1. Student tuition at ABC University is $150 per semester credit hour. The state supplements school revenue by matching student tuition dollar for dollar. In other words, for each dollar a student pays in tuition, the state pays a dollar that is also considered revenue. Average class size for a typical three hour course is 30 students. Labor costs are $3,000 per class, materials costs the school $10 per student per class and overhead costs are $15,000 per class. For this problem, ABC University measures output as the total amount of revenue generated.
a) What is the multifactor productivity performance for a course at ABC University?
b) If instructors work an average of 10 hours per week for 16 weeks for each three-credit hour class of 30 students, what is the labor-hours productivity ratio?
c) Suppose the next year, tuition increases to $200 per semester credit hour but the state only pays $80 per semester hour instead of the matching it had previously paid. The instructors worked on average 8 hours per week for 16 weeks for each three credit hours class of 30 students. What is the labor-hours productivity ratio here and what is the percent change from b)?
2. A large health maintenance organization (HMO) was created as a result of a corporate merger two years ago. To help in preparing a staffing plan, the operations manager needs to develop a forecast for the Number of Lawsuits for Month 25. Following is the Number of Lawsuits for the past 24 months.
|
Month
|
Number of Lawsuits
|
Month
|
Number of Lawsuits
|
Month
|
Number of Lawsuits
|
|
1
|
16
|
9
|
51
|
17
|
63
|
|
2
|
25
|
10
|
56
|
18
|
57
|
|
3
|
16
|
11
|
67
|
19
|
48
|
|
4
|
24
|
12
|
45
|
20
|
55
|
|
5
|
38
|
13
|
53
|
21
|
61
|
|
6
|
46
|
14
|
61
|
22
|
51
|
|
7
|
54
|
15
|
55
|
23
|
56
|
|
8
|
52
|
16
|
69
|
24
|
53
|
Calculate your forecast results to one (1) decimal place (xx.x).
a) Make a forecast for the Number of Lawsuits for Month 25 using the moving average, weighted moving average and exponential smoothing forecasting methods on the following basis:
- For the moving average, use a three-period moving average
- For the weighted moving average, use a two-period a weighted moving average with a weight of 0.65 for the most recent period and the appropriate weight for second most recent period.
- For exponential smoothing, using an σ = 0.30, and the forecast for the Number of Lawsuits for Month 14 is 63.
b) From the results of a), which method provides the better forecast for Month 25? Why? Your selection criteria must be based on one of the numerical evaluation methods we used in our related homework problem using the forecast results for Month 18 through Month 24. Only saying "it is the easier method" is not acceptable.
3. Ray-D-O's! is considering modifying the design of its popular radio so that the component boards can be soldered without flux, a substance that requires the use of a toxic solvent in the cleanup process. The company is currently spending $4 to manufacture each additional unit. The new design would save $0.75 per unit, as the flux would no longer need to be purchased or cleaned off the radio's component board. It would however, require an upgrade to the workstations to allow for more precise soldering. That upgrade would add $25 per hour to the cost of running the plant. Assume there are 20 production days per month, and the plant runs two eight-hour shifts per day. This company is a small operation with only one worker per shift. Only use the information provided in answering these questions.
a) Over what range of radio production would it prefer each of the radio designs? Assume that all of the available hours would be used producing the radios.
b) Suppose that the company is going to produce 9,000 radios per month. How much would the new design have to save per unit in order for the company to be indifferent between the two design options?
a) For the current design and with the current price of $9.50 per unit, the marketing group has said that there is a demand for 8,000 units per month. However, if the company were to drop the price by $0.25 per unit and adopt the new design, the demand would increase to 9,000 units per month. The other information for the new design is provided in a) above. Looking at these two options, which strategy should the company adopt? All of the other information provided in part a) applies in this analysis. Show your work supporting your decision.
4. a) Compare the advantages and disadvantages of using an assemble-to-order process to the advantages and disadvantages of a make-to-order process for a fast food hamburger restaurant.
b) Henry Smith, the manager of the local branch of the state Department of Motor Vehicles, is attempting to analyze the driver's license renewal operation. He has completed the data collection and has the following information.
