Scheduling electric buses in public transport: Modeling of the charging process and analysis of assumptions

The Electric Vehicle Scheduling Problem (E-VSP) complicates traditional bus scheduling for public transport by restricting the range of the buses. To compensate for these limitations, detours to charging stations become necessary in order to charge the vehicle batteries. Charging is a nonlinear process with regard to real conditions, especially when taking partial and opportunity charging into account. However, within most existing solution methods for the E-VSP, the work of charging a vehicle battery is substantially simplified. In most cases, charging is assumed to be performed within linear or even constant time windows. In this paper, we analyze the impact of simplifying assumptions about charging times of electric buses on solutions of the E-VSP. Therefore, we propose charging models reflecting the nonlinear charging process precisely. Furthermore, we enhance an existing solution method for the E-VSP and provide an algorithm for incorporating partial and opportunity charging. Through a comprehensive computational study using real-world bus timetables, we identify major discrepancies between model assumptions and real charging behaviours of electric buses. On the one hand, we show that the assumption of constant charging times generally leads to overestimated time windows for charging, which increases the total costs. On the other hand, we demonstrate that assuming linear charging times underestimates the time windows actually required for charging, widely leading to infeasible vehicle rotations. We investigate this issue by using the technical data of lithium-ion batteries, which are mainly used in practice at present.