On cut-based inequalities for capacitated network design polyhedra

In this article we study capacitated network design problems. We unify and extend poly-hedral results for directed, bidirected and undirected link capacity models. Based on validinequalities for a network cut we show that regardless of the link capacity model, facets of thepolyhedra associated with such a cut translate to facets of the original network design polyhedraif the two subgraphs defined by the network cut are (strongly) connected. Our investigationof the facial structure of the cutset polyhedra allows to complement existing polyhedral resultsfor the three variants by presenting facet-defining flow-cutset inequalities in a unifying way. Inaddition, we present a new class of facet-defining inequalities, showing as well that flow-cutsetinequalities alone do not suffice to give a complete description for single-commodity, single-module cutset polyhedra in the bidirected and undirected case – in contrast to a known resultfor the directed case. The practical importance of the theoretical investigations is highlighted inan extensive computational study on 27 instances from the Survivable Network Design Library(SNDlib).