Approximation Algorithms for Problems Combining Facility Location and Network Design

We present approximation algorithms for integrated logistics problems that combine elements of facility location and transport network design. We first study the problem where opening facilities incurs opening costs and transportation from the clients to the facilities incurs buy-at-bulk costs, and provide a combinatorial approximation algorithm. We also show that the integer programming formulation of this problem has small integrality gap. We extend the model to the version when there is a bound on the number of facilities that may be opened.