Minimizing the maximum travel time in a combined model of facility location and network design

This paper presents a combined Facility Location/Network Design Problem which simultaneously considers the location of facilities and the design of its underlying network so as to minimize the maximum customer-facility travel time. The model generalizes the classical p-center problem and has various applications in regional planning, distribution, telecommunications, emergency systems, and other areas. Two mixed integer programming formulations are presented and compared. Several valid inequalities are derived for the most promising of these formulations to strengthen its LP relaxation bound and to reduce the enumeration tree. Numerical results of a series of computational experiments for instances with up to 100 nodes and 500 candidate links are reported.