Hospitals use appointment systems to manage patient access. Appointment rule, which consists of the length of the booking window, block capacity, and block service time, is critical to achieve efficiency and timely access to healthcare delivery. In this paper, we use a renewal process model to evaluate interday appointment planning and design improved appointment rules for hospitals, especially for those with limited or insufficient resources. We present an associated embedded Markov chain to derive the steady-state distribution. To balance the waiting time and probability of healthcare access, we propose three performance measures, namely, slot utilization, appointment success rate, and patient waiting time, for our evaluation. We then conduct a numerical study to examine the impact of each appointment rule parameter. Qualitative results show that extending the booking window does not significantly reduce system congestion, and a narrowed appointment block is a suitable design for highly in-demand doctors. We use our model and method to design an optimal appointment rule for an actual hospital in Beijing, China. The improved appointment rule is practical and useful for the decision-making of hospital managers.
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