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The bottleneck

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? 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 hap- pen as the flow rate approaches the capacity of the system?

a) Capacity of the process and bottleneck

The capacity of the process is the maximum number of customers that can be processed per hour. In this case, the capacity of the process is 5 customers/hour, because the stylists are the bottleneck. The stylists can only process 5 customers per hour, because they are the slowest step in the process.

b) Average throughput time

The average throughput time is the total time spent in the system divided by the number of customers processed. In this case, the average throughput time is 29 minutes, because the total time spent in the system is 1+25+3 = 30 minutes and the number of customers processed is 5.

c) What will happen as the flow rate approaches the capacity of the system?

As the flow rate approaches the capacity of the system, the average throughput time will increase. This is because the system will be more likely to be full, which will mean that customers will have to wait longer to be processed. Additionally, the system will be more likely to experience bottlenecks, which will also increase the average throughput time. Here is a table summarizing the results:

Characteristic	Value
Capacity	5 customers/hour
Bottleneck	Stylists
Average throughput time	29 minutes
Average number of customers in the system	2 customers

Additional thoughts The stylists could increase the capacity of the process by working more quickly. However, this may not be feasible, as they may already be working at their maximum capacity. Additionally, increasing the speed of the stylists may lead to a decrease in the quality of the services provided. The Stylish Hair Salon could also increase the capacity of the process by adding more stylists. However, this would be a costly investment, and it is not clear that it would be necessary. The salon could also try to reduce the number of customers in the system by advertising less or by raising prices. However, this may also not be feasible, as the salon may need to attract a certain number of customers in order to be profitable. Ultimately, the Stylish Hair Salon will need to decide how to balance the capacity of the process with the quality of the services provided and the cost of doing business.

Sample Solution

The capacity of the process is the maximum number of customers that can be processed per hour.