As information, if I have questions about your work, I might follow-up with questions asking for clarification. Thanks for understanding.

Name ____Solutions______

MBA 626 – Dr. Levy

Summer, 2013

Test 1

July 5 – July 6, 2013

1. ______ (22 points)

2. ______ (18 points)

3. ______ (20 points)

4. ______ (18 points)

5. ______ (22 points)

6. ______ (18 points)

7. ______ (14 points)

8. ______ (20 points)

9. ______ (20 points)

10. ______ (28 points)

Total ______ (200 points)

SHOW ALL WORK!!!!

I neither received nor provided help on this test.

Name ___________________________________ Date ___________________
Answer Page for Selected Problems

Provide only your final answers (for example, the final numbers, selection, etc.) to the following problems. Remember to show your work and answers for these problems on the problem pages.
Example only: the break-even point is 100,000 units as this is the point where the cost of the two options is equal. Below that level we prefer option A and above that we would use option C

#1

#2

#3

#5

#6

#7

#8

#9

#10
1. (22 points)

The H&S Motor Company produces small motors at a production cost of $30 per unit. Defective motors can be reworked at a cost of $12 each. The company produces 100 motors per day and averages 80 percent good quality motors. Based on past experience, 50% of the defective motors can be reworked prior to shipping to customers. These are also considered good motors. A good motor can be sold for $100 while a defective motor can be scrapped and sold for $15. Income consists of both the revenue from the sold motors and the scrapped motors.

a) Using the number of good motors shipped as the measure of output and the cost of production as the input, what is the company’s productivity if no defective motors are reworked?

Productivity = 0.80*100/(100*$30) = 80/$3000 = 0.0267 units/ input $

b) Suppose that the company now uses the total income as the output measure and the cost of production as the input. What is the company’s productivity if no defective motors are reworked?

Productivity = (0.80*100 * $100 + 0.20*100*$15)/(100*$30) = = $8300/$3000 = $2.77/ input $

c) Now suppose the company reworks the defective motors that can be reworked. Using the number of good motors shipped as the measure of output and the cost of production as the input, what is the company’s productivity now?

Productivity = (0.80*100+10*100)/(100*$30+0.10*100*12) = (80 + 10)/(3000 + 120)= 90/3120 = 0.02885 units / input $

d) What is the percent change in productivity comparing the productivity in c) to the productivity in a)

% change = (0.02885 – 0.0267)/0.0267 * 100% = 8.05%
2. (18 points)

A toy company buys large quantities of plastic pellets for use in the manufacture of its products. The production manager wants to develop a forecasting system for plastic pellet prices. The price per pound of plastic pellets has varied as shown:

|Month |Plastic Pellets Price/Pound |Month |Plastic Pellets Price/Pound |
|1 |$0.39 |9 |$0.35 |
|2 |$0.41 |10 |$0.38 |
|3 |$0.45 |11 |$0.39 |
|4 |$0.44 |12 |$0.43 |
|5 |$0.40 |13 |$0.37 |
|6 |$0.41 |14 |$0.38 |
|7 |$0.38 |15 |$0.36 |
|8 |$0.36 |16 |$0.39 |

Make a forecast for Month 17 using the moving average, weighted moving average, and exponential smoothing methods as follows:
a) For the moving average, use a 3-period moving average.
b) Use a two-period weighted moving average. Unfortunately, you spilled water on the sheet with the weights to be used for the weight moving average and this blurred the weight for the most recent period. However, you can tell that the weight for the second most recent month is 0.30.
c) For exponential smoothing, using an α = 0.25, and the forecast for Month 5 was $0.39.
d) Using the methods in a) through c), which method provides the better forecast for Month 17? Why? Your selection criteria must be based on the forecasts for Months 13 through 16 using one of the one of the numerical evaluation methods we have learned and used on homework assignments this term.

Provide your forecasts to three decimal places ($0.xxx).

See next page

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3. (20 points)

Barney’s Boston Bagel ‘n Bun Bakery is looking into a new type of bag tie that will better seal, and more importantly, better reseal the company’s bagels after they have been taken home. The process that it is using at this time without the new bag tie is referred to as Current. According to a competitive analysis of Barney’s bagels compared to those of the competition, the new bag ties would dramatically increase the shelf life of the bagels. Barney currently sells all the bagels the company can make, 5,000 bags of bagels a week. The new tie would cost $0.02 more than the old one, but the longer shelf life would create incremental value to the customer

a) In addition to the cost of the new ties, assume that the new tie would require a machine that would add $200 per week to the company’s fixed costs. How much more should Barney’s charge per bag in order to make the same profit as it made using the Current process?

