The success of a free-floating car-sharing service depends on a good allocation of the vehicles across the city, i.e. where and when they are needed by citizens. This requires predicting the demand across the geographical regions and across time, which is challenging due to the sparsity and variability of the data. Furthermore, the purpose of these predictions is to help computing the best possible car positions for the next day, hence the need to model both the prediction task and the optimisation task in a compatible way. As the allocation optimisation involves reasoning about the number of cars to assign to geographical regions, we propose to predict the expected utilisation of a car when added to a region. We discuss the challenges in modeling both the machine learning and the relocation problem, and we propose a integer linear programming method that solves the relocation problem while taking into account the model predictions and relocation distances. We experiment with the datasets from a citywide car sharing company and show how our method can increase the allocation strategies and hence profitability of the service.