Integrated electric bus timetabling and scheduling problem

• Published in: Transportation research. Part C, Emerging technologies Vol. 149; p. 104057
• Main Authors: Xu, Xiaoming, Yu, Yanhong, Long, Jiancheng
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.04.2023
• Subjects: Lagrangian relaxation heuristic; Time-space network; Timetabling; Vehicle scheduling; Time-space network; Timetabling; Vehicle scheduling; Lagrangian relaxation heuristic
• DOI: 10.1016/j.trc.2023.104057
• ISSN: 0968-090X

Vehicle timetabling and scheduling in a public transit system are usually performed separately, with the output of timetabling serving as the input of scheduling. An obvious drawback of this sequential planning method is that the trade-off between bus timetables and vehicle schedules may be neglected when determining solutions, which in turn results in that the obtained solutions may be inferior to those produced using an integrated framework. For example, a well-planned timetable may result in a schedule that requires a large vehicle fleet size with more operational cost, while a well-planned schedule may reduce the quality of a bus timetable by limiting the use of vehicles. In this paper, we introduce a time-space network-based framework for integrating electric bus timetabling and scheduling, with minimum and maximum headway times, depot requirements, deadheading and vehicle battery capacities considerations. The underlying time-space network is constructed with well-designed inventory arcs that represent multiple operations a bus may execute, thus decreasing the network size. Using the constructed network, we formulate the considered problem with a multi-commodity network flow model and develop a Lagrangian relaxation heuristic that consists of three phases, including generating relaxed solutions, making relaxed solutions feasible, and improving feasible solutions, to solve the integrated model. Tests on a set of instances confirm that the proposed integrated solution method can efficiently produce bus timetables and schedules with valid bounds, indicate that the integrated method can produce better solutions where the profit is increased by 5.29%–20.28%, and show how the headway times, service trip profit and operating cost settings affect the solution. •An integrated electric bus timetabling and scheduling problem is presented.•Minimum and maximum headway times, battery capacities, etc, are considered.•A multi-commodity network flow model for the integrated problem is presented.•A Lagrangian relaxation heuristic is developed based on a time-space network.•Tests on bus lines show the advantages of the integrated optimization method.