An integer programming model was proposed by Sapountzis (Sapountzis 1984) considered the allocation of blood units from a regional Blood Transfusion Service BTS to the hospitals in that area; the studied case was Glasgow and West of Scotland BTS which serves around 68 hospitals in the West of Scotland. The blood shelf life in Scotland is about 28 days, which means blood units that are not used by that date are said to be expired and shoudl be returned to the Blood bank. However, in Glasgow and West Scotland BTS it is not permitted to receive the expired units from hospitals since it would lower the safety standards. Therefore, to reduce the wastage of the blood without increasing the workload of the BTS, it is important to allocate blood units to the hospitals based on their activity. The BTS transfuse required blood units based on either routine orders or urgent, fresh blood requests (usually for paediatrics or cardiac surgery) to fulfil each hospital's demands, the main objective of this model was to minimise the expected number of expired units at each hospital. By comparing the mathematical programming model with the manual system (that does not take into account the characteristics of each hospital), a reduction percentage of 6.1% and 3.6% respectively for the number of expired units was achieved.