Optimizing urban bus operations during fleet electrification: A mixed fleet scheduling model with a column generation algorithm

Abstract

Electric buses play a critical role in advancing urban green transportation. However, in the transition period remaining before full conversion to electric buses is achieved, it is essential to address the scheduling challenges associated with operating mixed fleets of electric and diesel buses. To support decision-making for city bus operators, this study develops a mixed-integer linear programming model based on a multi-layer time-space network, aiming to minimize total operational cost. This study contributes to the literature by incorporating partial charging strategies and time-of-use electricity pricing, thereby capturing real-world constraints imposed by battery capacity limits and power grid restrictions, which are largely absent in prior research. To address the computational complexity inherent in this NP-hard problem, a column generation algorithm coupled with a vehicle-based network decomposition heuristic is developed to enhance solution efficiency. Computational experiments using real-world instances are conducted to evaluate algorithmic performance. The results demonstrate that the solution approach outperforms the Gurobi commercial solver in both solution quality and computational time, proving that the proposed framework can generate robust analytical outputs. A set of scenarios and sensitivity analyses is then conducted to evaluate how variations in key operational parameters, such as charger locations, fleet electrification shares, energy-consumption efficiency, fixed-cost subsidies, and electricity-price subsidies, affect the objective value and decision variables. These findings provide critical decision support for managing the operational and charging complexities associated with scheduling in the transition to city bus fleet electrification.