Modelling Health Emergency: An Efficient Approach in Operating via Simulations

Abstract

This thesis aimed to develop a mathematical model to minimise patient wait times and stay length in the Australian Nepean Hospital's emergency department (ED). The model used integer programming to analyse patient movements and identify bottlenecks. The thesis also adopted a discrete event simulation (DES) generic model for ED patient flow to investigate weekday and weekend patients’ arrival and waiting times and staff utilisation rates, identify resource management problems, and test multiple possible scenarios solutions. The model was based on Nepean hospital’ ED data from the Nepean Blue Mountains Local Health District and analysed during the COVID-19 pandemic. We used Arena software to develop the model, identifying areas where patients may experience long wait times and supporting decision-making to improve ED efficiency. The study aimed to improve patient experience and efficiency.

The research reveals that priority queuing theory is crucial for understanding the ED system, with the DES model being more appropriate. The Acute care zone has the longest wait time and highest nurse utilisation, with physician utilisation consistently exceeding 95%. The COVID-19 pandemic has not significantly impacted patient arrivals, but staff reallocation is necessary for efficiency and patient health. The thesis proposes three efficient scenarios based on ED preferences and limits: moving one physician to a new peak hour shift, hiring an extra physician, or rostering a nurse from the Subacute care zone to the morning shift. These results help decision-makers optimise service delivery, reduce wait times, and improve staff utilisation.