From diesel to electric : exploring fleet increment curves for zero-emission bus transition

Abstract

Bus electrification is a key trend in the global evolution of public transportation systems. However, replacing diesel buses (DBs) with Battery electric buses (BEBs) is a long-term process, where the limited driving range and prolonged charging times might necessitate a larger BEB fleet to maintain trip services compared to the replaced DB fleet. To quantify this fleet expansion across variable replacement decisions, we introduce the fleet increment curve (FIC), a novel conceptual idea that guides BEB procurement decisions during the transition to the zero-emission bus (ZEB) system. First, the FIC is derived from solving a series of mixed-integer linear programming (MILP) (namely MILP-FIC model) by varying the replaced DB fleet as inputs, where each MILP is developed by means of linearization techniques, while formulating the mixed-fleet operation under limited charging accessibility. To solve the MILP-FIC, Lagrangian relaxation (LR) is applied to relax charging accessibility constraints, decomposing the problem into route-specific subproblems. Subsequently, representing FIC by-products as piecewise linear functions enables extended models developed for addressing long-term fleet replacement scheduling and charging resource allocation. A general fleet replacement scheduling is presented, which accommodates multiple BEB types (varying battery capacities and charging power) by deriving type-specific fleet procurement curves. We use real-world bus route data from Hong Kong to explore the FIC, revealing how route characteristics—such as trip frequency, trip duration, and energy consumption—interact with charging site characteristics (e.g., siting and sizing) to shape the FIC. The curves typically follow a non-decreasing trend, while an S-shaped trend occurs across certain routes. Additionally, the results demonstrate the effective incorporation of FIC into the planning for ZEB transition, providing valuable insights for bus operators.