1. (24 points) Considering the number of pieces processed per hour as its output, Merrifield Post Office is evaluating the productivity of its mail processing centers. The centers differ in the degree of automation, the type of work that can

1. (24 points)

 

Considering the number of pieces processed per hour as its output, Merrifield Post Office is evaluating the productivity of its mail processing centers.  The centers differ in the degree of automation, the type of work that can be performed, and the skill of the workers.

 

Center	1	2	3
Pieces processed per hour	1,000	2,000	3,000
Number of workers per hour	10	5	2
Hourly wage rate	$5.50	$10.00	$12.00
Overhead rate per hour per center	$10.00	$25.00	$50.00

 

1. a) Calculate the multifactor productivity for each center
2. b) Workers in Center 1 are scheduled to receive a 20% pay raise next month. What will be the change in the multifactor productivity rate? Also, what is the percentage change in the multifactor productivity performance?
3. c) A new processing machine is available for Center 2 that will increase the output to 2,600 pieces an hour although this will increase the overhead rate by $20.00 per hour. Merrifield will only install the new processing machine if it increases the multifactor productivity of Center 2 by at least 10%. Should Merrifield install the new processing machine?  Justify your answer.  Also, what is the percentage change in the multifactor productivity performance?

 

2. (20 points)

 

Holding goods in inventory is costly because inventoried goods are susceptible to breakage and other forms of physical damage.  Often, the amount of damage (in dollars) increases with the level of inventory (expressed in dollars), but some of the damage is unrelated to the amount of inventory.  The following data show a company’s inventory damage experience.

 

Period	Inventory Level (Millions of Dollars)	Damage (Thousands of Dollars)	Average Age of Inventory (Days)
1	$11	$80	31
2	$15	$90	45
3	$13	$70	98
4	$10	$60	15
5	$7	$50	25
6	$9	$70	31
7	$13	$80	82
8	$14	$65	72
9	$10	$70	50
10	$12	$60	45

 

You are interested in developing a forecast for the Inventory for period 11. Provide your forecasts to one decimal place ($xx.x).

 

11. a) Develop a 4-period moving average, a 3-period weighted moving average forecast, and an exponential smoothing forecast for period 11. For the weighted moving average, the weights should be 0.7 and 0.2 for the most recent and next most recent periods.  The sum of the weights for the three periods should be consistent with the method we have studied in class.  For the exponential smoothing method, let the starting forecast for period 3 be 14.0 and let α = 0.3.  Provide the forecasts for period 11.

 

 

 

 

 

1. b) Of these three forecasting methods, which appears to be the best method based on the forecasting results for periods 8 through 10? Selecting a method because it is easy is not acceptable. Your results must be analytically based on the forecasts results from periods 8 through 10 and using one of the evaluation methods we have learned and used in our weekly homework assignments.

 

 

 

3. (27 points)

 

Joe Austin is opening a laundry and dry cleaning store in northern Wisconsin.  He is going to operate the store 250 days per year.   Joe is considering a couple of options for the machine that he will use to press the shirts.  One press (Press A) will cost $12,100 and with this press he estimates that it will cost $0.323 to press a shirt.  The second press (Press B) he is considering will cost $15,400 to purchase and it will cost $0.244 to press a shirt.  Regardless of the press he purchases, he will charge a customer $1.10 per shirt.  Joe will continue to operate 250 days per year.  For the following analyses, Joe will ignore taxes and depreciation.  He wants to recover the cost of the press he buys during the first year.

 

1. a) Over what range of shirts per year would each of the presses be preferred over the other press?  Show your work.

 

 

 

1. b) Considering only Press A, Joe now wonders how many shirts per year he would need to press if he wants to recover the cost of Press A during the first year and he cuts his price to $1.01 per shirt. How many shirts per year would Joe need to press to break-even?  Show your work.

