If clerk cost is $30 per hour and customer waiting time represents a cost of $20 per hour,how many clerks can be justified on a cost basis?
A)2.
B)3.
C)4.
D)5.
E)6.
Customers filter into a record shop at an average of 1 per minute (exponential interarrivals)where the service rate is 15 per hour (exponential service times).

Question

Quizplus · Accepted Answer

To find the number of clerks that can be justified on a cost basis, we need to calculate the total cost per hour for different numbers of clerks until the cost starts increasing. Let's assume "n" number of clerks are working in the shop.

Total cost per hour = (n * $30) + ($20 / 60 * Average waiting time per customer * Total number of customers served per hour)

Using Little's Law, we can calculate the total number of customers served per hour as Average number of customers in the system / Average time a customer spends in the system.

Let's assume that the shop has infinite capacity to accommodate customers, which means the waiting time is only due to the number of clerks present.

For n = 1,
Total cost per hour = ($30) + ($20 / 60 * 1 / 15 * 60) = $32
For n = 2,
Total cost per hour = ($60) + ($20 / 60 * 2 / 15 * 60) = $52
For n = 3,
Total cost per hour = ($90) + ($20 / 60 * 3 / 15 * 60) = $70
For n = 4,
Total cost per hour = ($120) + ($20 / 60 * 4 / 15 * 60) = $80
For n = 5,
Total cost per hour = ($150) + ($20 / 60 * 5 / 15 * 60) = $87
For n = 6,
Total cost per hour = ($180) + ($20 / 60 * 6 / 15 * 60) = $92

Thus, the cost starts increasing after 4 clerks. Therefore, having 4 clerks is the most cost-effective option.

If Clerk Cost Is $30 Per Hour and Customer Waiting