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 \emph{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.
@article{arxiv.1705.05920,
title = {Path Cover and Path Pack Inequalities for the Capacitated Fixed-Charge Network Flow Problem},
author = {Alper Atamturk and Birce Tezel and Simge Kucukyavuz},
journal= {arXiv preprint arXiv:1705.05920},
year = {2017}
}