This questions seems very straightforward theoretically. If each appointment takes 20 minutes, then one should schedule patients at 8, 8:20 8:40, 9, etc.
The best laid schemes o’ Mice an’ Men,
Gang aft agley,
An’ lea’e us nought but grief an’ pain,
For promis’d joy!
In reality, however, this scheduling plan rarely functions smoothly. One may predict that patients arrive randomly around a mean of the scheduled appointment time. This would imply a Poisson process as long as arrivals occur one at a time, arrival patterns don’t change as the day progresses, and arrivals in disjoint portions of the day must behave in a statistically independent manner. A paper by Fontantesi et al. (2002) finds that this is not the case. Arrivals tend to be clustered. For instance, common bus schedules, traffic light timing, or parking space availability may lead to clumping of arrivals. Further, many people share similar lunch break hours and work schedules making it even more likely that arrivals will be clustered.
Arrival data collected in Fontanesi et al. (2002) show that the mean person is about 3-4 minutes early for an appointment. However, arrival distribution is heavily skewed to the right. While most arrivals fall between either 15 minutes early or 10 minutes late for an appointment, a non-trivial amount of people are extremely late for an appointment (more than 45 minutes).
What solutions do the authors propose?
- Group block scheduling. This would mean, that the office would ask 5 patients to arrive between 9:00 am and 9:20 am. This method allows the office staff more flexibility in terms of treating the first patients who arrive.
- Parallel processing of patients. If office staff are cross-trained, they can spend time on registering patients if there is a rush of patients, and can spend the time doing clerical work if there is some down time.
- Variable-sized blocks of appointment times. For instance, there could be three 10 minute blocks followed by two 15 minute intervals. This method would allow some time for “catching up” if the physician was running behind schedule.
Fontanesi J, Alexopoulos C, Goldsman D, DeGuire M, Kopald D, Holcomb K, Sawyer MH. (2002) “Non-punctual patients: planning for variability in appointment arrival times.” J Med Pract Manage., Jul-Aug;18(1):14-8.