Utes Barber Shops (Q1 - Q6)

Newt Utes needs to decide where to get a haircut. He has narrowed the choice down to two local hair salons - Large Hair Salon (LHS) and Small Hair Cutters (SHC).

During busy periods, a new customer walks into LHS every 15 minutes on average, with a standard deviation of 15 minutes. At SHC, a customer walks in every hour on average, with a standard deviation of 1 hour. LHS has a staff of 4 barbers, while SHC has 1 barber. The average service time at both salons is 30 minutes, with a standard deviation of 30 minutes.



Q1. If Newt walks into LHS during a busy period, how long must he wait in line (in minutes) before he receives a haircut? (Only include the waiting time, not any service time)

Q2. What is the total average flow time (in minutes) of LHS, which includes both the waiting time and the time in service?

Q3. How many customers, on average will be in LHS, including both customers waiting in line and customers being served?

Q4. What is the average number of customers in service (excluding those that are waiting in line) in LHS?

Q5. If Newt goes to SHC, how long (in minutes) must he wait in line before his haircut starts?

Q6. LHS will buy out SHC. LHS will then close SHC's operations and serve all customers, including existing SHC customers, at the LHS location only. Assuming that the previous traffic of SHC customers now flows to the LHS location, what is the new inter-arrival time (in minutes) at LHS?

Max Stamp (Q7)

Q7. Max Stamp approves study abroad documents for the University of Utah. Students must wait in line with their forms outside Max's office. One student at a time is allowed in his office and Max takes precisely 25 minutes to evaluate each student's set of documents. On average 2.2 students per hour go to his office and they spend on average 160 minutes trying to get their forms approved (time waiting in queue plus time in Max's office having him evaluate their documents). On average, how many students are waiting outside of Max's office? (Hint: You do not need to know CVa and CVp to solve this question but if you want, you can assume that CVa=1 and the standard deviation of the processing time is zero.)

Hospital Trauma Bays (Q8 - Q12)

The local hospital's emergency department has 6 trauma bays. On average, patients requiring a trauma bay arrive every 30 minutes (with a coefficient of variation of 1). If the hospital has an available trauma bay, it is immediately allocated to a needy patient. If there are no trauma bays available, the patient is sent to another hospital. On average, a patient's length of stay in a trauma bay is 1.5 hours (with a standard deviation of 1.5 hours). The hospital's emergency department operates 24 hours a day.



Q8. What percentage of the patients requiring trauma bays end up being sent to another hospital? (Write your answer in %, that is, if your answer is 22.6%, write 22.6 as you answer.)

Q9. How many patients are treated in the trauma bays of this hospital on an average 24 hour day?

Q10. When a patient is sent to another hospital, the hospital has to put a staff with adequate skills to guarantee the patient's life, which costs the hospital $200 per patient sent. What is the average daily cost (in $) for the hospital from patients that are being sent to other hospitals?

Q11. New state regulations require that every emergency department be able to accommodate at least 97% of all patients needing a trauma bay without any waiting. What is the minimum number of trauma bays necessary to meet this requirement? (Assume that the time spent in the trauma bay cannot be changed)

Doc On Call (Q12 - Q14)

A company has started a phone service that uses overseas doctors to provide emergency medical consultations. The responding doctors are based in a country with low wages but with a highly skilled pool of physicians. Responding to each call takes on average 15 minutes. At any given moment in time, there are 4 doctors overseas on duty. Calls arrive every 5 minutes on average and standard deviation of the inter-arrival time is 5 minutes. The company receives $50 from the patient's insurance company for each consultation. If one of the 4 overseas doctors is available, the firm pays $20 to the doctor and makes $30 in profit. If no doctor is available overseas, the call is rerouted to the U.S. where a local physician answers the question. A local physician is always available to take a call. In this case, the firm pays the $50 to the local physician, so there's no profit for the company.



Q12. What is the percentage of calls being answered by a physician in the US? (Write the percentage, that is, if your answer is 53.22%, input 53.22 as the answer.)

Q13. How much (in $) does the company pay the physicians in the US over a 4 hour period?

Q14. What would be the cost saving per hour (in $) from paying less money to the US physicians, if 10 doctors are on duty overseas at any given time?

Q15. Find ONE statement that is FALSE:

A. A process being "in control" means that there are only common causes but no assignable cause of variation in the process.
B. A process that is in control delivers the quality demanded from the customer or a downstream operation in the process.
C. The control limits are set according to how the process performed in the past.
D. Specification limits are something that are given exogenously and cannot be changed by changing the process parameters.
E. A process that is capable is in contro