Bed Allocation in a Public Health Care Delivery System

Due to changing patient loads and demand patterns over time, assigning bed complements for various medical services in a hospital is a recurring problem facing the administrators. For a large public health care delivery system, we present an approach for periodically reallocating beds to services to minimize the expected overflows. Using a queueing model to approximate the patient population dynamics for each service---with admission rates provided by forecasts---the expected overflows under each configuration are computed via a Normal loss integral. Bed allocation is done in two stages. First, we establish a base line requirement for each service so that it can handle a prescribed amount of patient load based on a yearly projection of demand. We then use marginal analysis to distribute the remaining beds to minimize the expected total average overflows while taking month-to-month demand fluctuations into account. The proposed model requires only a modest amount of computation, because of several simplifying assumptions, which were tested for reasonableness. For the two largest services, we used empirical data to evaluate the nonhomogeneous Poisson representation of admissions, and we performed simulation experiments to assess the extent of discrepancy in performance characteristics caused by the ignorance of day-of-week effect on admission rates. In view of the intrinsic complexity of the underlying system, the results obtained from the validation studies suggest that the model is relatively "robust" with respect to the case under consideration. It is hoped that the simplicity of the model and the usefulness of the results will induce practitioners to use this type of formal analysis for bed allocation in an institutional setting on a routine basis.