Complexity Analysis of Optimal Recharge Scheduling for Electric Vehicles

The massive introduction of electric vehicles (EVs) will make fleet managers spend a significant amount of money buying electric energy. If the energy price changes over time, an accurate scheduling of recharging times may result in significant savings. In this paper, we evaluate the complexity of the optimal scheduling problem (SP) considering a scenario with a fleet manager having full knowledge of the customers' traveling needs at the beginning of the scheduling horizon. We prove that the problem has polynomial complexity and provide complexity lower and upper bounds. Moreover, we propose an online suboptimal scheduling heuristic that schedules the EVs' recharge based on historical traveling data. We compare the performance of the optimal and suboptimal methods to a benchmark online approach that does not rely on any prior knowledge of the customers' requests, in order to evaluate whether the additional complexity required by the proposed strategies is worth the achieved economic advantages. Numerical results show up to of 35% cost savings with respect to the benchmark approach.