Analysis of quota assignment and time block duration in multi-block appointment systems

The objective of this study is to propose performance evaluators and optimizers for the quota appointment system in many hospitals and clinics used to smooth the patient flow. This type of queueing system with finite population and controlled arrivals is studied on a single server with exponential service time. Given a target waiting time set by the hospital, the quota assignment giving the minimum chance of underachievement in each time block is derived using a dynamic programming approach. This enables exact calculations of performance measures of expected waiting time, server overtime and congestion measured in headcount. The optimal time block duration, in addition to the quota assignment, is examined using an extended dynamic programming formulation. Special cases of absentees, late arrivals and re-entry patients are then incorporated into the basic model. Performance measures are evaluated through two approaches, according to the priorities of treatment for the special cases.