|Speaker :||Patrice Marcotte|
|UniversitÃ© de MontrÃ©al|
|Time:||11:00 am - 12:00 pm|
|Location:||LINCS Meeting Room 40|
In a competitive setting, we consider the problem faced by a firm that makes decisions concerning both the location and service levels of its facilities, taking into account that users patronize the facility that maximizes their individual utility, expressed as the sum of travel time, queueing delay, and a random term. This situation can be modelled as a mathematical program with equilibrium constraints that involves discrete and continuous variables, as well as linear and nonlinear functions. This program is reformulated as a standard bilevel program that can be approximated, through the linearization of the nonlinear functions involved, as a mixed integer linear program that yields â€˜quasi-optimal’ solutions. Since this approach does not scale well, we have in parallel developed heuristic procedures that exploit the very structure of the problem. Based on theoretical and computation results pertaining to this application, we will discuss further developments in the area of nonlinear facility location.