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New Valid Inequalities for the Fixed-Charge and Single-Node Flow Polytopes

Adam N. Letchford (a.n.letchford***at***lancaster.ac.uk)
Georgia Souli (g.souli***at***lancaster.ac.uk)

Abstract: The most effective software packages for solving mixed 0-1 linear programs use strong valid linear inequalities derived from polyhedral theory. We introduce a new procedure which enables one to take known valid inequalities for the knapsack polytope, and convert them into valid inequalities for the fixed-charge and single-node flow polytopes. The resulting inequalities are very different from the previously known inequalities (such as flow cover and flow pack inequalities), and define facets under certain conditions.

Keywords: polyhedral combinatorics; branch-and-cut; mixed-integer linear programming

Category 1: Integer Programming ((Mixed) Integer Linear Programming )

Category 2: Integer Programming (Cutting Plane Approaches )

Citation: Eventually published as: A.N. Letchford & G. Souli (2019) New valid inequalities for the fixed-charge and single-node flow polytopes. Operations Research Letters, 47(5), 353-357.

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Entry Submitted: 10/23/2018
Entry Accepted: 10/23/2018
Entry Last Modified: 04/30/2020

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