Multi-depot electric vehicle scheduling in in-plant production logistics considering non-linear charging models

Abstract

Electric vehicle scheduling is concerned with assigning a fleet of electrically powered vehicles to a set of timetabled trips. Since the range of these vehicles is limited, charging breaks need to be scheduled in-between trips, which require detours and time. This paper presents a novel electric vehicle scheduling problem with multiple charging stations in an in-plant logistics setting with the objective of minimizing the required fleet size. Contrary to previous works, we consider constant, linear and non-linear battery charging functions, which, among other things, allows to model realistic non-linear lithium-ion battery charging. We present an integer programming model and an exact branch-and-check solution procedure, which is based on decomposing the problem into a master and a subproblem. The former is concerned with assigning vehicles to trips while relaxing the battery constraints. The latter schedules charging breaks and checks if the master problem’s solution is feasible with regard to the non-relaxed battery constraints. Our computational tests show that solving the IP model with a standard solver (CPLEX) is inferior to the branch-and-check approach, which generally performs well even for practically relevant instance sizes. Furthermore, we derive some insights into the influence of the charging mode and maximum battery capacity on the required fleet size. Lastly, we investigate the effects of the number of warehouses (with respective charging stations).