Path Cover and Path Pack Inequalities for the Capacitated Fixed-Charge Network Flow Problem
研究了带容量固定费用网络流中的路径子结构，推导出易于计算的路径覆盖和路径打包不等式，并通过分支切割算法验证了其有效性。
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.