Development of a mathematical model based on markov Modeling of blood banks to minimize blood bank costs considering waste and shortage costs

The amount of blood in a blood bank should be determined based on the needs of the hospital, and it is appropriate to meet the demand if the demand suddenly increases in the presence of unexpected events, such as earthquakes, floods, and wars. If there is not enough stock, it must be procured from other sources, which will lead to shortage costs. Additionally, since blood is a perishable substance and has a limited lifetime, if the useful life of blood is over, the remaining blood cannot be used, which leads to waste, and this action is subject to a cost called the cost of waste. Our aim in this article is to investigate and analyze the sensitivity of the parameters involved in blood management so that by developing a mathematical model, we can try to determine the level of blood inventory for a specific blood type such that blood bank costs are optimized according to the existing constraint that total cost is the summation of the costs of shortage and wastage. Modeling of the problem is done using Markov chains, and in this paper, we tried to obtain the optimal inventory level via a numerical approach; sensitivity analysis was subsequently used to evaluate the impact of variations in the parameters, and it was found that among all the parameters, the demand rate and maximum age of usable blood had the greatest impact on the total cost and total blood inventory.