Path Cover and Path Pack Inequalities for the Capacitated Fixed-Charge Network Flow Problem

  • Alper Atamturk
  • Simge Küçükyavuz
  • Birce Tezel
    • Categories (Mixed) Integer Linear Programming, Cutting Plane Approaches Tags , , , Short URL: https://optimization-online.org/?p=14270

    Capacitated fixed-charge network flows are used to model a variety of problems in telecommunication, facility location, production planning and supply chain management. In this paper, we investigate capacitated path substructures and derive strong and easy-to-compute path cover and path pack inequalities. These inequalities are based on an explicit characterization of the submodular inequalities through a fast computation of parametric minimum cuts on a path, and they generalize the well-known flow cover and flow pack inequalities for the single-node relaxations of fixed-charge flow models. We provide necessary and sufficient facet conditions. Computational results demonstrate the effectiveness of the inequalities when used as cuts in a branch-and-cut algorithm.

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    BCOL Research Report 15.03, IEOR, UC Berkeley

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