On the role of time-of-use electricity price in charge scheduling for electric bus fleets

As electric buses become increasingly popular, it is imperative to optimize the schedules of electric buses with explicit consideration of their charging requirements. Unfortunately, existing studies failed to properly model the impacts of essential operating factors, including the time-of-use (TOU) electricity price, partial charging, and limited chargers. Our paper proposes a mixed-integer nonlinear program to minimize the total operating cost of an electric bus fleet for fulfilling a group of timetabled trips, considering the above realistic features simultaneously. To effectively solve the problem of global optimality, we convert this model to an equivalent set partitioning model and develop a specialized branch-and-price approach subsequently. Our approach's computational efficiency is verified via extensive numerical experiments. The model is applied to a real-world case study in Nanjing, China. Results show that incorporating the TOU electricity price into the electric bus scheduling problem can produce a sizeable cost saving of up to 22%. Managerial insights unveiled by the numerical results are discussed. These insights inform the practitioners of how the operations of electric buses can be both cost-effective and grid-friendly.