Recent Modeling and Analytical Advances in Hospital Inpatient Flow Management

Inpatient flow management plays a critical role in care delivery, patient outcomes, and hospital operational and financial costs. Modeling and performance analysis of inpatient flow present unique features and challenges that differ from operations in other service industries. In this study, we review recent modeling and analytical advances in the setting of inpatient flow management, with a particular focus on service time models motivated from the observations of inpatient discharges. We first compare two new service time models developed to capture the time‐of‐day inpatient flow dynamics, and reveal interesting connections between the two models. We then review analytical methods developed to analyze systems with the new service time models. Based on one method, which is amenable to a one‐dimensional exact analysis under certain conditions, we further introduce its approximations that have explicit analytical forms and enable efficient computations in large systems. In particular, we showcase how to leverage a powerful tool, Stein’s method framework, in the hospital setting for steady‐state approximations and characterizing error bounds. We conclude this study by a literature review on other important aspects in inpatient flow management and propose future research directions, from both the modeling and analytical perspectives.