  Traditional car-sharing services are based on the two-way scheme, where the
user picks up and returns the vehicle at the same parking station. Some
services permits also one-way trips, which allows the user to return the
vehicle in another station. The one-way scheme is quite more attractive for the
users, but may pose a problem for the distribution of the vehicles, due to a
possible unbalancing between the user demand and the availability of vehicles
or free slots at the stations. Such a problem is more complicated in the case
of electrical car sharing, where the travel range depends on the level of
charge of the vehicles. The paper presents a new approach for the Electric
Vehicle Relocation Problem, where cars are moved by personnel of the service
operator to keep the system balanced. Such a problem generates a challenging
pickup and delivery problem with new features that to the best of our knowledge
never have been considered in the literature. We yield a Mixed Integer Linear
Programming formulation and some valid inequalities to speed up its solution
through a state-of-the art solver (CPLEX). We test our approach on verisimilar
instances built on the Milan road network.
