Research on the combinatorial optimization of EBs departure interval and vehicle configuration based on uncertain bi-level programming

Document Type

Journal Article

Publication Date


Subject Area

mode - bus, infrastructure - vehicle, infrastructure - fleet management, operations - scheduling, operations - coordination, planning - methods, planning - service level


Electric buses, uncertainty theory, bi-level programming, timetable optimizationv, ehicle configuration


Based on uncertainty theory, this paper proposed a vehicle scheduling method considering the dynamic departure interval and vehicle configuration of electric buses (EBs). An uncertain bi-level programming model (UBPM) is established, which takes the total cost of passenger travel (CP) as the upper and total cost of EBs (CB) as the lower. A chance constrained programming model (CCPM) based on the randomness of passenger waiting time and the uncertainty of interstation running time is proposed as the upper model. With a certain confidence level of service level as constraints, the goal is to minimize the total cost of passenger travel. Then, an expected value model (EVM) based on the fluctuation of energy consumption is proposed as the lower model. Taking the number of EBs as the constraint condition, the goal was to minimize the energy consumption of EBs. Finally, a practical bus route is taken as an example to verify the effectiveness of the proposed method. The results demonstrated that the optimal scheduling plan considering the uncertain variables can reduce the passenger travel cost. Collaborative optimization of EBs vehicle configuration can reduce energy consumption, delay, and the number of EBs.


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