A stochastic programming approach to perform hospital capacity assessments

This article introduces a bespoke risk averse stochastic programming approach for performing a strategic level assessment of hospital capacity (QAHC). We include stochastic treatment durations and length of stay in the analysis for the first time. To the best of our knowledge this is a new capability, not yet provided in the literature. Our stochastic programming approach identifies the maximum caseload that can be treated over a specified duration of time subject to a specified risk threshold in relation to temporary exceedances of capacity. Sample averaging techniques are applied to handle probabilistic constraints, but due to the size and complexity of the resultant mixed integer programming model, a novel two-stage hierarchical solution approach is needed. Our two-stage hierarchical solution approach is novel as it combines the application of a meta-heuristic with a binary search. It is also computationally fast. A case study of a large public hospital has been considered and extensive numerical tests have been undertaken to highlight the nuances and intricacies of the analysis. We conclude that the proposed approach is effective and can provide extra clarity and insights around hospital outputs. It provides a way to better calibrate hospitals and other health care infrastructure to future demands and challenges, like those created by the COVID pandemic.