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In dynamic ride-sharing systems, intelligent repositioning of idle vehicles enables service providers to maximize vehicle utilization and minimize request rejection rates as well as customer waiting times. In current practice, this task is often performed decentrally by individual drivers. We present a centralized approach to idle vehicle repositioning in the form of a forecast-driven repositioning algorithm. The core part of our approach is a novel mixed-integer programming model that aims to maximize coverage of forecasted demand while minimizing travel times for repositioning movements. This model is embedded into a planning service also encompassing other relevant tasks such as vehicle dispatching. We evaluate our approach through extensive simulation studies on real-world datasets from Hamburg, New York City, and Manhattan. We test our forecast-driven repositioning approach under a perfect demand forecast as well as a naive forecast and compare it to a reactive strategy. The results show that our algorithm is suitable for real-time usage even in large-scale scenarios. Compared to the reactive algorithm, rejection rates of trip requests are decreased by an average of 2.5 percentage points and customer waiting times see an average reduction of 13.2%.