1. Introduction
The blood supply chain is considered of a vital priority, and its study has occupied a large portion of operation research. Studies fro this supply chain provided analytical and simulation models. Since this problem comprises multiple process and products, on different decision-making levels, a few studies focused on addressing the supply chain as a whole while the majority focused on certain aspects of it. Those aspects include, but not limited to, the development of approximate ordering and issuing policies for inventory systems, distribution scheduling, and the analysis of multi-product system. They targeted those models to be implanted as decision rules within an individual hospital blood bank, or on a larger scale as a decision support system for hierarchical planning in a regional blood centre. Blood as a product has a limited shelf life of around 35 days; we can recognise four main blood groups which are determined by the presence or absence of two antigens A- and B- on the red blood surfaces, but the presence of a protein called the Rh factor that gives a total of eight major blood types (O +, O-, A+, A-, B+, B-, AB+, and AB-).
In blood transfusion systems, it is vital that patients are assigned to the correct blood types, since not all blood types are compatible with each other and mixing incompatible blood types can lead to agglutination. Collected blood units can be further broken down into separate products of blood: red cells, white cells, plasma and platelets. They have different usage in the medical treatment of patients and serve different functions in the human body. Blood shelf life considered to be of a critical factor in blood assignment- transfusion system; since blood units that are not used within their life span considered to be as wastage units ‘expired’. The complicated nature of this supply chain calls for a thorough review to previous works and necessitate a breakdown for its different stages within the following section.