Question

3. The Stylish Hair Salon has three stylists who provide services to women. After checking in with the receptionist, which takes an average of 1 minute, the customer’s hair is washed, dried, and styled, taking an average of 25 minutes. The payment takes 3 minutes and is also performed by the receptionist.
a. What is the capacity of the process, and what is the bottleneck?
b. What is the average throughput time, and if the average flow rate is five customers per hour, what is the average number of customers in the system?
c. If the input to the system is random, what will happen as the flow rate approaches the capacity of the system?

please explain all numbers and provide details

Schroeder, Roger; Rungtusanatham, M. Johnny; Goldstein, Susan. Operations Management in the Supply Chain, 6th edition (McGraw-Hill/Irwin Series in Operations and Decision Sciences) (Page 131). McGraw-Hill Higher Education -A. Kindle Edition.

Answer 1

a. The receptionist takes 4 minutes per customer. Hence the capacity of the receptionist or the number of customers which he can serve per hour is 60/4 = 15 customers per hour.

Each stylist takes 25 minutes to serve the customer. Hence each stylist can serve 60/25 = 2.4 customers per hour. As there are 3 stylists the total capacity of the stylists is 3*2.4 = 7.2 customers per hour

We can see that the stylists have the lower capacity then receptionists and hence they are the bottleneck. The capacity of the process is 7.2 customers per hour.

b. The average throughput time is sum of all process times = 1+25+3 = 29 minutes

Average number of customers can be calculated by the Little's Law which states that I = R*T where I is inventory or the number of customers, R is the flow rate and T is throughput time. It is given that the flow rate is 5 and throughput is 29 minutes or 29/60 hours. Hence the number of customers is as below

Number of customers in the system = 29/60*5 = 2.42 customers

c. If the input to the system is random and flow rate approaches the capacity of the system, the number of customers waiting will keep on increasing. As the flow rate increases and approaches the capacity, the system would be less and less capable to serve the newly arriving customers as there would be customers already being served. Hence the newly arriving customers would have to wait and the number of customers waiting would increase as the flow rate approaches capacity.