Electric vehicle charge scheduling with flexible service operations

Patrick Sean Klein, Maximilian Schiffer

Driven by climate change, rising environmental awareness, and financial incentives, more and more commercial fleets transition to electric vehicles. However, this endeavor remains challenging as time-inefficient charge operations and lack of public charging infrastructure require fleet operators to invest into additional private on-premise charging stations. Here, grid capacity constraints and investment cost limit the number of available charging stations such that charging bottlenecks may arise. Accordingly, efficient scheduling of charge and service operations becomes inevitable to realize profitable fleets. Creating the underlying schedules constitutes a challenging optimization problem, especially when additional factors, such as battery degradation, variable energy prices, and non-linear battery behavior need to be considered. In this paper, we study the resulting joint charge and service operations scheduling problem, that combines the scheduling of vehicle service operations and charge scheduling. We propose an exact algorithm based on branch & price to solve this problem. This algorithm bases on an exact labeling algorithm developed for a novel resource constrained shortest path problem, which models our pricing problem, and leverages a custom branching rule and a primal heuristic to accelerate the branch & bound phase. We benchmark our algorithm in a comprehensive numerical study and show that it can solve realistic problem instances with computational times below one hour, thus enabling its application in practice. Additionally, we analyze the benefit of jointly scheduling charging and service operations in practice. We find that our integrated approach lowers the amount of charging infrastructure required for fleet operation by up to 57% besides enabling cost savings of up to 5%.

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