ReOpt: an Algorithm with a Quality Guaranty for Solving the Static Relocation Problem

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 numbers of free places and cars in each station. This leads to the problem of relocating cars between stations, which can be modeled within the framework of a metric task system. In this paper, we focus on the Static Relocation Problem, where the system has to be set into a certain state, outgoing from the current state. We present a combinatorial approach and provide approximation factors for several different situations.