New Formulations for the Electric Vehicle Routing Problem with Nonlinear Charging Functions

Electric vehicle routing problems (E-VRPs) are receiving growing attention from the operations research community. Electric vehicles (EVs) differ substantially from internal combustion engine vehicles. In the routing context, the main difference is due to the limited EV autonomy, which can be recuperated at charging stations. These are rather scarce, thus EVs typically have to perform detours to reach them. Various assumptions on the charging policy and objective function{, among others}, have led to the definition of several variants E-VRPs. Modeling the charging functions is a focal point of the majority of these problems. The majority of the research has focused on constant or linear charging function. To account for the nonlinear relation between the times spent charging and the amount of energy charged, the electric vehicle routing problem with nonlinear charging function has been recently introduced. In this research we propose new formulations for this problem. We present an arc-based tracking of the time and the state of charge which, according to our experiments, outperform the classical node-based tracking of these values. We also propose alternative formulations of the piecewise linear approximation of the nonlinear charging function. To prevent the use of charging stations nodes replication, we propose a recharging path-based model. We present a labeling algorithm to generate a tractable number of these paths. This latter model overcomes the limits of the classical models presented in the literature and also outperforms them in our experiments.