/pii/S1572528617301019

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Entry Submitted: 10/22/2014
Entry Accepted: 10/23/2014
Entry Last Modified: 08/09/2017

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