Demand-driven timetabling and vehicle scheduling optimization for electric bus transit lines

Abstract

Electric buses (EBs) have experienced rapid global expansion due to their substantial environmental and economic benefits. However, this transition presents new challenges for bus timetabling and vehicle scheduling, primarily arising from limited battery capacity and frequent charging requirements. This paper presents an integrated optimization framework for demand-driven timetabling and vehicle scheduling in EB transit lines that explicitly considers both passenger flow dynamics and battery constraints. We formulate a comprehensive mixed-integer programming (MIP) model using a space-time network representation to simultaneously optimize departure times, vehicle schedules, and passenger assignments. The objective function minimizes total costs, which encompass vehicle procurement, operational expenses, and passenger waiting times. To enhance computational efficiency, we reformulate the original MIP model into a path-based formulation and employ column generation (CG) techniques to decompose the problem into a restricted master problem (RMP) and pricing subproblems (PSP), which are solved iteratively. To obtain integer solutions, we develop a BP algorithm that integrates the CG procedure within a branch-and-bound framework. Computational experiments on both synthetic scenarios and a real-world case study demonstrate that our integrated approach achieves substantial reductions in overall costs and passenger waiting times compared to conventional two-stage optimization approaches that solve timetabling and vehicle scheduling sequentially.