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摘要
Guided by low-carbon development policies, many provinces and municipalities across the country have begun to popularize electric buses. However, the characteristics of the technical performance and operating environment of electric buses, such as their range, charging time constraints, and random road network environment, create new challenges for electric bus vehicle scheduling and charging plans. Stochastic travel times lead to delays in the connection of trips, and because of the interdependence of successive trips, delays in the upstream trips may cause delays in the downstream trips. This leads to the knock-on effect of delay propagation, making the risk tolerance of the trips and charging schedules very vulnerable and preventing the effectiveness of bus scheduling. In this study, we consider the effect of delay propagation in the electric bus scheduling problem, analyze the effect of stochastic travel times on bus trips and charging schedules, and develop optimization models from single-line to regional scheduling modes to obtain an economical and reliable bus scheduling solution. First, the network flow model was used to describe the electric bus scheduling process, and a Markov process was introduced to portray the delay propagation effect. On this basis, service quality indicators, such as expected waiting time and expected delay time, were calculated and added to the objective function, thereby developing a mixed-integer linear programming model. Then, a multi-commodity flow model was applied to extend the single-line scheduling model into a generic regional scheduling model, and a 'delay state layer' was designed to calculate the delay time distribution and save computational expenses. Finally, a case study was conducted with actual data from two electric bus lines in Guangzhou, and the commercial solver Gurobi was used to obtain the exact solution. The results show that the optimal time window interval for the charging schedule is 40 min. Under the optimal scheme, the vehicles can make full use of the idle time in daytime operation for charging, and this characteristic is not affected by the duration of the time window interval. As the delay penalty factor increases, the average value of the expected delay time first decreases and then keeps fluctuating, and when the delay penalty coefficient ≥ 2 CNY·min-2, the average value of the expected delay time is less than 15 s. Thus, this model can effectively reduce the delay. Under this condition, the average value of the expected waiting time increases and then fluctuates, which indicates that the model can intelligently adjust the order of connection between trips by increasing the waiting time as buffer time, so as to reduce the occurrence of delay. ? 2023 Xi'an Highway University.
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