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:
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?
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.
a. To smooth out the demand for the week, we can calculate the maximum number of appointments to be scheduled by dividing the total number of expected walk-ins for the week by the number of working days in the week.
Let's assume the expected number of walk-ins per day are as follows:
Monday: 30
Tuesday: 20
Wednesday: 25
Thursday: 35
Friday: 40
Total expected walk-ins for the week = 30 + 20 + 25 + 35 + 40 = 150
Assuming there are 5 working days in a week, the maximum number of appointments that should be scheduled for each day would be:
150/5 = 30
Therefore, the maximum number of appointments that should be scheduled for each day is 30.
b. Scheduling appointments at their maximum level is not recommended because it does not account for variability in patient arrivals. It is likely that the number of actual walk-ins will not match the expected values every day. If there are fewer walk-ins than expected, the physicians may be left with excess capacity and idle time, resulting in wasted resources. On the other hand, if there are more walk-ins than expected, the physicians may be overwhelmed, causing longer wait times, decreased quality of care, and dissatisfaction among patients and staff.
c. If most walk-ins arrive in the morning, appointments should be made in a way that allows for smooth patient flow and avoids excessive waiting. One approach would be to schedule more appointments in the morning when the walk-ins are higher and gradually decrease the number of appointments in the afternoon. This can be achieved by adjusting the scheduling algorithm to allocate more appointments earlier in the day and fewer appointments later in the day. By doing so, patients can be seen more promptly, reducing waiting times, and efficiently utilizing the physicians' time and resources.
a. To smooth out the demand for the week, we need to calculate the maximum number of walk-ins in a day and then schedule appointments accordingly.
To find the maximum number of walk-ins, we can look at the expected number of walk-ins by day of the week and select the highest value. Let's assume the table below represents the expected number of walk-ins per day:
Day of the Week | Expected Number of Walk-ins
------------------------------------------
Monday | 10
Tuesday | 8
Wednesday | 15
Thursday | 12
Friday | 5
Saturday | 3
Sunday | 2
From the table, we can see that the maximum number of walk-ins occurs on Wednesday with 15 patients. Therefore, to smooth out the demand, we should schedule a maximum of 15 appointments on any given day.
b. Scheduling appointments at their maximum level may not be recommended for several reasons:
1. It leaves no room for unexpected walk-ins or emergencies - If all the appointments are booked, there won't be any space available for urgent cases that require immediate attention. This can lead to delays in treatment or turn away patients seeking urgent care.
2. It can lead to long waiting times - If all the appointments are fully booked, patients may have to wait longer to see a physician. This can result in dissatisfaction and a poor patient experience.
3. It limits flexibility - Having some buffer appointments allows for flexibility in accommodating unexpected or urgent cases without disrupting the entire schedule.
c. To avoid excessive waiting, the appointments should be made at a time when the majority of walk-ins are likely to arrive in the morning. Since the question mentions that most walk-ins arrive in the morning, it would be ideal to schedule the appointments in the afternoon.
By scheduling appointments in the afternoon, the clinic can prioritize and allocate their resources efficiently. The staff can focus on attending to walk-ins in the morning, ensuring shorter waiting times and better patient flow. Patients with appointments can then be seen in the less crowded afternoon slots, minimizing waiting times for both walk-ins and appointments.