A new mathematical formulation to integrate supply and demand within a choice-based optimization framework
During the last decade, there has been an increasing trend to combine customer behavior models in optimization, since it provides a better understanding of the preferences of clients to policy makers while planning for their systems. These preferences are formalized with predefined discrete choice models, which are the state-of-the-art for the mathematical modeling of demand. However, their complexity leads to mathematical formulations that are highly non linear and non convex in the variables of interest. On the other hand, we are also interested in discrete optimization models where supply and demand closely interact, which is typically the case in transportation problems. Such models are associated with (mixed) integer optimisation problems, whose discrete variables are used to design and configure the supply. In this research we present a general methodology that integrates both supply and demand while keeping the discrete choice model inside the framework of a mixed linear integer problem that is scalable and solvable within reasonable time.
Record created on 2016-09-15, modified on 2017-02-16