Scheduling admissions and reducing variability in bed demand

Variability in admissions and lengths of stay inherently leads to variability in bed occupancy. The aim of this paper is to analyse the impact of these sources of variability on the required amount of capacity and to determine admission quota for scheduled admissions to regulate the occupancy pattern. For the impact of variability on the required number of beds, we use a heavy-traffic limit theorem for the G/G/a queue yielding an intuitively appealing approximation in case the arrival process is not Poisson. Also, given a structural weekly admission pattern, we apply a time-dependent analysis to determine the mean offered load per day. This time-dependent analysis is combined with a Quadratic Programming model to determine the optimal number of elective admissions per day, such that an average desired daily occupancy is achieved. From the mathematical results, practical scenarios and guidelines are derived that can be used by hospital managers and support the method of quota scheduling. In practice, the results can be implemented by providing admission quota prescribing the target number of admissions for each patient group.