A cutting plane algorithm for the Capacitated Connected Facility Location Problem

We consider a network design problem that arises in the cost‐optimal design of last mile telecommunication networks. It extends the Connected Facility Location problem by introducing capacities on the facilities and links of the networks. It combines aspects of the capacitated network design problem and the single‐source capacitated facility location problem. We refer to it as the Capacitated Connected Facility Location Problem. We develop a basic integer programming model based on single‐commodity flows. Based on valid inequalities for the capacitated network design problem and the single‐source capacitated facility location problem we derive several (new) classes of valid inequalities for the Capacitated Connected Facility Location Problem including cut set inequalities, cover inequalities and combinations thereof. We use them in a branch‐and‐cut framework and show their applicability and efficacy on a set of real‐world instances.