Model and Solution Methods for the Mixed-Fleet Multi-Terminal Bus Scheduling Problem

Public transport services are currently executing or planning a fundamental transition from traditional buses to electric buses. During this transition phase, the public transport offering is fulfilled with a mixed fleet across multiple bus terminals, which poses operational challenges for optimal vehicle scheduling, a problem not yet addressed in literature. As researchers in Transport Engineering and Operational Research at the University of Luxembourg, in collaboration with the Roma Tre University, we support the Ministry of Transport of Luxembourg and Volvo buses by modelling and simulating this transition phase, to help them managing and solving such challenges. In this work we develop a mixed-integer linear programming (MILP) formulation of the problem and implement a time-based decomposition framework, through which we can optimize real-life daily instances. This method is tested on the main urban bus lines that connect Central Station, Luxembourg Airport and ten other major terminals within Luxembourg City, providing (near) optimal solutions that explicitly consider the energy constraints arising from electric bus operations, while establishing an advantageous trade-off between delaying trips, to implement quick-charging of electric buses, and performing the same trip with costlier traditional buses. The results show a consistent decrease of operational costs as the percentage of e-buses in the fleet increases.