Carsharing systems have gathered increasing attention and are now recognised as innovative and ecological solutions to transportation issues. Especially, one-way carsharing systems offer a high level of service because they exempt users from the obligation to return the vehicle at the same station where it was borrowed. Unfortunately, this flexibility comes with design complexity. This paper addresses a part of those design issues and deals with fleet dimensioning including vehicle relocation operations. We propose mathematical programming oriented approach and we introduce a simple linear model based on integer flow variables. This model is organized around three optimization criteria: maximizing satisfied carsharing demands while minimizing the fleet of vehicles and the relocation operations. From random generated benchmarks, we study the scalability of our method and we show that computation times remain acceptable for representative problem complexities.