Platelet products are vital in the blood transfusion system since they are used for treating serious diseases such as cancer. They are expensive products (C$504 per unit) with a short shelf life of five to seven days. Since platelet demand is uncertain and highly variable, platelet inventory management is a challenging task. In this work, we propose a data-driven inventory management model for platelet products that incorporates demand forecasts in the inventory management process. The proposed model uses forecast-dependent target inventory levels to determine an ordering policy that has a goal of minimizing both the shortage and wastage. The data used in this study is a large clinical dataset of daily platelet transfusions for a centralized blood distribution centre for four hospitals in Hamilton, Ontario, spanning from 2016 to 2018. Experimental results show that our proposed policy performs well in minimizing shortages and wastages and that larger forecast errors can be tolerated as the system scales (for example as a result of demand aggregation and inventory pooling). We also perform sensitivity analysis to provide a more in-depth study of the proposed model. In particular, we suggest that by incorporating demand forecasts in the inventory management model, ordering less frequently than daily is feasible.