A robust optimal battery swapping station location model for commercial electric vehicles under demand uncertainty

The battery swapping mode has garnered growing attention for commercial electric vehicles (CEVs) due to its potential to substantially reduce charging downtime and improve fleet utilization over conventional charging. Its effective deployment, however, requires robust and cost-efficient battery swapping station (BSS) planning capable of handling demand uncertainty—driven by factors such as fluctuating fleet sizes, varying battery degradation rates, and unpredictable charging behavior. To address this challenge, this study proposes a mixed-integer linear programming (MILP) model to optimize BSS locations and battery inventory, minimizing total system costs including construction, operation, and detour costs associated with CEVs deviating from regular service routes to access BSSs. Demand uncertainty is captured via a budgeted uncertainty set to ensure computational tractability and robustness. Given the model's complexity, it is reformulated as a deterministic robust optimization problem and solved using a Benders decomposition approach. Numerical experiments, using real-world data from a BSS operator in Shanghai, validate the model's effectiveness in minimizing system cost while ensuring robust deployment decisions. Additionally, Benders decomposition algorithm improves computational efficiency by over 40 % on average compared to a commercial solver, with greater advantages observed as node- and system-level uncertainties increase. This modeling framework offers practical insights for policymakers and industry stakeholders developing scalable, resilient BSS networks to support the growth of CEV adoption.