A Distributionally Robust Joint Chance Constraint Optimization Model for Vehicle Battery Swapping Station Location Problem

The successful adoption of electric vehicles (EVs) hinges greatly on the provision of robust infrastructural support. This study introduces a distributionally robust optimization (DRO) model aimed at identifying the optimal locations and capacities for battery swapping stations (BBSs). The primary objective of this model is to minimize the total cost of the BBS system, encompassing operator and customer costs. Our model effectively mitigates over-conservatism by tackling the uncertainty issues associated with battery swapping demand, a prevalent challenge in existing models. Moreover, we encapsulate demand uncertainty within an ambiguity set and incorporate joint chance constraints, thereby enhancing the reliability of the BBS system. To make this complex, non-convex model tractable, we reformulate it into a mixed-integer linear programming (MILP) problem, thus enabling commercial solvers to effectively solve it. Numerical experiments demonstrate that the proposed model can effectively determine optimal solutions for the BBS system's location and capacity, satisfying battery demand while simultaneously minimizing total system costs. The experimental results also underscore the importance of the risk parameter and Wasserstein radius on BBS location and capacity. Our proposed model could serve as a valuable tool for relevant decision-makers in the design of BBS systems, thereby promoting the wider adoption of EVs.