On the Multi-Depot Electric Bus Vehicle Scheduling Problem with Time Windows: An Exact Continuous-Time Formulation

Abstract

The electrification of bus fleets is a systemic transition that goes beyond the acquisition of vehicles and charging infrastructure, requiring new operational practices and planning approaches for effective implementation. At the tactical level planning, vehicle scheduling must at least consider depot, charging, and time-window constraints, as well as electric-vehicle-specific characteristics such as battery capacity, energy consumption, and charging power rates. This study extends the Electric Bus Multi-Depot Vehicle Scheduling Problem with Time Windows (EB-MD-VSP-TW) by introducing continuous-time modeling at charging stations, aiming to improve the fidelity of charging operations in the calculated solutions. The proposed model is evaluated using both synthetic instances and real-world bus lines from Athens, Greece. Given the continuous-time EB-MD-VSPTW formulation, a heuristic solution approach is also proposed to produce feasible schedules for a set of four operational bus lines.