Theoretical bounds and approximation of the probability mass function of future hospital bed demand

Failing to match the supply of resources to the demand for resources in a hospital can cause non-clinical transfers, diversions, safety risks, and expensive under-utilized resource capacity. Forecasting bed demand helps achieve appropriate safety standards and cost management by proactively adjusting staffing levels and patient flow protocols. This paper defines the theoretical bounds on optimal bed demand prediction accuracy and develops a flexible statistical model to approximate the probability mass function of future bed demand. A case study validates the model using blinded data from a mid-sized Massachusetts community hospital. This approach expands upon similar work by forecasting multiple days in advance instead of a single day, providing a probability mass function of demand instead of a point estimate, using the exact surgery schedule instead of assuming a cyclic schedule, and using patient-level duration-varying length-of-stay distributions instead of assuming patient homogeneity and exponential length of stay distributions. The primary results of this work are an accurate and lengthy forecast, which provides managers better information and more time to optimize short-term staffing adaptations to stochastic bed demand, and a derivation of the minimum mean absolute error of an ideal forecast.