Minimizing Total Cost in Scheduling Outpatient Appointments

This paper considers various rules for scheduling appointments for medical clinic outpatients and investigates their ability to minimize a weighted sum of medical personnel's and patients' idle-time costs. It is shown that the idle times incurred by any given rule are affected by the following three "environmental factors" (in decreasing order of importance): the probability of no-show, the coefficient of variation of service times, and the number of patients per clinical session. Theoretically, an appropriate scheduling rule can be identified only if one knows the values of these parameters and the ratio between the medical personnel's and patients' idle-time costs. Under environments characterized by 27 different combinations of the three environmental factors, the performance of nine scheduling rules are evaluated using simulation. Some of the rules evaluated are original to this study. The results are presented in the form of "efficient frontiers," together with a simple procedure for identifying the best scheduling rule for given environmental-parameter values. This rule-identification procedure is shown to be easily adaptable for circumstances with limited knowledge about the environmental factors; it also reveals that the simple Bailey-Welch individual-appointment rules are surprisingly robust.