Outer approximation algorithms for the congested p-median problem
Author
Şelfun, Selva
Advisor
Yıldırım, Emre Alper
Date
2011Publisher
Bilkent University
Language
English
Type
ThesisItem Usage Stats
80
views
views
30
downloads
downloads
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.
Keywords
facility location problemp-median
outer approximation
linear constraints
disutility
waiting time
MINLP