An exact algorithm for the electric-vehicle routing problem with nonlinear charging time

In this paper, we consider the Electric-Vehicle Routing Problem (EVRP) with nonlinear charging time. Due to their limited travel ranges, electric vehicles have to be recharged (possibly multiple times) at specific recharging points, which incurs a routing problem for which the recharging constraint and time have to be addressed. It is well-known that the recharging of the battery of EVs takes considerable time, so it cannot be ignored. Moreover, the recharging time required to travel a given distance is highly nonlinear due to the battery charging mechanism. The goal of this study is to develop an algorithm that minimizes the total travel and charging times without approximation of the charging time function. Our solution approach is based on the segmentation of the vehicle tour. We then construct an extended charging stations network where any path in this network is also a tour in the original network. We develop the branch-and-price method on the extended charging station network to solve the problem to optimality. An extensive computational study on well-known benchmark problems confirms that the proposed approach can solve moderate-sized problems to the optimality.