Additional charge = $200/5,000 + $0.02 = $0.04 + $0.02 = $0.06

b) Instead of the modification in a), Barney’s is considering adding a faster machine along with a second baker. In addition to the additional cost of the new tie, this would add $1,500 per week to the company’s fixed costs but would triple the company’s output. How much should the company add to the price of a bag of bagels if it wants to increase profit by at least $3,000 per week compared to the Current operation.

Additional price = $0.02 + $1,500/15,000 + $3,000/15,000 = $0.02 + $0.10 + $0.20 = $0.32

c) Barney has decided to add $0.40 for the price of a bag and wants to make $3,000 per week compared to the Current operation. He will be adding the faster machine, the new tie and the second baker. How many bags of bagels will he need to produce to make $3,000 per week compared to the Current operation (which does not include the new bag time)?

0.40x – ($0.02x + $1,500) = $3,000
0.38x - $1,500 = $3,000
0.38x = $4,500
X = 11,842.11 or 11,843 bags
4. (18 points)

a) Operations management concepts can be applied to both manufacturing and service operations. It can often be more challenging to apply them in a service operation. Briefly describe at least two of the challenges that a service operation presents for the application of operations management concepts that are not found in a manufacturing operations. Briefly describe a way to address one of the challenges that you have identified.

Open-ended but should include at least two of the following: arrival rate is unpredictable, the arrival’s requirements (service needs) are unpredictable, service work cannot be inventoried in advance, the quality of the service is determined by the customer, amount of customer contact and customer interaction.
Needed to describe a way to address one of the challenges that was identified. Examples include schedule time slots, limit selection of service, customer surveys, etc.

b) Six Sigma and TQM approach quality from different perspectives. For a customer service operation, explain how each of these two approaches could be used to address the complaints that are being received from the customers about the poor customer service.

Open-ended, items to consider are the following:
TQM is a philosophy that stresses three principles for achieving high levels of process performance and quality: customer satisfaction, employee involvement, and continuous improvement (Heizer, Operation management, 9th edition). TQM is characterized by the Deming PDCA wheel . TQM can be considered to focus on managing the entire organization so that it excels on all dimensions. TQM is not quite as analytical as Six Sigma.
Six Sigma is a comprehensive and flexible system for achieving, sustaining, and maximizing business success by minimizing defects and variability in processes. Six Sigma is characterized most commonly by the DMAIC process. Focuses on reducing variability, centering the mean and meeting customer’s requirements. Six Sigma is a more analytical tool than TQM. This often on improving a specific problem.
Needed to also address how these two quality approaches can address complaints being received in a customer service operation. Needed to specifically connect to a customer service operation. For example, for TQM establish a process of identifying and addressing customer complaints by involving the employees. Once data is collected, could use a Cause-and-Effect diagram or a Pareto chart to identify the leading causes. After work on correcting these, review the performance through a customer satisfaction survey.
For example for a Six Sigma analysis, perform a statistical analysis of the customer complaints, concerns, etc. From this, perform an analysis of the leading problems that will lead to resolving the customer service problems, etc.

5. (22 points)

A company is going to introduce a new cell phone. ABC Cell Services is going to sell the phones and has established specification limits of 5.0 ounces and 5.5 ounces for the weight of the phone. The company currently believes that its phones currently weigh 5.2 ounces.

a) If the company wants to have a Cpk of 2.0 or greater (equivalent to a six sigma process), what is the maximum value of the standard deviation (σ) so that the Cpk of the process indicates that the company can provide the six sigma process (process capability = 2.0)?

Cpk = min [ (USL- xmean)/3σ , (xmean – LSL)/3σ] = min[ (5.5-5.2)/3(σ), (5.2-5.0)/3(σ)]

A Cpk >= 2.0 yields a process performing at a six sigma level

(5.5-5.2)/3σ >= 2.0
0.3/3σ>=2.0
0.15 >= 3σ σ =< 0.05

(5.2-5.0)/3σ >= 2.0
0.2/3σ>=2.0
0.1 >= 3σ σ =< 0.033

Hence, σ =< 0.033

b) Suppose that the company is operating at a standard deviation (σ) of 0.025. What is the range on the mean of the process to maintain a Cpk of 2.0 or greater?

