Carsharing is today considered as an ecological and innovative solution to improve urban mobility. The one-way version, where vehicles can be drop-off in any station, brings however some challenging open questions. The system has to be design as part of the global transportation one and vehicle relocation operations must be included to get the higher level of service. In this paper, we consider a one-way carsharing system where stations and their location are fixed. The optimization problem consists in maximizing the total number of satisfied demands for a limited number of vehicles and relocation operations. We propose a formal definition and a mathematical model using Integer Linear Programming (ILP). We show that the problem size is strongly related to the number of possible relocation operations and a polynomial subcase is exhibited. Numerical results highlight that vehicle relocations can be drastically reduced without deteriorating the quality of solutions. Our method can thus be easily used in system management to evaluate possible implementation of vehicle relocation strategies.