Hospital Inpatient Operations : Mathematical Models and Managerial Insights

One key factor contributing to the emergency department (ED) overcrowding is prolonged waiting time for admission to inpatient wards, also known as ED boarding time. To gain insights into the inpatient flow management to reduce this waiting time, we study the operations in the inpatient department of a Singaporean hospital. We focus on understanding the effect of an early discharge policy, implemented in late 2009, on the fraction of patients who have to wait in ED for six hours or longer to be admitted. Based on a comprehensive empirical analysis of the inpatient department [40], we propose a novel stochastic network model with the following characteristics to model the inpatient operations: (1) A patient’s service time is endogenous, depending on her admission and discharge times, and her length of stay. As a consequence, the service times are not independent, identically distributed. (2) Preand post-allocation delays for each patient’s bed-request, even if a bed is available at the time of request, allow modeling secondary bottlenecks such as temporary nurse shortage. (3) Patients waiting for a bed can be overflowed to a non-primary ward when the overflow trigger time reaches a certain threshold, where the threshold is time-dependent. We show, via simulation studies, that our model is able to approximately replicate the hourly performances (e.g., waiting time) of the inpatient operations at this hospital. The model allows one to evaluate the impact of operational policies on waiting times and overflow proportions. In particular, our model predicts that implementing a hypothetical Period 3 policy can eliminate the excessive waiting for those patients who request beds in mornings. The policy constitutes the following components: a discharge distribution with the first discharge peak between 8 and 9am and 26% of patients discharge before noon, and stable-mean allocation delays throughout the day. Although Period 3 policy is not completely practical, it can serve as a goal for hospital managers to aim at.