Optimal admission and queuing control with reneging behavior under premature discharge decisions

Abstract

AbstractQueues or waiting lines are a common phenomenon in healthcare facilities. The increasing number of admissions to hospital emergency departments (EDs) has resulted in overcrowded EDs and decreased quality of care. Patients may renege with dissatisfaction while waiting, prolonged hospital stays, or the cancelation of surgeries, especially for those with acute diseases. This paper studies patient admission and queuing control policies, considering premature discharge decisions and reneging behavior. First, we formulate this problem as an infinite‐horizon total discounted cost Markov decision process to balance bed utility and experiences of patients waiting for admission to minimize the total expected cost for the hospital. Then, we characterize an optimal admission threshold policy by analyzing the structural properties of the optimal value function. Numerical experiments are employed to discuss how the optimal dynamic policy depends on some key parameters of the system. Finally, the performance of the optimal policy is discussed through comparison with the benchmark: A myopic rule (first come, first served) mimicking the decision‐making in practice under different scenarios. The numerical results show that the reneging behavior can affect the superiority of the optimal policy compared to the benchmark, and the optimal policy can significantly reduce the number of waiting patients without increasing the total expected cost when the system is overloaded.