Integrating advanced discrete choice models in mixed integer linear optimization

The integration of discrete choice models in optimization is appealing to operators and policy makers (the supply) because it provides a better understanding of the preferences of clients (the demand) while planning for their systems. Notwithstanding the clear advantages, the complexity of discrete choice models leads to mathematical formulations that are highly nonlinear and nonconvex in the variables of interest, and therefore difficult to be included in mixed integer linear problems (MILP), which are the common optimization models considered to design and configure a system. In this research, we present a general framework that integrates discrete choice models within MILP. The abovementioned limitations are overcome with simulation. We illustrate a concrete application on benefit maximization and we test the resulting model on a case study from the recent literature in which a mixtures of logit model is estimated. The results show that this approach is a powerful tool to characterize features of the systems based on the heterogeneous behavior of customers.