Cpk = min [ (USL- xmean)/3σ , (xmean – LSL)/3σ] = min[ (5.5-X)/3(0.025), (X-LSL)/3(0.025)]

(5.5-X)/3(0.025) >= 2.0
5.5-X >=0.15
X =< 5.35

(X-5.0)/3(0.025) >= 2.0
X-5.0 >=0.15
X >= 5.15

c) Suppose that the company can maintain an average weight of 5.2 ounces and a standard deviation (σ) of 0.04 ounces. The company does not believe it can improve on these values. The company wants to see if ABC would be willing to adjust its spec limits rather them keep them at 5.0 and 5.5 if necessary to meet the minimum Cpk of 2.0. What should the company tell ABC that it would need to adjust the spec limits to in order to ensure a Cpk of 2.0 or greater?

Cpk = min [ (USL- xmean)/3σ , (xmean – LSL)/3σ] = min[ (USL-5.2)/3(0.04), (5.2-LSL)/3(0.04)]

(USL-5.2)/3(0.04) >= 2.0
USL-5.2 >= 0.24
USL >= 5.44

(5.2-LSL)/3(0.04) >= 2.0
5.2-LSL >= 0.24
LSL =< 4.96

Must lower the LSL to 4.96. Not necessary to adjust the USL as it is greater than 5.44 but must ensure that it is not increased to more than this.
6. (18 points)

Joe Builder has located a piece of property that he plans to buy and build on and then sell to a third party. The land is currently zoned for four homes per acre, however Joe is planning to request that it be rezoned. What Joe builds depends on the approval of the rezoning request and your analysis of his situation. With his input and your help, the decision process has been reduced to the following costs, alternatives and probabilities:

Cost of land: $2 million
Probability of rezoning: 0.60
If the land is rezoned, there will be additional costs for new roads, lighting, etc. of $1 million. This will be referred to as property improvements.

If the land is rezoned, Joe must decide whether to build a shopping center or 1,500 apartments. In either case, Joe is planning to sell the property after he has built either the shopping center or apartments. He is certain that he can sell the property, although there are probabilities associated with who would be the buyer. If a shopping center is built, it can be sold to either an insurance company for a profit of $5 million before the cost of the land and the property improvements or to a large department store chain for a profit of $4 million before the cost of the land and property improvements are considered. The probability of selling it to the department store chain is 70 percent so that the probability of selling it to the insurance company is 30 percent. If, instead of the shopping center, he decides to build the 1,500 apartments, the probabilities on the profits for selling them are as follows:

40 percent chance he can get a profit of $2,000 for each apartment before the cost of the land and property improvements are considered, or
60 percent chance he can get a profit of $3,000 for each apartment before the cost of the land and property improvements are considered.

If the land is not rezoned, Joe will comply with the existing zoning restrictions and simply build 600 homes on which he expects to make a profit of $4,000 on each one before the cost of the land is considered.

Using the decision tree and expected value approach, determine the best solution for Joe and his expected net profit.

Can include an additional branch to the left deciding whether to buy the land or not.

Decision: apply for rezoning and if successful build the shopping center. If not rezoned, then build the houses. Expected payoff is $940,000.

Note: choosing to rezone or not rezone is not a decision but a state of nature. Also, selling to the insurance company or a large department store is not a decision that is made but a state of nature.
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Rezoned shopping center: Point 1: Expected value = .70($4 Million) + .30($5 Million) = $4.3 Million Rezoned apartments: Point 2: Expected value = .60($4.5 Million) + .40($3 Million) = $3.9 Million Since a shopping center has more value, prune the apartment choice. In other words, if rezoned, build a shopping center with a profit of $4.3 Million - $3 Million = $1.3 Million If not rezoned: Point 3: Expected Profit is $2.4 Million - $2 Million = $.4 Million

Expected profit is .60($1.3 Million) + .40($.4 Million) = $.94 Million

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. 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 |$190,000 |$240,000 |
|Customer service |0.40 |2.5 |3.0 |
|Service quality |0.10 |1.8 |2.4 |
|Security and safety |0.10 |2.4 |1.8 |
|Market share |0.10 |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.

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

Select the Strip Mall Site, see next page for the work

b) Suppose the 3.0 value for the Customer Service for the Strip Mall Site is questionable. At what Customer Service score would the bank change its decision from what it found in a)?

