A spa is structured as a two-stage process. Upon arrival, customers wait in a co

Question

A spa is structured as a two-stage process. Upon arrival, customers wait in a common area an average of 6 minutes before proceeding to the _rst available manicurist. There is a total of six manicurists. The average time for a manicure is 16 minutes regardless of the manicurist providing it. Customers then proceed to pay, but they typically must wait in line an average of 2 minutes before they are able to do so since there is only one cashier who takes on average 4 minutes to process each payment.

(a) What is the cycle time of the two-stage process?

(b) What is the capacity of the two-stage process?

Explanation / Answer

Consider the following notation:

(a) The cycle time of the two-stage process:

= Waiting time in common area/person + Average time with manicure/person + Waiting time in line before payment/ person + Average time with cashier/person

= 6 + 16 + 2 + 4 minutes

= 28 minutes

Answer: Cycle time of the two-stage process = 28 minutes

(b) The capacity of the two-stage process:

Capacity of the two-stage process

= Maximum (Capacity of manicurist at manicure stage expressed in minutes/ customer, Capacity of processing payment at cashier stage expressed in minutes/ customer)

Capacity of manicurist (6 in numbers) = 16 minutes for 6 customers = 2.67 minutes / customer

Capacity of cashier = 4 minutes / customer

Therefore,

Capacity at two-stage process = Maximum (2.67 minutes/ customer, 4 minutes/ customer) = 4 minutes/customer

Therefore , the capacity of the system is = 60 / 4 = 15 customers/ hour

Answer: The capacity of the two-stage process is 15 customers/hour

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