The vehicle relocation problem for the one-way electric vehicle sharing: an application to the Milan case

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 allow also one-way trips, where the user can return the vehicle in another station. The one-way scheme is 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 electric car sharing, where the travel range depends on the level of charge of the vehicles. In a previous work, we introduced a new approach to relocate the vehicles where cars are moved by personnel of the service operator to keep the system balanced. Such relocation method generates a new challenging pickup and delivery problem that we call the Electric Vehicle Relocation Problem (EVRP). In this work we focus on a method to forecast the unbalancing of a car-sharing system. We apply such method to the data yielded by the Milan transport agency taking into account the location and capacity of the present charging stations in Milan. In this way, using a Mixed Integer Linear Programming formulation of EVRP, we can estimate the advantages of our relocation approach on verisimilar instances