Incorporating advanced behavioral models in mixed linear optimization

Discrete choice models are the state-of-the-art for the mathematical modelling 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. 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 nonlinearity 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 have performed some preliminary experiments for small instances with promising results. Nevertheless, for more general cases, additional techniques as decomposition methods may be required.