In this research, among the levels of the blood supply chain, hospital is chosen for study because of its importance. A model of inventory management of hospital blood bank is presented. In this case, we consider some assumptions which are more realistic. These assumptions include two types of emergency and ordinary demands, young blood demand, and finally, a cross-match process. In the existing articles, although blood groups considered in mathematical models, the priority of allocation of blood groups is not considered in these articles. In this study, three mathematical models are developed with deterministic parameters. In the first model, the assumption of ordinary and emergency demand,...