Integrated optimization of charging facility planning and en-route charging scheduling for heterogeneous electric bus systems

This paper proposes an integrated optimization framework for electric bus systems, jointly addressing strategic charging facility planning and operational charging scheduling. The model accommodates heterogeneous fleets with varying energy consumption rates, explicitly models deadhead movements between routes and chargers, and enforces tight temporal tracking of charging start times and durations to avoid charger conflicts and minimize idle charger usage. To address computational challenges on large-scale transit networks, a decomposition-based heuristic algorithm (DHA) was developed. The framework is validated on a real-world transit instance in Kingston, Canada. Results show that the integrated approach yields cost-efficient combinations of fleet composition, charger deployment, and charging schedules; a heterogeneous fleet matched to route requirements outperforms homogeneous alternatives. DHA provides substantial reductions in computation time with only minor losses in solution quality, making it suitable for large-scale exploratory analysis and preliminary design, while CPLEX can be used to refine high-quality candidates. Sensitivity analyses reveal that restricting en-route or overnight depot charging notably increases fleet sizes and system costs, while total costs exhibit a U-shaped relationship with charging power and duration. These findings offer actionable guidance for transit planners prioritizing investments and designing resilient charging strategies during staged electrification.