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In spite of significant advancements in medicine, there is still a shortage of human blood in the world. At present, there is no alternative chemical process or product that can produce blood, and only humans are capable of doing so. It is for this reason that blood is such an important component of our healthcare system. Due to the perishability of blood, managing blood inventories can be challenging. The challenge is to maintain a high level of supply while minimizing loss due to expiration. The purpose of this study is to present a mathematical model that reduces inventory costs, determines the optimal ordering policy in hospitals, and prevents the loss of blood units. To determine the optimal inventory level and order volume, a mixed integer programming model is presented in both deterministic and non-deterministic conditions. In order to address the uncertainty in the problem, a robust optimization approach is used. This model minimizes the transfer of blood groups and transmission between hospitals by considering compatibility and priority. A sensitivity analysis has also been conducted on the model. Based on a case study, it is demonstrated that the costs of buying, storing, ordering, and wasting two important RBCs and platelets can be reduced., (Copyright © 2022 Elsevier Ltd. All rights reserved.)