Data 604 Homework 9

Kelton et al. (2014). Simio and Simulation: Modeling, Analysis, Applications (3rd Ed.)

Chapter 7: Problem 6

7.6) A small free clinic has a single doctor who sees patients between 8:00 a.m. and noon. She spends 6 to 14 minutes (an average of 10) with each patient and so can theoretically see 6 patients per hour or a total of 24 each day. Staff is currently scheduling patient arrivals every 10 minutes, but have found that patients arrive as much as 15 minutes early or 30 minutes late, thus causing disruption to other patients. Worse, about 10 percent of patients never show up at all causing the doctor’s time to be wasted and wasting an appointment that could have been used by other sick patients. Staff would like to evaluate alternative scheduling strategies such as scheduling 2-3 arrivals every 20 minutes with the main objective of maximizing the doctors utilization (e.g., she would like to really see 24 patients each day if possible). Assume that the doctor will stay until all patients are seen, but she is very unappy if she needs to stay past 12:30. Measure system performance mainly on the number of patients actually seen, but also consider the average patient waiting time, and how late the doctor must typically stay to see all scheduled patients.

Modeling patient arrivals at the clinic

Old appointment schedule: 1 patient scheduled every 10 minutes from 8 a.m. to 12 p.m.

New appointment schedule 1: 2 patients scheduled every 20 minutes from 8 a.m. to 12 p.m.

New appointment schedule 2: 3 patients scheduled every 30 minutes from 8 a.m. to 12 p.m.

New appointment schedule 3: 6 patients scheduled every hour from 8 a.m. to 12 p.m.

Comparison of average number of patients seen, average patient wait time in minutes, and time last patient departed clinic across appointment schedules

Given the variability between patients’ scheduled and actual arrival times - modeled here as a triangular distribution with miminum -15, mode 0, and maximum 30 minutes relative to the scheduled appointment - and likelihood of not appearing at all (10%), it appears that scheduling 3 patients per half-hour time slot over the course of the clinic’s operating hours offers the best trade-off between average wait time among patients before seeing the doctor and the time of the last seen patient’s exit from the clinic. Average number of patients seen each day remained fairly constant across each of the schedules included in the 100 replication experiment.