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Planning a trip with an electric vehicle requires consideration of both battery dynamics and the availability of charging infrastructure. Recharging costs for an electric vehicle, which increase as the battery's charge level increases, are fundamentally different than refueling costs for conventional vehicles, which do not depend on the amount of fuel already in the tank. Furthermore, the viability of any route requiring recharging is sensitive to the availability of charging stations along the way. In this paper, we study the problem of finding an optimal adaptive routing and recharging policy for an electric vehicle in a network. Each node in the network represents a charging station and has an associated probability of being available at any point in time or occupied by another vehicle. We develop efficient algorithms for finding an optimal a priori routing and recharging policy and then present solution approaches to an adaptive problem that build on a priori policy. We present two heuristic methods for finding adaptive policies-one with adaptive recharging decisions only and another with both adaptive routing and recharging decisions. We then further enhance our solution approaches to a special case of grid network. We conduct numerical experiments to demonstrate the empirical performance of our solutions.

Recharging decisions for electric vehicles require many special considerations due to battery dynamics. Battery longevity is prolonged by recharging less frequently and at slower rates, and also by not charging the battery too close to its maximum capacity. In this paper, we address the problem of finding an optimal recharging policy for an electric vehicle along a given path. The path consists of a sequence of nodes, each representing a charging station, and the driver must decide where to stop and how much to recharge at each stop. We present efficient algorithms for finding an optimal policy in general instances with deterministic travel costs and homogeneous charging stations, and also for two specialized cases. In addition, we develop two heuristic procedures that we characterize analytically and explore empirically. We further analyze and test our solution methods on model variations that include stochastic travel costs and nonhomogeneous charging stations.