Exact Approaches for Designing Multifacility Buy-at-Bulk Networks

Abstract

We study a problem that integrates buy-at-bulk network design into the classical facility location problem. We consider a generalization of the facility location problem where multiple clients may share a capacitated network to connect to open facilities instead of requiring direct links. In this problem, we wish to open facilities, build a routing network by installing access cables of different costs and capacities, and route every client demand to an open facility. We provide a path-based formulation and we compare it with the natural compact formulation for this problem. We then design an exact branch-price-and-cut algorithm for solving the path-based formulation. We study the effect of two families of valid inequalities. In addition to this, we present three different types of primal heuristics and employ a hybrid approach to effectively combine these heuristics in order to improve the primal bounds. We finally report the results of our approach that were tested on a set of real world instances, as well as two sets of benchmark instances and evaluate the effects of our valid inequalities and primal heuristics.