A new mathematical formulation to integrate supply and demand within a choice-based optimization framework

Discrete choice models are the state-of-the-art for the mathematical modeling of demand. Based on the concept of random utility, they are able to predict the choice behavior of individuals. However, these models are highly non linear and non convex in the variables of interest, and therefore difficult to be included in mixed linear optimization models. Furthermore, these models are of great importance in transportation revenue management systems. In this research, we propose a new mathematical modeling framework to include general random utility assumption inside discrete optimization framework. In order to tackle the non-linearity and non-convexity imposed by choice-models, we rely on simulation to capture the probabilistic nature of demand. Since the formulation has been designed to be linear, the price to pay is the high dimensionality of the problem. We propose an alternative formulation aiming at reducing the size of the problem. We have performed some preliminary experiments for small instances in order to compare the performances of the two models. Note that regardless from the implemented formulation, additional techniques such as decomposition methods may be required for more general instances.