Electric bus fleet composition and scheduling

The low energy density of batteries and the long recharging times constitute a significant barrier for electrification of public transportation (PT) systems since electric buses (EB) require too heavy and expensive batteries to achieve the operational availability of their combustion engine counterparts. New recharging technologies such as fast chargers and dynamic wireless power transfer (DWPT) emerge as promising solutions to overcome these challenges. Optimizing the bus fleet composition and the schedules is essential to take advantage of these emerging technologies and achieve electrification of PT in a cost-efficient way. To address this challenge, this paper proposes an integer (binary) programming formulation to find the optimal electric bus fleet composition and scheduling that minimizes the total procurement cost of the buses and the operating cost of the schedules. A column generation (CG) approach is devised to obtain provably high-quality solutions, for large problem instances. The success of the approach is due to a novel dynamic programming algorithm we develop to solve the generalized resource-constrained shortest path problem that needs to be solved in each CG iteration to find out new schedules to include in the model. Extensive computational studies on large real-world PT networks attest to the efficacy of the suggested methodology and reveal valuable managerial insights from a system-wide perspective