Inventory control of blood and its products is the most important challenge in efficiently managing a blood supply chain as blood products are perishable. In addition, the replenishment of blood, which donors supply, and the demand of patients for blood products are uncertain. In particular, platelets with the shortest lifespan, up to five days, are the most expensive blood products. Therefore, this study investigates the problem of platelet inventory control in a hospital network using integer programming. Due to the uncertainty of the demand of patients in hospitals, a scenario-based robust optimization approach is applied to minimize the worst-case performance of the system. The proposed model is coded and solved using GAMS software. The results demonstrate that using a robust optimization approach reduces hospital costs by 7.6% on average compared to a solution that ignores uncertainty. Moreover, the efficiency of hospitals' inventory control depends on the capacity of the Blood Transfusion Organization to deliver fresh platelets.