Dynamic Routing for the Electric Vehicle Shortest Path Problem with Charging Station Occupancy Information

Abstract: We study EVs traveling from origin to destination in the shortest time, focusing on long-distance settings with energy requirements exceeding EV autonomy. The EV may charge its battery at public Charging Stations (CSs), which are subject to uncertain waiting times. We model CSs using appropriately defined queues, whose status is revealed upon the EV arrival. However, we consider the availability of real-time binary Occupancy Indicator (OI) information, signaling if a CS is busy or not. At each OI update, we determine the sequence of CSs to visit along with associated charging quantities. We name the resulting problem the Electric Vehicle Shortest Path Problem with charging station Occupancy Indicator information (EVSPP-OI). In this problem, we consider that the EV is allowed to partially charge its battery, and we model charging times via piecewise linear charging functions that depend on the CS technology. We propose an MDP formulation for the EVSPP-OI and develop a reoptimization algorithm that establishes the sequence of CS visits and charging amounts based on system updates. Specifically, we propose a simulation-based approach to estimate the waiting time of the EV at a CS as a function of its arrival time. As the path to a CS may consist of multiple intermediate CS stops, estimating the arrival times at each CS is fairly intricate. To this end, we propose an efficient heuristic that yields approximate lower bounds on the arrival time of the EV at each CS. We use these estimations to define a deterministic EVSPP, which we solve with an existing algorithm. We conduct a comprehensive computational study and compare the performance of our methodology with a benchmark that observes the status of CSs only upon arrival. Results show that our method reduces waiting times and total trip duration by an average of 23.7%-95.4% and 1.4%-18.5%, respectively.