Modeling multi-stage healthcare systems with service interactions under blocking for bed allocation

Balancing bed allocation is a critical but cumbersome decision-making process in hospitals due to limited capacity, fluctuations in the rate of patient arrival and service interactions among various units; typically, this will cause blockages in multi-stage healthcare services. Accurately estimating the blocking probability is an important task in order to improve the performance of healthcare systems. Early studies assumed either unlimited bed capacity or no service interaction among units. In this study, we consider the correlation between the blockage and service time of the subsequent stage and apply a multi-stage tandem-queuing model with limited bed capacity and service interactions to model healthcare systems. We develop two effective heuristics to estimate the patient-blocking probability, which are then used to develop an integrated mathematical model for bed allocation. We collect real-world data from a tertiary hospital in China to delineate the effect of service interactions while estimating the blocking probability and use non-parametric rank-sum tests to verify and compare the relative performances of the proposed model against two popular heuristics. Our comparative results illustrate that the proposed model is as accurate as simulations. We also observe that increasing the number of beds during the first stage is more effective in reducing blockage than doing so later in case of a limited number of beds.