Relocation in Carsharing Systems Using Flows in Time-Expanded Networks

Abstract

In a carsharing system, a fleet of cars is distributed at stations in an urban area, customers can take and return cars at any time and station. For operating such a system in a satisfactory way, the stations have to keep a good ratio between the total number of places and cars in each station, in order to refuse as few customer requests as possible. This leads to the problem of relocating cars between stations, which can be modeled by means of coupled flows of cars in convoys in a time-expanded network. We present an integer programming formulation for a max-profit flow problem to balance the profit of accepted customer requests against the cost for relocation. This enables us to compute optimal offline solutions only since the computation times are too high for the online situation. We, therefore, devise a heuristic approach based on the flow formulation and show experimentally that it computes reasonable solutions in short time, so that it suits for the online situation.