Problem 1 – Queuing Theory – see Week 11
Keuka Park Savings and Loan currently has one drive-in teller window. Cars arrive at a mean rate of 10 per hour. The mean service rate is 12 cars per hour. I have done the calculations for you.
To improve its customer service, Keuka Park Savings and Loan (Problem 4) wants to investigate the effect of a second drive-in teller window. Assume a mean arrival rate of 10 cars per hour. In addition, assume a mean service rate of 12 cars per hour for each window. What effect would adding a new teller window have on the system? Does this system appear acceptable?
|
Single server queuing Model |
|
|
Lambda |
10 |
|
Mu |
12.00 |
|
Probability system is empty |
0.17 |
|
Average number in queue |
4.17 |
|
Average number is system |
5.00 |
|
Average time in queue |
0.42 |
|
Average waiting time in system |
0.50 |
|
Probability arrival has to wait |
0.83 |
|
Multiple Server Queuing Model |
|
|
Lambda |
10 |
|
Mu |
12 |
|
Number of servers |
2 |
|
Probability system is empty |
0.412 |
|
Average number in queue |
0.175 |
|
Average number in system |
1.008 |
|
Average time in queue |
0.018 |
|
Average waiting time in system |
0.101 |
|
Probability arrival must wait |
0.245 |
Assume that it costs $35,000 per year to add a server and a onetime charge of $100,000 to add the second station.
Also assume that we place a VLC of $20.00 an hour for a customer to wait.
Finally assume the S&L operates 2,080 hours a year.
When does this pay off – if it does. What things would you tout in advertising about the change if you make it?
Problem #2 – Chapter 5
A manager of Paris Manufacturing that produces computer hard drives is planning to lease a new automated inspection system. The manager believes the new system will be more accurate than the current manual inspection process. The firm has had problems with hard drive defects in the past and the automated system should help catch these defects before they are shipped to the final assembly manufacturer. The relevant information is provided below.
Current Manual Inspection System
Annual fixed cost = $35,000
Inspection variable cost per unit = $15 per unit
New Automated Inspection System
Annual fixed cost = $165,000
Inspection variable cost per unit = $0.55 per unit
a. Suppose annual demand is 11,000 units. Should the firm lease the new inspection system? Show your work!
b. Assume the cost factors given above have not changed. A marketing representative of NEW-SPEC, a firm that specializes in providing manual inspection processes for other firms, approached the Paris Manufacturing and offered to inspect parts for $17 each with no fixed cost. They assured Paris Manufacturing the accuracy and quality of their manual inspections would equal the automated inspection system. Demand for the upcoming year is forecast to be 11,000 units. Should the manufacturer accept the offer? Show your work!
Problem #3 – Chapter 15
A bank has set a standard that mortgage applications be processed within a certain number of days of filing. If, out of a sample of 2,500 applications, 85 fail to meet this requirement, what is the epmo metric and what sigma level does it correspond to?
What is epmo?
What is the number in this problem?
What is the resulting sigma level?
Does this hit or miss the mark for six sigma operations? By how far?
Would you consider this important?
Why?
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