Contextual stochastic optimization for determining electric vehicle charging station locations with decision-dependent demand learning

We consider a two-stage contextual stochastic electric vehicle (EV) charging station location problem, where the uncertain customer demand depends on both exogenous contextual information (e.g., gross domestic product and education level) and our first-stage location/capacity decisions, leading to decision-dependent uncertainty. For example, opening a charging station increases the demand around that area. We model this problem using the empirical residuals-based decision-dependent sample average approximation (ER-DD-SAA) framework, which explicitly embeds demand learning into the optimization by leveraging the empirical residuals. We theoretically analyze the consistency and asymptotic optimality of the ER-DD-SAA framework. To learn the latent decision-dependent customer demand, we propose a nonlinear regression model that involves an exponential term on the distance between charging stations and customer sites, which is challenging to regress directly. To overcome this issue, we devise a two-step regression approach. We first regress on the distance and location/capacity decisions while keeping all other exogenous covariates the same. In the second step, we use classical linear regression as well as modern machine learning tools (e.g., random forest, decision trees, and gradient boosting) to learn the impact of the rest of the covariates on customer demand. We conduct synthetic experiments and a case study based on real-world data in New York State to illustrate the effectiveness of our proposed ER-DD-SAA model.