Integrating discrete choice models in mixed integer linear programming to capture the interactions between supply and demand

The integration of discrete choice models in mixed integer linear programming (MILP) 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 MILP models are considered to design and configure the systems. However, the complexity of discrete choice models leads to mathematical formulations that are highly nonlinear and nonconvex, and makes them difficult to be included in MILP. In this research, we present a general framework that overcomes these limitations by relying on simulation in order to integrate advanced discrete choice models in MILP. A concrete application on benefit maximization from an operator selling services to a market is used to illustrate the employment of the framework.