Integrated Optimization of Scheduling and Flexible Charging in Mixed Electric-Diesel Urban Transit Bus Systems

Abstract

The transition of transit fleets to alternative powertrains offers a potential pathway to reducing the cost of mobility. However, the limited range and long charging durations of battery electric buses (BEBs) introduce significant operational complexities, necessitating innovative scheduling and charging strategies. This study proposes an integrated mixed-integer linear programming model to optimize vehicle scheduling and charging strategies for mixed fleets of BEBs and diesel buses. Unlike existing models, which often assume a fixed BEB fleet size or restrict charging to a single charger type, our approach simultaneously determines the optimal fleet composition, scheduling, and flexible partial charging strategy incorporating both slow and fast chargers at garages and terminal stations. The model minimizes combined fleet purchase and operational costs. A queuing strategy is introduced, departing from traditional first-come, first-served methods by dynamically allocating waiting and charging times based on operational priorities and resource availability, improving overall scheduling efficiency. To overcome computational complexities arising from numerous variables, a column generation framework is developed, facilitating scalable solutions for large-scale transit networks. Numerical experiments using real-world transit data from the Chicago Transit Authority and the Pace suburban bus systems demonstrate the model's effectiveness. Results indicate that while a full transition to alternative powertrains results in a modest cost increase, optimal mixed-fleet configurations can actually reduce total system costs. Furthermore, sensitivity analyses reveal that restricting charging to garages significantly increases fleet size and operational costs, underscoring the potential of distributed opportunistic charging.