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Running a cost-effective human blood transfusion supply chain challenges decision makers in blood services world-wide. In this paper, we develop a Markov decision process with the objective of minimising the overall costs of internal and external collections, storing, producing and disposing of blood bags, whilst explicitly considering the probability that a donated blog bag will perish before demanded. The model finds an optimal policy to collect additional bags based on the number of bags in stock rather than using information about the age of the oldest item. Using data from the literature, we validate our model and carry out a case study based on data from a large blood supplier in South America. The study helped achieve an overall increase of 4.5% in blood donations in one year. [ABSTRACT FROM AUTHOR]