Optimal dispatching of electric and hybrid buses subject to scheduling and charging constraints

We consider the problem of optimally determining the sequence of electric and hybrid buses departing from a multi-line bus terminal, considering both service constraints (schedule adherence) and energy constraints (electric bus charging status, bus recharging scheduling in capacitated facilities). The problem is formulated as a Mixed Integer Linear Program, with the objective of minimizing the total operational cost for the bus lines in question. System dynamics are captured by practical sets of constraints, ranging from scheduling adherence to discharge-recharge dynamics. Individual operational costs at the bus level and at the trip level are fully parametrized, allowing for extensive sensitivity analysis. We investigate a real-life case study based on the city of Luxembourg, where two charging stations have been installed in the central station's bus terminal. Experimental results show that, while full electrification is indeed possible, the required fleet size depends strongly on the given line(s) timetable.