A cutting-plane algorithm based on cutset inequalities for multicommodity capacitated fixed charge network design

The multicommodity capacitated fixed charge network design problem is a well-known NPhard problem which arises in a wide variety of applications, most notably in transportation and telecommunications. In this paper, we propose to improve the mixed integer programming (MIP) formulation of the problem by using a polyhedral approach. We present a cutting-plane algorithm which incorporates valid inequalities (VI) based on cutsets of the network. We identify and study, in the field of cutset type inequalities, three families of VI: the well-known cover inequalities, the minimum cardinality inequalities, and the network cutset inequalities. We develop efficient separation heuristics and lifting procedures, as well as a cutset generation algorithm. We present computational results on a large set of instances of various characteristics. Our results show that the cutting-plane algorithm achieves better lower bounds with competitive computational effort when compared to the results obtained when solving a large-scale formulation with the state-of-the-art MIP software package CPLEX.