A Branch-and-cut Algorithm for the Capacitated Location-routing Problem

This paper describes a branch-and-cut algorithm for the Capacitated LocationRouting Problem (CLRP). In the CLRP customers with known demands must be served from capacitated facilities by an unlimited fleet of homogeneous, capacitated vehicles. The problem is to select a subset of potential facilities and to design vehicle routes around these facilities so that every customer is visited exactly once and capacities are respected. The problem is formulated as a two-index vehicle-flow problem with homogeneous vehicles. We present strengthenings of some known valid inequalities and introduce new families that improve the formulation. Results of computational experiments show that our formulation with the additional cuts provides tight lower bounds that are competitive with the ones reported in the literature for other vehicle-flow formulations. Moreover, our algorithm solves an open instance containing 88 customers and 8 facilities.