Robust multistage location of battery swapping stations

Battery swapping is undergoing a revival driven by the rapid growth of the electric vehicle industry and significant advancements in battery technology. Due to limited budgets and increasing demand, the battery swapping industry must develop progressively over multiple stages. However, there is limited literature addressing the multistage location planning of battery swapping stations. To fill this research gap, this paper addresses the multistage location planning of battery swapping stations by explicitly considering both decision-dependent and time-dependent swapping demands. Specifically, we propose a dynamic distributionally robust optimization framework incorporating a designed ambiguity set that effectively captures the complex time-and-decision-dependent nature of the problem. In parallel, we model the operational dynamics of swapping stations as a continuous-time Markov chain, integrating this representation into our location planning model. To efficiently solve this multistage non-convex optimization problem, we first establish the monotonicity of average waiting time and lost demand at the station level, which enables the construction of logic-based Benders cuts. Moreover, we derive an analytical upper bound on the dual variables to tighten the model formulation. Leveraging these theoretical foundations, we develop an enhanced stochastic dual dynamic integer programming (ESDDiP) algorithm, which incorporates logic-based Benders cuts in the forward step and introduces two novel upper bound estimation methods. Through comprehensive numerical analysis, we validate the effectiveness of our proposed algorithm and model, providing managerial insights for battery swapping.