State Automobile License-Renewals Process Times
|
Step
|
Average Time to Perform (seconds)
|
|
1. Review renewal application for correctness
|
15
|
|
2. Process and record payment
|
30
|
|
3. Check file for violations and restrictions
|
40
|
|
4. Conduct eye test
|
30
|
|
5. Photograph applicant
|
40
|
|
6. Issue temporary license
|
30
|
Henry found that each step was assigned to a different person. Each application is a separate process in the sequence shown above and when a worker is through with his work for one person, he starts the next person in line.
i) What is the maximum number of applications per hour that can be handled by the present process?
ii) How many applications can be processed per hour if a second clerk is added to check for violations and restrictions while all other operations continue to have one clerk?
5. Smith Manufacturing, a parts reseller, is currently considering using one of several suppliers. For a specific part, Smith's upper specification limit (USL) is 12.6 centimeters (cm) and its lower specification limit (LSL) is 9.9 centimeters (cm). Smith wants both the process capability ratio and process capability index to be at least 1.20 at the minimum?
a) The first supplier, WEBLE, can adjust its standard deviation but cannot shift the mean of its process. The mean of WEBLE's process is 11.0 cm and the standard deviation is 0.5 cm. What is the maximum standard deviation (σ) of this process if the company wants to ensure that it can maintain a minimum acceptable Cpk?
b) The second supplier, FASTENER, is currently operating with a mean of 11.2 and a standard deviation of 0.41 cm. Can the company meet the customer's specification requirements at this time? If it cannot, explain if it is due to a drifting of the mean or too much variability.
c) The third supplier, BUB, has a process whose standard deviation is 0.36 cm but the mean of its process is not known. BUB says it cannot or will not be able to change the standard deviation of its process. What are the upper and lower limits on the mean of the process to maintain a Cpk of 1.2 or greater?
6. ABC Company is considering the possibility of building an additional factory that would produce a new addition to their product line. The company is currently considering two options. The first is a small facility that it could build at a cost of $6 million. If demand for new products is low, the company expects to receive $10 million in discounted revenues (present value of future revenues) with the small facility. On the other hand, if demand is high, it expects $12 million in discounted revenues using the small facility. The second option is to build a large factory at a cost of $9 million. Were demand to be low, the company would expect $7 million in discounted revenues with the large plant. If demand is high, the company estimates that the discounted revenues would be $14 million. In either case, the probability of demand being high is 0.20 and the probability of it being low is 0.80. Not constructing a new factory would result in no addition revenue being generated because the current factories cannot produce these new products. For this analysis, use only the information provided.
a) Construct a decision tree to help ABC make the best decision.
b) Based on your analysis and using an expected value approach, which facility should be built?
c) Suppose the probability of the demand being low is uncertain at this time. Since the probability of low demand is uncertain, this would also mean the probability of demand being high is also uncertain. With everything else remaining the same as in a), what is the probability of low demand that make the two facility options equal based on the expected values.
d) Provide an interpretation of the results you found in c).
7. The local blood donor clinic is considering 3 sites for the location of its new clinic. It has collected the following information. Different SME's (subject matter experts) scored each of the non-economic factors. So, unfortunately, the scores for the non-economic factors are scaled differently. The scales are indicated on the table. The highest score is always the best value. For each of the Non-economic factors, it is possible to score the maximum for that factor.
|
Factor
|
Factor Weight
|
Scale
|
Site A
|
Site B
|
Site C
|
|
Building Cost
|
0.3
|
|
$4 million
|
$5.0 million
|
$3.5 million
|
|
Non-economic factors
|
|
|
|
|
|
|
Road Access
|
0.25
|
1-5
|
2.5
|
4.0
|
5.0
|
|
Bus Access
|
0.2
|
1-5
|
4.0
|
2.5
|
1.5
|
|
Safety
|
0.2
|
1-4
|
3.5
|
3.0
|
4.0
|
|
Site Size
|
0.05
|
1-3
|
2.0
|
1.5
|
2.5
|
Using the factor rating (scaling) approach we studied in class and modified as appropriate, which site do you recommend? Why?
