Outer approximation algorithms for the congested p-median problem

Abstract

In this thesis, we study a generalization of the p-median problem, which is a well-known facility location problem. Given a set of clients, a set of potential facilities, and a positive integer p, the p-median problem is concerned with choosing p facilities and assigning each client to an open facility in such a way that the sum of the travel times between each client and the facility that serves that client is as small as possible. The classical p-median problem takes into account only the travel times between clients and facilities. However, in many applications, the disutility of a client is also closely related to the waiting time at a facility, which is typically an increasing function of the demand allocated to that facility. In an attempt to address this issue, for a given potential facility, we define the disutility of a client as a function of the travel time and the total demand served by that facility. The latter part reflects the level of unwillingness of a client to be served by a facility as a function of the level of utilization of that facility. By modeling this relation using an increasing convex function, we develop convex mixed integer nonlinear programming models. By exploiting the fact that nonlinearity only appears in the objective function, we propose different variants of the well-known outer approximation algorithm. Our extensive computational results reveal that our algorithms are competitive in comparison with the off-the-shelf solvers.