Valid inequalities and separation for capacitated fixed charge flow problems

Three-partition Inequalities for Constant Capacity Capacitated Fixed-charge Network Flow Problems

Flow cover inequalities are among the most effective valid inequalities for solving capacitated fixed-charge network flow problems. These valid inequalities are implications on the flow quantity on the cut arcs of a two-partitioning of the network, depending on whether some of the cut arcs are open or closed. As the implications are only on the cut arcs, flow cover inequalities can be modeled b...

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

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 inequalitie...

Iterative Methods for Equilibrium Problems, Variational Inequalities and Fixed Points

Three-partition flow cover inequalities for constant capacity fixed-charge network flow problems

Flow cover inequalities are among the most effective valid inequalities for capacitated fixed-charge network flow problems. These valid inequalities are based on implications for the flow quantity on the cut arcs of a two-partitioning of the network, depending on whether some of the cut arcs are open or closed. As the implications are only on the cut arcs, flow cover inequalities can be obtaine...

Initialization of the Benders master problem using valid inequalities applied to fixed-charge network problems

Network problems concern the selection of arcs in a graph in order to satisfy, at minimum cost, some flow requirements, usually expressed in the form of node–node pair demands. Benders decomposition methods, based on the idea of partitioning of the initial problem to two sub-problems and on the generation of cuts, have been successfully applied to many of these problems. This paper presents a n...