 

 

 

 

1. c) Suppose Joe has decided that Press B will provide a higher quality finished shirt so he will raise the price to $1.15 per shirt if he buys that press. It also turns out that Press B has a higher capacity than Press A. Using Press A, 80 shirts per day can be pressed, while using Press B  85 shirts per day can be pressed.  He believes the demand will exceed the capacity of either press.  Considering the original information and this additional information, which press should Joe select if he wants the better bottom line performance?

 

 

 

 

1. d) It turns out that Press A is no longer available to purchase. As an alternative to purchasing Press B, Joe is considering outsourcing the pressing operation to a third party.  What is the maximum price per shirt that he would be willing to pay the third party and be indifferent between this option and Press B using this information for Press B:  $15,400 price for the press, $0.244 cost to press the shirt, $1.15 per shirt price, 85 shirts per day, and 250 days per year?  Assume that he will charge the customer $1.12 per shirt if he decides to outsource the pressing operation and this can also provide 85 shirts per day.  Assume 85 shirts per day will be pressed for either option.

 

4. (10 points)

 

A company is looking at improve its output of products that are accepted by its customers, hence raising the quality of its products.  A question has been asked related to this though.  “If line employees are required to work on quality improvement activities, the company’s long-term productivity will suffer.”  Discuss this from a company perspective addressing the impact of the long-term consequences of this statement on both company production and company productivity. Consider as an example of line employees those employees working on an assembly line.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5. (23 points)

 

Meena Company has been producing computer chips with an average life of 290 hours and a standard deviation (s) of 24 hours.  The customer specifications are 300 + or – 100 hours for the upper and lower specification limits respectively.  So the upper and lower spec limits are 400 hours and 200 hours respectively.

 

1. a) Meena has the opportunity to obtain a large order from XYZ Computers if it can produce the computer chips with specification limits of 300 + or – 100 hours. If the minimum acceptable process capability is 1.33 (a 4-sigma process), can Meena 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.

 

 

 

 

 

 

 

1. b) Suppose that Meena is producing computer chips with a σ = 24 hours and it cannot improve on this. Using the process capability index, what are the upper and lower limits for the mean of the process so that Meena can meet the customer requirements at a process capability of 4-sigma limits? Interpret your results.

 

 

 

 

 

 

 

 

1. c) Now suppose that Meena has introduced some changes in its operations. The customer has also agreed to use Meena if Meena can provide a process capability of 1.40 or greater.  After the first 20 days of production under the new process, it finds that the average life is 295 hours but it has not determined the standard deviation (s).  What is the maximum acceptable value of the standard deviation (σ) for Meena to be selected?  The customer’s spec limits are still 300 + or – 100 hours.

 

 

 

 

 

 

 

 

 

6. (14 points)

 

A hardware store orders snow blowers during the summer for delivery in the fall.  Each snow blower costs the store $400 and if sold prior to or during the winter sells for a full price of $550.  The store’s manager doesn’t want to carry any unsold snow blowers in inventory from one year to the next, so he reduces the price to $350 in the spring in order to get rid of any leftovers.  He will be able to sell all of these at this price.  Based on past experience, the store’s manager expects that the demand for snow blowers at full price will be between 6 and 8.  The store manager estimates the probabilities of selling different numbers of snow blowers at full price to be the following: probability of 6 is 0.40, the probability of 7 is 0.35 and the probability of 8 is 0.25.

 

1. a) Draw the decision tree that the hardware store manager can use to analyze this problem.

 

 

 

 

 

1. b) Using an expected value approach, how many snow blowers should the hardware store manager order to maximize its profit?

 

 

 

 

 

7. (14 points)

 

The Security National Bank is considering two locations for a new branch.  The two choices are a major mall and a strip mall.  The site selection team is evaluating two sites, and they have scored the critical success factors for each as shown below.  They have identified both the relocation cost and the monthly projected profit.  The weights reflect the same relative importance as we have used in class.  They want to use these ratings to compare the locations.

 

Critical Success Factor	Factor Weight	Major Mall Site	Strip mall Site
Relocation cost	0.30	$270,000	$190,000
Monthly profit	0.30	$75,000	$50,000
Customer service	0.20	2.4	2.1
Service quality	0.10	1.8	2.4
Security and safety	0.05	2.4	1.8
Market share	0.05	1.8	2.1

 

The non-economic scores are on a 0 to 3.0 basis with 3.0 being best and it is possible to achieve the 3.0 score.

