Complexity Analysis of Optimal Recharge Scheduling for Electric Vehicles

Abstract : The massive introduction of Electric Vehicles (EVs) will make fleet managers spend a significant amount of money to buy electric energy. If energy price changes over time, accurate scheduling of recharging times may result in significant savings. In this paper we evaluate the complexity of the optimal scheduling problem 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 sub-optimal scheduling heuristic that schedules the EVs’ recharge based on historical travelling data. We compare the performance of the optimal and sub-optimal 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.