A study on flow decomposition methods for scheduling of electric buses in public transport based on aggregated time–space network models

Over the past few years, many public transport companies have launched pilot projects testing the operation of electric buses. The basic objective of these projects is to substitute diesel buses with electric buses within the companies’ daily operations. Despite an extensive media coverage, the share of electric buses deployed still remains very small in practice. In this context, new challenges arise for a company’s planning process due to the considerably shorter ranges of electric buses compared to traditional combustion engine buses and to the necessity to recharge their batteries at charging stations. Vehicle scheduling, an essential planning task within the planning process, is especially affected by these additional challenges. In this paper, we define the mixed fleet vehicle scheduling problem with electric vehicles. We extend the traditional vehicle scheduling problem by considering a mixed fleet consisting of electric buses with limited driving ranges and rechargeable batteries as well as traditional diesel buses without such range limitations. To solve the problem, we introduce a three-phase solution approach based on an aggregated time–space network consisting of an exact solution method for the vehicle scheduling problem without range limitations, innovative flow decomposition methods, and a novel algorithm for the consideration of charging procedures. Through a computational study using real-world bus timetables, we show that our solution approach meets the requirements of a first application of electric buses in practice. Since the employment of electric buses is mainly influenced by the availability of charging infrastructure, which is determined by the distribution of charging stations within the route network, we particularly focus on the influence of the charging infrastructure.