Determine the average number of planes that will stack up

Question

Answer for selected Problems

1. 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 four-period moving average

- For the weighted moving average, use a two-period weighted moving average with a weight of 0.70 for the most recent period and the appropriate weight for second most recent period.

- For exponential smoothing, using an σ = 0.25, and the forecast for the Number of Lawsuits for Month 15 is 57.

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 19 through Month 24. Only saying "it is the easier method" is not acceptable.

2. An automobile manufacturer is considering one of two systems for its windshield assembly line. The first is a robotic system that should save money due to a reduction in labor and material cost. This robotic system will cost $400,000. Current practice is to recover this cost over the first two years. One full-time technician and one full-time material handler will be needed with this system. The full-time technician costs $60,000 per year and the material handler costs $52,000 per year.

If the company selects the manual system, it will need four full-time material handlers at a cost of $52,000 each per year. If the manual system is selected, the company will incur additional costs of $0.50 per windshield installed. (Hint: This is the savings referred to in the first paragraph.)

Assume that only one windshield is installed per automobile.

a) How many automobiles are needed to be produced over the next two years to make the robotic system an attractive investment? Ignore the time value money and assume that the entire cost of the robotic system will be recovered during the first two years.

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?

c) 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.

3. 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.

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?

4. 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).

5. 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	5-Jan	2.5	4	5
Bus Access	0.2	5-Jan	4	2.5	1.5
Safety	0.2	4-Jan	3.5	3	4
Site Size	0.05	3-Jan	2	1.5	2.5

Using the factor rating (scaling) approach we studied in class and modified as appropriate, which site do you recommend? Why?

6. 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	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. It is believed that there will be a one semester lag between the enrollment and the units leased. In other words, the number of units leased in a semester is a function of the university enrollment in the prior semester. What is the linear regression relationship the manager should use and what is the forecast for the Number of Units Leased for Semester 9?

c) Suppose the manager believes that the Number of Units Leased is a function only of the Average Lease Price for that semester. 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 average lease price for that semester is $450?

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.

7. 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 control limits on eight chocolate chips per cookie which again is a proxy for the weight of the chocolate chips in a cookie. Too few or too many chips (ounces) affect the desired cookie taste. 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) What conclusions can be reached on the cookie-production process based on the results of your control chart analysis.

8. 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) What is the probability that a plane approaching the airport will find at least two other planes already in the "system" waiting to land?

d) 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?

e) 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?

Show all work and Attach excel files.