0.3(3) + 0.4(2.5) + 0.1(1.8) + 0.1(2.4) + 0.1(1.8) = 0.3(2.38) + 0.4x + 0.1(2.4) + 0.1(1.8) + 0.1(2.1)
2.500 = 1.343 + 0.4x
0.4x = 1.157
X = 2.89375

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8. (20 points)

The registrar at State University believes that decreases in the number of freshman applications that have been experienced are directly and linearly related to tuition increases. They have collected the following enrollment and tuition data for the past ten years:

|Year |1 |2 |3 |4 |5 |
|1 |5 |6 |5 |11 |9 |
|2 |10 |7 |8 |12 |8 |
|3 |6 |8 |6 |13 |7 |
|4 |7 |9 |10 |14 |8 |
|5 |7 |10 |10 |15 |9 |

Assume that these 15 days are sufficient to perform this analysis.

c) Construct a 2σ control chart for the proportion absent and plot the sample data points. Base the center line and control limits using the historical absentee rate prior to the elimination of the flex time.

Pbar = total # absent / total # observations = 115 / (15*110) = 0.070 = 7.0%

Pbar based on prior performance = 250/5000 = 0.05 and σ based on 0.05 σ = √ (pbar) (100-pbar)/sample size = √ (.05)(1.0-0.05)/110 = 0.021 Control limits = 0.05 ( 2(0.021) = 0.05 ( 0.042 = 0.008 (LCL) and 0.092 (UCL)

Pbar based on prior performance = 250/5000 = 0.05 and σ based on current p-bar of 0.07
See below for σ calculation

Control limits = 0.05 ( 2(0.024) = 0.05 ( 0.048 = 0.002 (LCL) and 0.098 (UCL)

Pbar based on current performance = 115/1650 = 0.07 – NOTE THIS IS NOT CORRECT PER THE INSTRUCTIONS σ = √ (pbar) (100-pbar)/sample size = √ (.07)(1.0-0.07)/110 = 0.024 Control limits = 0.07 ( 2(0.024) = 0.07 ( 0.048 = 0.022 (LCL) and 0.118 (UCL)

b) Has there been a change in the absenteeism rate? Explain why or why not and base it on the control chart results.

As a result of the change, there appears to be an increase in the absenteeism. There is an upward trend, with 13 points about p = 0.05, although all points are within the control limits. The absenteeism should be investigated.

c) Suppose the insurance industry’s standard for absenteeism is 4% (lower limit) to 8% (upper limit). What would you conclude about ABC’s performance compared to the industry standard? Explain your reason and base it on the control chart results.

In addition to the comments in b), the absenteeism for ABC has several points (5) above the UIL. Thus, the company is not performing as well in this area.

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10. (28 points)

The Judy Gray Income Tax Service is analyzing its customer service operations during the month prior to the April filing deadline. On the basis of past data, it has been estimated that customers arrive according to a Poisson process with an average arrival rate of one every 12 minutes. The time to complete a return for a customer is exponentially distributed with a mean of 10 minutes. When the person is being helped, she meets with Judy in her office. If the individual is waiting for help, she will be in the waiting area. Based on this information, answer the following questions.

Do not round your results to integer numbers.

Λ = 5 per hour, μ = 6 per hour

a) If you went to Judy, how much time should you allow for getting your return done? Measure this time from when you first arrive at her office.

W = 1/(( - () = 1 / (6-5) = 1 hour

b) On the average, how many customers should the waiting area be designed to hold?

Lq = (2/((* (( - ()) = 52/(6*(6-5)) = 25/6 = 4.17 customers

c) What is the probability that an arriving customer would find at least two other people in the waiting area waiting for help?

Prob at least two others in line = Prob >= 3 in system = 1 – (P0 + P1 + P2)
Prob (>= 3) = 1 – ((1-5/6) + (1-5/6)(5/6)+ (1-5/6)(5/6)2)) = 1 – (1/6 + (1/6)(5/6) + (1/6)(5/6)2) = 1 – (1/6 + 5/36 + 25/216) = 1 – 91/216 = 125/216 = 0.579

d) At this time, Judy is not going to add another person to help complete the tax returns. If the arrival rate remains unchanged but the average time in the system must be 40 minutes or less, what would need to be changed and what would the value of the change need to be?

Λ = 5 per hour, so must change μ

Goal W = 40 minutes = 2/3 hours
W = 1/(( - () = 1 / (( - 5)
2/3 = 1 / (( - 5)
2(( - 5) = 3
2( = 13
( = 6.5 per hour

e) Judy is now considering adding a person to help her process the tax returns. This person will help Judy by checking the paper work for the customers. Judy believes that this will allow her to complete the returns in six minutes 40 seconds on average. Judy would need to pay this person $50 per hour. Judy believes that she has to reduce her cost of the service by $15 per hour for every hour a customer is in her office either waiting for help or being helped. Should she add this person or continue working by herself? Base your analysis on the economics of the two options.

