Uphill struggles, downhill gains: How road gradients and load dynamics influence electric vehicle routing decisions?

In this study, we investigate the Electric Vehicle Routing Problem with Time Windows incorporating partial recharges, factoring in energy consumption associated with road gradients, cargo weight, and the benefits of regenerative braking. Traversing arcs with positive road gradients demands more energy compared to flat networks. When an electric vehicle (EV) traverses uphill, energy consumption increases significantly, especially if it carries heavy loads, and can result in infeasible routes due to battery limitations. Conversely, as the EV travels downhill, gravity assists the vehicle’s movement, allowing for gentler accelerator use or braking to maintain constant speed. Hence, energy can be recovered due to regenerative braking technology, resulting in energy savings and improved efficiency. We propose four different mathematical models and compare their performances. To assess the impact of road gradients, we generate a new dataset based on benchmark instances by assigning altitudes to each node in the network, employing clustering techniques to ensure consistency by adjusting node elevations relative to their cluster centers. We consider three terrain types characterized by progressively steeper average absolute road gradients. The results demonstrate that accounting for road gradients, cargo load, and regenerative braking significantly impacts routing decisions and can render the problem infeasible in networks with steep roads. While road gradients generally increase energy consumption, our findings indicate that in some instances, regenerative braking can improve the solution. This study underscores the importance of considering multiple factors affecting energy consumption to develop more effective transportation strategies for EVs.