A matheuristic for the electric vehicle routing problem with time windows and a realistic energy consumption model

The main goal of this paper is to time-effectively route and schedule a fleet of Electric Vehicles (EVs) on a road network in order to serve a set of customers. In particular, we aim to propose an optimized route planning by exploiting the advantages of these vehicles. Nowadays, in fact, electromobility plays a key role for reducing the harmful emissions due, instead, to the use of traditional vehicles. The starting point of this research is represented by the fact that the advanced recent technologies for the EVs allow also partially recharging their batteries. In this work, an Electric Vehicle Routing Problem with Time Windows (E-VRPTW) is addressed from a time effective point of view under the assumption that partial recharges are also allowed. For this purpose, the E-VRPTW is mathematically formulated as a Mixed Integer Linear Program in which both the total number of EVs used and the total time spent by them outside the depot are minimized. Due to the NP-hardness of the problem, a Variable Neighborhood Search Branching (VNSB) matheuristic is also designed for determining good quality solutions in reasonable computational times. Numerical results carried out on some benchmark instances taken from the literature provide useful insights regarding both the solution quality of the proposed formulation, compared to a previous one, and the performances of the VNSB.