Note: This is still a single server operation with the additional person just helping to speed up the operation. This is often seen in fast food restaurants where an individual is helping fill drinks, etc. but now waiting on any customers.

Total cost of operation = cost of service + cost of time in the system
Total cost of operation = cost of servers + (()(W)(cost of time in the system)

Formulas: Total Cost = (# servers)*(hrly cost of server) + λ*W*(hrly cost of time in system)
Alternate: Total Cost = (# servers)*(hrly cost of server) + L*(hrly cost of time in system)

Note: since Judy’s cost is a constant, we can ignore this in the calculations

For current operation: λ = 5 per hour, μ = 6 per hour
L = (/(( - () = 5 / (6-5) = 5/1 = 5 customers W = 1/(( - () = 1 / (6-5) = 1/1 = 1 hour
Total Cost = (1)($0) + 5(1)($15) = $75
Alternate Total Cost = (1)($0) + (5)($15) = $75

For operation with helper: λ = 5 per hour, μ = 9 per hour
L = (/(( - () = 5 / (9-5) = 1.25 customers W = 1/(( - () = 1 / (9-5) = 0.25 hours
Total Cost = (1)($50) + 5(0.25)($15) = $68.75
Alternate Total Cost = (1)($50) + (1.25)($15) = $68.75

Hire the helper
Please read and follow all instructions on this page and the next page!!
Failure to follow instructions can result in point deductions!!
You must show your work!!

MBA 626-Dr. Levy
Summer, 2013
Test 1 Submission Requirements

If you received this test other than on Friday, July 5, your due date is provided in the email that forwarded the test to you. Otherwise, you must have it (the test and work that you want graded) returned to me by midnight (11:59 P.M. CT), Saturday, July 6. You may fax it to me at 402.505.5771 (please include a cover sheet addressed to me), send it electronically via email or via the Test One document in the Assignments folder, mail it to me, or UPS/FedEx/etc it. If mailing it, it must be postmarked by Saturday, July 6. If you are faxing it or sending it electronically, you do not need to mail a paper copy of your work. However, I do recommend that you mail one in the event that there is a problem with your electronic or fax submission. If you are sending a mail copy of your test and work as back-up, it does not need to be postmarked by your test submission due date. However, this submission will need to be postmarked within two days of your test submission due date. My mailing address is:

Dr. David Levy
College of Business, HUM 200C
Bellevue University
1000 Galvin Rd South
Bellevue, NE 68005

Fax: 402.505.5771

This is an honor code test. You are expected to neither receive nor provide help on this test!!! Of course, you can use your course material and software programs.
Please read and follow these Notes!!!!!!
Notes:
1. Page 4 (the page after the scoring sheet) provides a summary sheet for providing just your final answers for selected problems. You should still provide your work and final answers for these problems on the appropriate problem page. 2. In the event that you believe that the problem is not clear or missing information, please state your assumptions and work accordingly. As appropriate and necessary, I will grade accordingly. 3. It is important to show your work or a sufficient amount of work so that I can understand if errors are math based or process based. If I only have answers and they are wrong, it is difficult to give partial credit. For example, for your calculations, you should provide the basic formula you are using at a minimum. 4. The answers to any problems that are entirely discussion questions must be typed and limited to a maximum of one page (double spaced, size 12 Times Roman or Arial font, one-inch margin on all four sides) per question. For example, if a problem has two short discussion questions, you can use a maximum of one page per discussion question. I will quit grading after one page. 5. If you do any work by hand, you may fax that part to me and send the rest electronically. 6. If providing software solutions, do not provide only the link to the software where I would need to either key the Solve button for the POM software or interpret your output for any of the software. You must provide the software output rather that you want graded. If I need to key the Solve button to obtain the answers, there will be a minor deduction. 7. If submitting electronically, please consolidate problems into a single document if possible or two documents if you are using both Word and Excel. If you are scanning each page as a separate document, I would prefer that you fax these. If using Excel, please format the page for printing to minimize the formatting that I will need to do. 8. If you are faxing it or sending it electronically, you do not need to mail a paper copy of your work. However, I do recommend that you mail one in the event that there is a problem with your electronic or fax submission. If you are sending a mail copy of your test and work as back-up, it does not need to be postmarked by your test submission due date. However, this submission will need to be postmarked within two days of your test submission due date.

9. If you provide software solutions, you must clearly mark and label your answers to each part of the problem.