Mobility Award winner May 2017

My PhD research is about capturing the interactions between the demand and the supply under a single modeling framework. To this end, we integrate the well known discrete choice models, which represent the mathematical modelling of the demand, into mixed integer linear programming (MILP) models, which constitute a significant share of the mathematical models designing and configuring the supply. This integration is challenging since both formulations are built on different types of assumptions, and has been somehow relaxed in the existing literature.

In the first stage of the PhD, we have developed a general framework that is able to integrate a discrete choice model into a MILP model. In order to test the formulation, a concrete application has been defined. More precisely, we assume an operator selling services to a market, each of them at a certain price and at a certain capacity, both to be decided. The goal is to find the best strategy in terms of pricing and capacity allocation in order to maximize the benefit of the operator, which is understood as the difference between the generated revenue and the operating costs. The experiments performed on a case study from the recent literature show that this formulation is a powerful tool to configure systems based on the heterogeneous behavior of customers. Notwithstanding its advantages, the dimension of the resulting problem is high, and therefore solving it is computationally expensive.

To address this issue, and taking advantage of the structure of the problem, we consider decomposition techniques in order to speed up the solution approach. The general idea is to decompose the problem into smaller subproblems that can be solved in an easier way and that can be parallelized. Prof. Bernard Gendron, from the Centre interuniversitaire de recherche sur les réseaux d’entreprise, la logistique et le transport (CIRRELT) in Montreal (Canada), has been working on this field for many years. His expertise on this topic will provide the required knowledge to develop a Lagrangian relaxation method that will allow to converge to a solution strategy that will make our approach operational for real applications.