Battery electric bus infrastructure planning under demand uncertainty

The electrification of city bus systems is an increasing trend, with many cities replacing their diesel buses with battery electric buses (BEBs). Due to limited battery capacities, and to random battery discharge rates-which are affected by weather, road and traffic conditions-BEBs often need daytime charging to support their operation for a whole day. The deployment of charging infrastructures, as well as the number of stand-by buses available, has a significant effect on the operational efficiency of electric bus systems. In this work, a stochastic integer program has been developed to jointly optimise charging station locations and bus fleet size under random bus charging demand, considering time-of-use electricity tariffs. The stochastic program is first approximated by its sample average and is solved by a customised Lagrangian relaxation approach. The applicability of the model and solution algorithm is demonstrated by applications to a series of hypothetical grid networks and to a real-world Melbourne City bus network. Managerial insights are also presented.