Determining the optimal number of beds in the subacute section of a large hospital

Austin Health (AH) currently operates inpatient Continuing Care services across two satellite campuses, and faces the problem of calculating the optimal number of beds needed in its subacute wards. It is inefficient if a patient needs to wait in an acute ward for a bed in a subacute ward, just as is operating too many beds in the subacute ward to always meet demand. In recent years the demand for acute beds has increased, creating pressure for faster patient movements and more admissions at times of high demand, with the consequent need to determine best-performing bed configurations. Additional constraints, related mostly to availability of medical resources, were of concern to AH staff and were considered when developing the model. The subacute bed allocation problem is significant because it cannot be formulated in closed form using simple probability distributions, but demands the use of actual variable data on admissions and separations to ensure a reliable result. The solution approach we used to tackle the problem is based on the combined use of the cross-entropy method for optimisation. It uses the simulation of subacute ward occupation and demand using a parametric bootstrap to generate data to solve this problem. We used a simulation model to represent the six wards under study and the dynamic relationships that describe this system. To obtain the optimal bed configurations, we use the cross-entropy method for optimisation. This is a modern optimisation method whose working principle is based on the fact that cross-entropy divergence can be used as a measure of closeness between two sampling distributions. Optimisation by cross-entropy estimates a sequence of parametric sampling distributions that converges to a distribution with probability mass concentrated in a region of near-optimal solutions. We used a parametric bootstrapping approach to generate the admission data that is used as an input to the optimiser. The expected result is a slight increase in the number of existing beds. We justify the effectiveness of the proposed approach for determining the optimal number of beds on the grounds that the actual results and the general behaviour of the optimisation software in its current version match the intuition of hospital staff on the behaviour of the system.