We study spare parts inventory control for an aircraft component repair shop. Inspection of a defective component reveals which spare parts are needed to repair it, and in what quantity. Spare part shortages delay repairs, while aircraft operators demand short component repair times. Current spare parts inventory optimization methods cannot guarantee the performance on the component level, which is desired by the operators. To address this shortfall, our model incorporates operator requirements as time-window fill rate requirements for the repair turnaround times for each component type. In alignment with typical repair shop policies, spare parts are allocated on a first come first served basis to repairs, and their inventory is controlled using (s, S) policies. Our solution approach applies column generation in an integer programming formulation. A novel method is developed to solve the related pricing problem. Paired with efficient rounding procedures, the approach solves real-life instances of the problem, consisting of thousands of spare parts and components, in minutes. A case study at a repair shop reveals how data may be obtained in order to implement the approach as an automated method for decision support. We show that the implementation ensures that inventory decisions are aligned with performance targets.