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

The objective of this study is to propose performance evaluatorsand optimizers for the quota appointment system in many hospitalsand clinics used to smooth the patient flow. This type of queueingsystem with finite population and controlled arrivals is studiedon a single server with exponential service time. Given a targetwaiting time set by the hospital, the quota assignment givingthe minimum chance of underachievement in each time block isderived using a dynamic programming approach. This enables exactcalculations of performance measures of expected waiting time,server overtime and congestion measured in headcount. The optimaltime block duration, in addition to the quota assignment, isexamined using an extended dynamic programming formulation.Special cases of absentees, late arrivals and re-entry patientsare then incorporated into the basic model. Performance measuresare evaluated through two approaches, according to the prioritiesof treatment for the special cases.