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

摘要

Capacitated fixed-charge network flows are used to model a variety ofproblems in telecommunication, facility location, production planning andsupply chain management. In this paper, we investigate capacitated pathsubstructures and derive strong and easy-to-compute \emph{path cover and pathpack inequalities}. These inequalities are based on an explicitcharacterization of the submodular inequalities through a fast computation ofparametric minimum cuts on a path, and they generalize the well-known flowcover and flow pack inequalities for the single-node relaxations offixed-charge flow models. We provide necessary and sufficient facet conditions.Computational results demonstrate the effectiveness of the inequalities whenused as cuts in a branch-and-cut algorithm.