Bus Fleet Electrification Planning Through Logic-Based Benders Decomposition and Restriction Heuristics

Abstract

To meet sustainability goals and regulatory requirements, transit agencies must plan partial and full transitions to electric bus fleets. This paper presents a comprehensive and computationally efficient multi-period optimization framework integrating the key decisions required to support such electrification initiatives. Our model is formulated as a two-stage integer program with integer subproblems. These two levels optimize, respectively, yearly fleet sizing and charging infrastructure investments, and hourly vehicle scheduling and charging operations. We develop an exact logic-based Benders decomposition algorithm enhanced by several acceleration techniques, including preprocessing, master problem strengthening, and efficient cut separation methods applied to different relaxations of the operational problem. These accelerations achieve speedups of up to three orders of magnitude and provide new theoretical and practical insights into Benders cut selection. We also propose a heuristic tailored for long-term, citywide electrification planning. This approach imposes and progressively relaxes additional scheduling constraints derived from auxiliary problems. It delivers high-quality solutions with optimality gaps below 1% for instances an order of magnitude larger than those considered in prior work. We illustrate our model using real data from the Chicago public bus system, providing managerial insights into optimal investment and operational policies.