What can we learn from supermarkets? An application of the Poisson distribution (order-up-to) model to improve blood culture bottle supplies

Abstract

The order-up-to inventory model is a method for identifying and maintaining the optimal product level for items that that hold value over time and have recurring demand. Typically, supermarkets utilise it to manage stock-levels of non-perishable goods. This project aimed to improve blood culture bottle supplies following reports by junior doctors of shortages when dealing with septic/unwell patients. Data regarding blood culture bottle use was acquired from four hospitals within one trust in London (245 wards). The mathematical 'order-up-to' inventory model (an iterative Poisson distribution) was applied to the 6 months' data. The model found three predictable levels of demand to stock wards with no shortages in 99.3% of circumstances (based on historical data). Wards were stocked with blood culture bottles as per their required demand. A collection method and infrastructure was designed to implement the new policy and was applied to a London tertiary centre. A review of doctors, nurses and ward-managers found significant improvements in supply with no shortages since the model was applied. Issues with the dataset were identified for intensive therapy unit / high dependency unit. The 'order-up-to' inventory model provides a useful tool within hospitals for improving stock levels of blood cultures bottles and with that the satisfaction of trainees and patient safety.