Optimization of electric bus scheduling considering stochastic volatilities in trip travel time and energy consumption

This paper develops a vehicle scheduling method for the electric bus (EB) route considering stochastic volatilities in trip travel time and energy consumption. First, a model for estimating the trip energy consumption is proposed based on field-collected data, and the probability distribution function of trip energy consumption considering the stochastic volatility is determined. Second, we propose the charging strategy to recharge buses during their idle times. The impacts of stochastic volatilities on the departure time, the idle time, the battery state of charge, and the energy consumption of each trip are analyzed. Third, an optimization model is built with the objectives of minimizing the expectation of delays in trip departure times, the summation of energy consumption expectations, and bus procurement costs. Finally, a real bus route is taken as an example to validate the proposed method. Results show that reasonable idle times can be generated by optimizing the scheduling plan, and it is helpful to stop the accumulation of stochastic volatilities. Collaboratively optimizing vehicle scheduling and charging plans can reduce the EB fleet and delay times while meeting the route operation needs.