Integrating advanced discrete choice models in mixed integer linear optimization

The integration of customer behavioral models in operations research (OR) is appealing to operators and policy makers (the supply) because it provides a better understanding of the preferences of customers (the demand) while planning for their systems. These preferences are formalized with discrete choice models, which are the state-of-the-art for the mathematical modeling of demand, whereas mixed integer linear programming (MILP) models are considered to design and configure the systems. Notwithstanding the clear advantages of this integration, 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 MILP. In this paper, we present a general framework that overcomes these limitations by integrating in MILP advanced discrete choice models. A concrete application on benefit maximization from an operator selling services to a market is used to illustrate the employment of the framework. A case study from the recent literature is considered to perform various experiments, such as price differentiation by population segmentation. The results show that this approach is a powerful tool to configure systems based on the heterogeneous behavior of customers, and it allows to investigate advanced marketing strategies and business models.