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This paper presents a mixed-integer mathematical program with embedded equations developed from concepts of queueing theory and Jackson networks for estimating the steady-state maximum potential hospital capacity for COVID-19 patient care in extreme surge conditions, where a hospital must turn nearly all of its existing resources toward the care of pandemic patients. Estimating the potential maximum hospital capacity for pandemic patient care can aid in assessing regional healthcare capacity during surges in pandemic patient demand, predicting shortfalls, and designing preparedness and response actions. To obtain such estimates and inform action, the program determines a best assignment of a heterogeneous staff of nurses and doctors to key units appropriate for their skills to create the optimal allocation of staffed beds. An alternative trial-and-error approach is offered that decision-makers without optimization or software expertise can use to obtain similar estimates. Under a given assignment of resources, a variety of key performance indicators can be obtained through the direct use of the queueing equations. Results of comparisons to outcomes from a detailed discrete event simulation model of an identical hospital design show the accuracy of the equations to be high despite the added simplifications needed for the use of a closed-form equation-based methodology.

Maximizing hospital capacity to serve pandemic patient surge in hot spots via queueing theory and microsimulation