A hybrid analytical model for an entire hospital resource optimisation.

Given the escalating healthcare costs around the world (more than 10% of the world's GDP) and increasing demand hospitals are under constant scrutiny in terms of managing services with limited resources and tighter budgets. Hospitals endeavour to find sustainable solutions for a variety of challenges ranging from productivity enhancements to resource allocation. For instance, in the UK, evidence suggests that hospitals are struggling due to increased delayed transfers of care, bed-occupancy rates well above the recommended levels of 85% and unmet A&E performance targets. In this paper, we present a hybrid forecasting-simulation-optimisation model for an NHS Foundation Trust in the UK. Using the Hospital Episode Statistics dataset for A&E, outpatient and inpatient services, we estimate the future patient demands for each speciality and model how it behaves with the forecasted activity in the future. Discrete event simulation is used to capture the entire hospital within a simulation environment, where the outputs is used as inputs into a multi-period integer linear programming (MILP) model to predict three vital resource requirements (on a monthly basis over a 1-year period), namely beds, physicians and nurses. We further carry out a sensitivity analysis to establish the robustness of solutions to changes in parameters, such as nurse-to-bed ratio. This type of modelling framework is developed for the first time to better plan the needs of hospitals now and into the future.