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

Abstract: To meet sustainability goals and regulatory requirements, transit agencies worldwide are planning partial and complete transitions to electric bus fleets. This paper presents the first comprehensive and computationally efficient multi-period optimization framework integrating the key planning decisions necessary to support such electrification initiatives. Our model, formulated as a two-stage integer program with integer subproblems, jointly optimizes yearly fleet and charging infrastructure investments as well as hourly vehicle scheduling and charging operations. To solve instances of practical relevance to proven optimality, we develop a logic-based Benders decomposition method enhanced by several techniques, including preprocessing, partial decomposition, and a range of classical and monotone Benders cuts derived from relaxations of the operational subproblems. These accelerations yield speedups of up to three orders of magnitude and lead to practical and theoretical insights into Benders cut selection. We also propose a heuristic tailored for long-term, citywide electrification planning. This approach, which imposes and progressively relaxes additional scheduling constraints, consistently delivers high-quality solutions with optimality gaps below 1% for instances an order of magnitude larger than those considered in prior studies. We illustrate our model using data from the Chicago public bus system, providing managerial insights into optimal investment and operational policies.