Coordinated Scheduling of Electric Buses for Multiple Routes Considering Stochastic Travel Times

Bus terminals function as both the origins of multiple routes and charging places for electric buses (EBs) in large cities. Coordinated scheduling of routes starting from the same terminal can avoid the simultaneous charging demands of EBs, reducing queuing times for charging. The synchronous degradation in the state of health of EB batteries can also be realized with the coordinated scheduling, so as to lighten the burden of public transit corporations caused by frequent battery retirements. This study proposes a multiroute coordinated scheduling method where an electric bus is not fixed to serve on a certain route but runs different routes based on requirements. Utilizing chance constraint programming, an optimization model was formulated considering the stochastic volatility in trip travel times and time-of-use tariff, addressing objectives to minimize the average queuing time for EB charging, the difference in operating intensities, and the charging cost. The Big M method was applied to convert the chance constraint programming model to a deterministic model, which is specifically a 0-1 integer programming model, and then solved by employing the branch-and-price method. Numerical tests were carried out using data from three real EB routes. Results indicate that the proposed scheduling method can reduce the average queuing time for charging, the daily charging cost, and the difference in operating intensities while maintaining the synchronous degradation of all EB batteries.