Joint robust optimization of bed capacity, nurse staffing, and care access under uncertainty

Effective and efficient care of hospital patients relies on well-coordinated resource allocation. Determining the number of beds and nurses in clinical units depends, among other considerations, on admission volumes, lengths of stay, and staffing availability, all of which are stochastic in practice. Given these uncertainties, this paper develops two robust optimization models to help plan the most effective bed and nurse resource allocation in terms of costs and access in a single clinical unit while allowing resources to be shared between units for flexibility. Ellipsoidal, budgeted, and data-driven formulations are compared for “conservatism," a measure of costs incurred to achieve robustness. In addition to existing formulations we develop uncertainty sets based on least-squares ellipsoidal fitting, which produces better solutions in our application. A case study involving different patient types and care levels reduces the number of patients that cannot be admitted (non-admissions) by up to 85% for the budgeted model and up to 100% for the data-driven model, with resource sharing reducing costs by 1% and 2%, respectively, compared to the non-sharing models. While the least-squares ellipsoidal model increases costs from the current scenario by 2% to achieve robustness, the budgeted and data-driven counterparts increase costs by 54% and 57%, respectively. These results have important implications for how uncertainty sets are formed when applying robust optimization to healthcare problems.