Consider a barber shop with 4 barber chairs. The owner is trying to decide how many barbers to hire. It takes on average 18 minutes to cut each customers hair and clean the workstation. A customer arrives on average once every 8 minutes with a standard deviation of 30 minutes.
a) What is the coefficient of variation of the inter-arrival times?
b) Assuming the availability of the barbers is 0.8 and the effective coefficient of variation of the barbers is 1, what is the effective service rate given there are 3 barbers?
c) If there are 3 barbers what is the utilization and how many customers will be in the barber shop on average?
d) Assuming the availability of the barbers is 0.8 and the effective coefficient of variability of the barbers is 1, what is the effective service rate given there are 4 barbers?
If there are 4 barbers what is the utilization and how many customers will be in the barber shop on average?
e) If there are 20 seats in the waiting room what do you recommend for the total number of barbers?
f) After the hair cut the cashier must check them out. What is the coefficient of variation of the arrivals to the cashier given the system determined in part f?
g) If the average number of arrivals remained the same but the standard deviation decreased to 8 minutes for the inter-arrival times, what would be the difference in customers in the barber shop for both 3 and 4 barbers? Would this change your answer for part f?