Scheduling electric vehicles

Abstract

The vehicle scheduling problem (VSP) is a traditional problem in public transport. One of the main assumptions is that buses can be operated the whole day without any interruption for refueling etc. Recently, new technological innovations have led to the introduction of electric vehicles (EVs). For these new vehicles, we cannot ignore the need of refueling during the day, as the range of an electric bus is severely limited, because of the capacity of the batteries. In this paper, we study the electric VSP (e-VSP), where we use EVs with a limited range. During the day the batteries can be charged; in this paper we assume that a battery cannot be replaced/substituted. We present two models that differ in the level of detail resembling the actual processes. In our first model, we assume a linear charging process, work with a constant price of electricity during the day, and do not take the effect of the depth-of-discharge on the lifetime of the battery into account. Our second model resembles practice much better: we allow any type of charging process, work with the actual electricity prices, and take the depreciation cost of the battery into account. To keep this model tractable, however, we approximate the exact value of the charge by discretizing it. The refined model can be solved to optimality using integer linear programming for instances of small/medium size, and therefore, we describe two other solution methods based on column generation 123Public Transp (2017) 9:155-176 DOI 10.1007/s12469-017-0164-0 that find good, but not necessarily optimal, solutions for large instances. We have tested our algorithms on real-world instances.

Collaborative Optimization of Vehicle and Charging Scheduling for a Bus Fleet Mixed With Electric and Traditional Buses

“…Reference [18] presented a mixed integer programming formulation and a large neighborhood search heuristic for the E-VSP to minimize the number of needed vehicles and the total deadheading distance. Reference [19] presented an integer linear programming, and developed a column generation for the E-VSP. Reference [20] solved the E-VSP by integrating an incremental mixed integer programming algorithm, a greedy algorithm and a Tabu search-based local search algorithm.…”

“…Constraints (10) and (18) guarantee that the vehicle departed from the depot will eventually return to the depot. Constraints (11) and (19) indicate the numbers of eBus and fuel buses that perform tasks during the day, respectively. Constraints (12) and (20) indicate that the number of vehicles that performing the trips is equal to the number of vehicles that housed in the depot.…”

Comparison of management strategies for the charging schedule and all-electric operation of a plug-in hybrid-electric bi-articulated bus fleet

“…However, only a few studies focused on the charging schedule of buses. For example, while van Kooten Niekerk et al (2017) analysed the bus fleet management for only one bus depot, other studies also included the operation on bus routes, such as Qin et al (2016) who simulated fast charging strategies to reduce the charge demand of electric buses. Wang et al (2017) focused, among other aspects, on the optimisation of the charging schedule for electric buses with the objective to minimise the annual total operating costs of the charging system.…”

Integrated Vehicle Scheduling and Vehicle Assignment

“…A time-space network-based model that allows the charging of the vehicles is given in Reuer et al [23]. In [25], multiple models are presented for the E-VSP that consider battery charge. The solution is once again obtained using a column generation approach.…”