Overnight charging scheduling of battery electric buses with uncertain charging time

With the rapid development of battery electric buses (BEBs) in urban public traffic, it arises the problem of BEB charging scheduling, which aims to supply electric power for all the BEBs to meet the bus timetable in the smallest cost. Practical experience reports that both weather temperature and accumulative battery using time have a non-negligible impact on battery charging efficiency, and bring about the uncertainty of charging time of a battery. It may cause a negative influence to the departure schedule of the BEBs. Motivated by the above observation, this work investigates a BEB charging scheduling problem with uncertain charging time. The objective is to minimize the expected total charging cost, which consists of in-service cost, energy consumption cost and penalty cost due to over-low charging. We first prove the strong NP-hardness of the considered problem. A stochastic linear programming model is then established. A scenario-reduction based enhanced sample average approximation approach and an improved genetic algorithm are proposed to solve large-scale instances of the considered problem. Numerical experiments and comparisons with adapted previous algorithms are conducted to demonstrate the effectiveness of the proposed approaches.