Question

Find a Doctor, is a small startup that helps people find a physician that best meets their needs (location, insurance accepted, etc.) During a "slow" time for them, they have 7 staff members taking calls from customers. On average, one call arrives every 13 minutes. On average, each staff member spends 23 minutes with each customer.

What is the utilization rate (in percentages) of the staff members?

Answer 1

The utilization rate for the staff members at the startup Find a Doctor is approximately 47.62%. This is calculated based on the provided average call arrival rate and the average time each staff member spends on a call.

Step-by-step explanation:

The student asked how to calculate the utilization rate for staff members at a startup called Find a Doctor. Utilization rate is a measure of the efficiency with which employees are being used to handle workload. To calculate the rate, use the formula: Utilization rate = (Total Time Spent on Calls / Total Available Time) x 100%. Given that a call arrives every 13 minutes and each staff member spends 23 minutes on a call, we can calculate the arrival rate (lambda λ) as 1/13 calls per minute and the service rate (mu μ) as 1/23 calls per minute.

Since there are 7 staff working, the total available time per minute is 7 staff x 1/23 calls per staff member per minute. The utilization rate (ρ) is thus λ / (7 x μ), which can be simplified to (1/13) / (7/23), resulting in approximately 0.4762 or 47.62% utilization. This means that the staff are busy with calls 47.62% of the time on average.