Energy-aware Vehicle Routing in Networks with Charging Nodes

We study the problem of routing vehicles with energy constraints through a network where there are at least some charging nodes. We seek to minimize the total elapsed time for vehicles to reach their destinations by determining routes as well as recharging amounts when the vehicles do not have adequate energy for the entire journey. For a single vehicle, we formulate a mixed-integer nonlinear programming (MINLP) problem and derive properties of the optimal solution allowing it to be decomposed into two simpler problems. For a multi-vehicle problem, where traffic congestion effects are included, we use a similar approach by grouping vehicles into subflows. We also provide an alternative flow optimization formulation leading to a computationally simpler problem solution with minimal loss in accuracy. Numerical results are included to illustrate these approaches.