Using the factor scoring (rating) method as we learned in class, which site should Security National Bank use based on the above information?

 

 

 

 

 

 

 

8. (21 points)

 

Joan Newman has collected the following data relative to housing and university enrollment.

 

Semester	University Enrollment (thousands)	Average Lease price ($ per month)	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

 

Your work must reflect the correct independent and dependent variables based on the problem statements.  This is part of the solution that is required. Provide your forecasts to one decimal place ($xxx.x).

 

1. a) Joan believes that there is a linear relationship between university enrollment and the number of apartment units leased based only on university enrollment. What is this regression relationship and what is the forecast of apartments leased if the enrollment is expected to be 6,500 students? How strong is this relationship?

 

 

 

 

 

1. b) Now, Joan wants to forecast the number of apartments leased based only on the average lease price. What is this regression relationship and what is your forecast if the average lease price is to be $465? How strong is this relationship?

 

 

 

 

 

10. c) It is believed that the university enrollment changes only with time. So, Joan decides to use a linear regression model to forecast the enrollment for semester 10. What would the forecast for the enrollment be?  Also, what is your confidence in this relationship, in other words, how strong is the relationship?
    (16 points)

 

You are the training director for an insurance firm.  Your company is concerned about the wide dispersion in analysis of claims between your claim adjusters.  As a result, you recently implemented a changed in the training of your claim adjusters.  You are now interested in determining if the training program has achieved its results.  You will base part of this decision on the consistency of the claims adjusters in processing claims.  You completed the new training program 10 days ago.  You have collected data over the past 10 days, all since the training program was implemented.  You took a sample of 200 claims per day.  The results are as follows:

 

Day	1	2	3	4	5	6	7	8	9	10
Claims with errors	7	6	7	8	7	9	12	11	13	14

 

The interpretation of this data is as follows.  On day 1, there were 200 claims sampled and 7 of these claims had errors.  On day 5, there were again 200 claims sampled and only 4 claims had errors.  The “claims with errors” data represents the number of claims with errors – not the total number of errors.

 

1. a) Using a control chart and 2σ (sigma) control limits, determine if the results of the training program indicate that the adjusters are now more consistent in the processing of claims. Explain your conclusions.

Notes:

• The centerline should be based on the data from these 10 days.
• Assume there is sufficient data to perform this analysis
• As part of your answer, provide the appropriate control chart(s).

 

 

 

1. b) Using this sample information, do the data indicate that the process is in control? Why or why not?

 

 

 

10. (31 points)

 

During the campus Spring Fling, the bumper car amusement attraction has a problem with cars becoming disabled and in need of repair.  Repair personnel can be hired at the rate of $23 per hour. One repairer can fix cars in an average time of 25 minutes.  While a car is disabled or being repaired, lost income is $45 per hour.  Cars tend to break down at the rate of two per hour.  Assume that there is only one repair person, the arrival rate follows a Poisson distribution and the service time follows an exponential distribution.

 

1. a) On average, how long is a disabled bumper car out of service and not able to take riders on the bumper car attraction?

 

 

 

 

 

 

1. b) On average, how many disabled bumper cars are out of service and waiting to be repaired?

 

 

 

 

 

 

1. c) When a bumper car becomes disabled, what is the probability that it will find that there are at least three cars already waiting to be repaired?

 

 

 

 

 

 

1. d) The amusement part has decided to increase its repair capacity by adding either one or two additional repair people. These will not work individually but they only work as one team. Thus if two or three people are working, they will work together on the same repair.  One repair worker can fix cars in an average time of 25 minutes.  Two repair workers working as a team take 20 minutes and three repair workers working as a team take 15 minutes.  What is the cost of the repair operation for the two repair strategies (adding 1 or 2 repair workers) that it is considering?  Considering the cost of the operation, would either of the worker options be preferred to the one worker operation?