MILP-Based Pareto Optimization of Electric Bus Scheduling and Charging Management

Effective scheduling and charging management of electric buses is essential for minimizing investment and operational costs while improving transit efficiency. The paper presents an optimization framework which provides a 3D Pareto frontier of fleet size, deadhead distance, and charging cost, while accounting for heterogeneous battery energy, charger power, charging spot capacities, integrated daily and night charging, and a charge sustaining condition. Two optimization approaches are developed: Mixed-Integer Linear Programming (MILP), which finds globally optimal solutions, and an Insertion Heuristic (IH), which generates feasible schedules in a computationally efficient way. The framework operates iteratively, starting with MILP to determine the minimum number of buses for feasible operation. Then, additional buses are incrementally incorporated, and for each fixed fleet size, a multi-objective optimization of scheduling and charging management is applied to minimize deadhead distance and charging costs using both approaches. A case study on a synthetic transport network demonstrates that the proposed IH algorithm achieves nearly optimal performance at a fraction of the computational time and memory requirements of the MILP approach. A Pareto analysis shows that increasing fleet size reduces deadhead distance and charging costs up to a saturation point, beyond which further additions yield minimal benefits.