8. Chasewood Apartments is a 300-unit complex near Fairway University that attracts mostly university students. The manager has collected the following data and wants to project the number of units leased in Semester 9 using simple linear regression. Here is the information that has been collected:
|
Semester
|
University Enrollment
(in thousands)
|
Average Lease Price ($)
|
Number of Units Leased
|
|
1
|
7.2
|
450
|
291
|
|
2
|
6.3
|
460
|
228
|
|
3
|
6.7
|
450
|
252
|
|
4
|
7.0
|
470
|
265
|
|
5
|
6.9
|
440
|
270
|
|
6
|
6.4
|
430
|
240
|
|
7
|
7.1
|
460
|
288
|
|
8
|
6.7
|
440
|
246
|
In answering these questions, you must identify and use the correct independent and dependent variables.
a) The apartment manager wants to forecast the Number of Units Leased as a function of time. What is the linear regression relationship the manager should use and what is the forecast for the Number of Units Leased for Semester 9?
b) Suppose the manager believes that the Number of Units Leased is a function only of University Enrollment. What is the linear regression relationship the manager should use and what is the forecast for the Number of Units Leased for Semester 9 if the enrollment is expected to 6,700 students for Semester 9?
c) Suppose the manager believes that the Number of Units Leased is a function only of the Average Lease Price. What is the linear regression relationship the manager should use and what is the forecast for the Number of Units Leased for Semester 9 if the forecast for the Average Lease Price is $460 for Semester 9?
d) Considering the strength of each of the relationships that you found in parts a) through c), would you use any of these to forecast the Number of Units Leased for Semester 9? Explain your answer.
9. Martha's Wonderful Cookie Company makes a special super chocolate-chip peanut butter cookie. Martha's used the number of chocolate chips as a proxy measure for the weight of chocolate chips in a cookie. The company would like the cookies to average approximately eight chocolate chips apiece and wants to base its statistical process control on eight chocolate chips per cookie. Too few or too many chips affect the desired cookie taste. The number of chocolate chips are not considered as defects but as a unit of measure. Ten samples of five cookies each during a week have been taken and the chocolate chips counted. The sample observations are as follows:
Chips Per Cookie
|
Sample
|
Cookie 1
|
Cookie 2
|
Cookie 3
|
Cookie 4
|
Cookie 5
|
|
1
|
7
|
6
|
9
|
8
|
5
|
|
2
|
7
|
7
|
8
|
8
|
10
|
|
3
|
5
|
5
|
7
|
6
|
8
|
|
4
|
8
|
8
|
5
|
10
|
8
|
|
5
|
7
|
6
|
9
|
8
|
4
|
|
6
|
7
|
6
|
5
|
4
|
5
|
|
7
|
9
|
10
|
8
|
9
|
7
|
|
8
|
11
|
9
|
9
|
10
|
6
|
|
9
|
5
|
5
|
9
|
8
|
8
|
|
10
|
6
|
8
|
8
|
5
|
9
|
Assume that we have sufficient data to prepare and analyze control charts.
a) Construct the appropriate control chart(s) to analyze the cookie-production process based on how the company is actually performing.
b) Comment on the cookie-production process based on the results of your control chart analysis.
c) Suppose it is industry standard practice for a chocolate chip cookie to have on average 4.5 to 7.5 chocolate chips. What would you conclude about this company's performance relative to the industry standards?
10.
The Peachtree Airport in Atlanta serves light aircraft. It has a single runway and one air traffic controller to land planes. It takes an airplane 12 minutes to land and clear the runway (following an exponential distribution). Planes arrive at the airport at the rate of one every 15 minutes. The arrival rate follows a Poisson distribution. A plane is considered to have entered the "system" once it has notified the airport that it is in the vicinity and wants to land. For purposes of this analysis, you can ignore the planes taking off.
a) Determine the average number of planes that will stack up (wait) to land.
b) Find the average time a plane must "wait in line" before it can land.
c) Calculate the average time it takes a plane to land and clear the runway once it has notified the airport that it is in the vicinity and wants to land.
d) What is the probability that a plane approaching the airport will find at least two other planes already in the "system" waiting to land?
e) Suppose that the cost assigned to a plane while it is waiting to land (in the stack) is $1,000 per hour and the cost per hour for the air traffic control operation is $2,000 per hour. What is the total cost of this operation considering both the waiting time and the air traffic control operation?
f) There is a second airport in the immediate vicinity of the Peachtree airport which is currently closed. The FAA is considering re-opening this one as there would be no cost to do this and it believes it would improve customer service. However the cost per hour for the air traffic control operation is $2,500 per hour at this second airport. It would still take an airplane 12 minutes to land and clear the runway (following an exponential distribution). The Peachtree airport and this second airport would work as a multiple server system. What would be the cost of this multiple server operation?