Electric Vehicle Location Routing Problem with Vehicle Motion Dynamics-Based Energy Consumption and Recovery

In this article we deal with the main critical issues of using electric vehicles in urban transport given the battery related limitations on driving range, and the network layout related limitations on the number of recharging stations. In this context, we seek the optimal routing plans together with the optimal locations of recharging stations for electric vehicle fleets through the Electric Vehicle Location Routing Problem with Intermediate Nodes (ELRP-IN) we propose. The ELRP-IN we formulate as a mathematical program considers the actual characteristics of battery discharging and recovering the braking energy. Energy consumption and recovery are determined through vehicle motion dynamics in conjunction with the 3-dimensional feature of the road geometry, passengers'/customers' demands on getting on and off, and the pre-defined speed profiles, where the graph corresponding to the road network is extended with the explicit consideration of intersections. By alternating the objectives adopted in the ELRP-IN formulation, we discuss through a number of numerical experiments involving real case instances the effects of both the objective functions and the parameters, including the consumption and the gain of energy, cost, traveled distance, and travel time, on the routing plans. Highlighting the finding that energy is not recovered in all the sections with descending grade, we reveal the direct effect of the elevation on the energy consumption, and hence on the location of a recharging station, where we discuss as well the limitation on energy recovery.