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In a carsharing system, a fleet of cars is distributed at stations in anurban area, customers can take and return cars at any time and station. Foroperating such a system in a satisfactory way, the stations have to keep a goodratio between the numbers of free places and cars in each station. This leadsto the problem of relocating cars between stations, which can be modeled withinthe framework of a metric task system. In this paper, we focus on the StaticRelocation Problem, where the system has to be set into a certain state,outgoing from the current state. We present a combinatorial approach andprovide approximation factors for several different situations.

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