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We study a joint inventory-routing problem for electric vehicle (EV) battery swapping systems that feature hybrid charging, where batteries may be charged either on-site at local stations or centrally at a depot, under uncertain vehicle arrival rates and stochastic battery charging durations. The system comprises a central charging station and multiple battery swapping stations, each experiencing random demand and constrained by service-level requirements. Returned batteries with short charging times are charged locally, while those exceeding a threshold are routed to the central station, introducing a two-echelon logistics structure with state-dependent flows.

We develop a two-stage optimization model that simultaneously determines the battery delivery routes and inventory replenishment levels across the network. The model incorporates a probabilistic stockout constraint to ensure high service quality and accounts for the impact of hybrid charging on inventory pooling and routing efficiency. To address the problem’s non-convexity and computational complexity, we derive closed-form approximations for service-level constraints and reformulate the problem using second-order cone programming. We further propose an efficient branch-and-cut algorithm enhanced with extended polymatroid cuts to improve tractability and scalability.

Our model generalizes existing battery logistics frameworks by integrating hybrid service modes, stochastic charging durations, and routing constraints into a unified optimization framework. Numerical results demonstrate the operational benefits of hybrid charging and validate the effectiveness of the proposed solution approach. This work provides a tractable, analytically grounded method for managing EV battery logistics in urban mobility systems under uncertainty.

(This is a joint work with Long He from George Washington University, Yuli Zhang from Beijing Institute of Technology and Ningwei Zhang from Lanzhou University)

A short Bio: Shanshan Wang, full professor in Department of Management Science and Engineering in Beihang University (BUAA). Prior to this, she was a postdoctoral fellow in The Chinese University of Hong Kong, and GERAD, HEC Montréal. Her research mainly focuses on distributionally robust optimization, and decomposition scheme for large-scale MILP. Her research is published in renowned scientific journals, e.g., Operations Research, IJOC, EJOR.