An outpatient clinic has kept a record of walk-in patients during the past year. The table below shows the expected number of walk-ins by day of the week:

Question

The clinic has a staff of five physicians, and each can examine 15 patients a day on average.
a. What is the maximum number of appointments that should be scheduled for
each day if it is desirable to smooth out the demand for the week?
b. Why would you recommend against scheduling appointments at their maxi¬
mum level?
c. If most walk-ins arrive in the morning, when should the appointments be made
to avoid excessive waiting?

Answer 1

a. To smooth out the demand for the week, we can first calculate the total number of walk-ins in a week and the total capacity of the clinic:

Monday: 100
Tuesday: 75
Wednesday: 80
Thursday: 90
Friday: 110
Total walk-ins per week: 455

Total capacity of the clinic per day: 5 physicians * 15 patients = 75 patients
Total capacity of the clinic per week: 75 patients * 5 days = 375 patients

Since we want to smooth out the demand, we divide the total walk-ins by the total capacity of the clinic per week to find the proportion of appointments to walk-ins:

Proportion of appointments to walk-ins: 375 / 455 = 0.824

Now, we multiply the expected number of walk-ins for each day by this proportion to find the maximum number of appointments that should be scheduled for each day:

Monday: 100 * 0.824 = 82 appointments
Tuesday: 75 * 0.824 = 62 appointments
Wednesday: 80 * 0.824 = 66 appointments
Thursday: 90 * 0.824 = 74 appointments
Friday: 110 * 0.824 = 91 appointments

b. Scheduling appointments at their maximum level could lead to increased patient waiting times and reduced flexibility in accommodating walk-ins, as the clinic would be operating at its full capacity. Additionally, patients may not show up to their scheduled appointments or extra walk-ins may arrive, which could cause difficulty in managing the flow of patients. A balance should be struck between accommodating appointments and ensuring sufficient availability for walk-ins.

c. To avoid excessive waiting for walk-ins, appointments should mainly be scheduled for the afternoons. This allows the mornings to be focused on providing services for the walk-in patients and ensures that the clinic is less congested during peak arrival times. Scheduling appointments in the afternoons also provides a better-managed flow of patients and helps to spread out the workload for the physicians throughout the day.