Modelling the blood bank inventory: simple formulae for stock management in clinical settings

Blood components are a perishable resource that play a crucial role in clinical medicine. The blood component inventory is managed by transfusion services, who ultimately aim to balance supply with demand so as to ensure availability whilst minimising waste. Whilst the blood component inventory problem has been the focus of theoretical approaches for over 50 years, evidence for the direct utilisation of existing models in the day-to-day management of blood stocks in clinical settings is limited. In this study we formulate a discrete mathematical model that describes the main processes in the management of a single population of red blood cells in a clinical setting: ageing, supply and demand. After time averaging the discrete model, a time-delayed integro-partial differential equation model is derived. Steady state analysis yields expressions for: a range of clinically relevant quantities (i.e. age distributions, total stock levels, wastage rates, age of transfused units); key performance indicators; and simple formulae that identify optimal restock thresholds in terms of parameters that are readily available in clinical settings. The approach is validated by testing predictions using data from a Scottish district general hospital. It is envisaged that the proposed methodology can ultimately be used to aid in situ rule-of-thumb decision making in clinical laboratory settings.