Project #53969 - OM Question 7-10

7.  (16 points)

 

A company is evaluating Kansas City and Atlanta as alternative locations for a new plant to manufacture PC’s for small businesses.  The following information has been collected.  They want to use this information to compare the two locations. 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.  On each  scale, the highest score is always the best value.  For example, for the scale 0-4, the best value is 4.  For each of the Non-economic factors, it is possible to score the maximum.   

 

 

Critical Success Factor

Factor Weight

Scale

Kansas City

Atlanta

Cost per computer 

0.50

 

$3,900

$4,300

Non-economic factors

 

 

 

 

Cost of living

0.10

0-2

1.2

1.4

Labor availability

0.10

0-3

2.1

2.1

Union activities

0.15

0-4

1.6

2.4

Proximity to similar industries

0.10

0-2

1.4

1.0

Local transportation systems

0.05

0-2

1.4

1.8

 

 

a) Using the factor scoring (rating) method as we learned in class, which site should be selected?  

 

 

 

 

 

b)  Suppose that the company wants to consider Omaha as a third site.  Although the cost per computer for Omaha has not been determined yet, the company does know it will be more than $3,900.  The scores for the qualitative factors have been determined and are the following:   

 

Critical Success Factor

Omaha

Cost per computer 

???

Cost of living

1.4

Non-economic factors

 

Labor availability

1.5

Union activities

2.2

Proximity to similar industries

1.0

Local transportation systems

1.2

 

Given the information provided in the problem and the additional information provided in this part of the problem, is there a Cost per computer that makes it possible for Omaha to be the preferred location? 

 

 

 

8.  (16 points)  

 

Let’s re-examine the information presented previously in problem 2. Following are the number of victories for the Blue Sox and the hotel occupancy rate for the past eight years.  You have been asked to test two forecasting methods to see which method provides a better forecast for the Occupancy Rate.  The forecasting methods to test are to see whether Occupancy Rate is a) a function of time or b) a function of the Number of Blue Sox Wins.  

 

Year

Number of Blue Sox Wins

Occupancy Rate

1

70

78%

2

67

83

3

75

86

4

87

85

5

87

89

6

91

92

7

89

91

8

85

94

 

For the following, calculate all forecasts to one decimal place (example, 93.2%)

 

a)  Suppose we believe that there is a linear relationship between the Year and the Occupancy Rate.  Develop a forecast for the Occupancy Rate assuming that this relationship is valid.  What is this relationship and what is the forecast for the Occupancy Rate for Year 10?  Provide both the appropriate regression relationship and the forecast.

 

 

 

 

 

 

b)  Now, suppose that we believe that there is a linear relationship between the Number of Blue Sox Wins and the Occupancy Rate.  What is this relationship and what is the forecast for the Occupancy Rate if the Number of Blue Sox Wins is 98 wins?  What caution(s) would you recommend about using the linear regression relationship for predicting the occupancy rate for this number of wins?   Provide both the appropriate regression relationship and the forecast.

 

 

 

 

 

 

 

c)  How strong are the relationships you found in both a) and b)?  You are wondering if either of these should be considered – not which is better.  Would you recommend using either of these relationships for forecasting?  Why? 

 

 

9. (17 points)

 

One of Alabama Air’s top competitive priorities is on-time arrivals.  The airline defines “on-time” to mean any arrival that is within 20 minutes of the scheduled time.  The airline’s management has monitored the performance for the past 15 weeks.  They checked a random sample of 100 flight arrivals each week for on-time performance.  The table that follows contains the number of flights that did not meet Alabama Air’s definition of on-time.

 

Week

1

2

3

4

5

6

7

8

0

10

11

12

13

14

15

Late Flights

2

4

10

4

1

1

13

9

11

1

3

4

2

2

8

 

Assume that there is sufficient data to perform the appropriate SPC analysis.

 

a)  Using a 95% confidence level, develop the appropriate control limits for the percentage of late flights.  Plot these control limits on a control chart.  

 

 

 

 

 

 

 

b)  Also, plot the percentage of late flights in each sample on the control chart.

 

 

 

c) Based on the results of a) and b), what would you conclude about Alabama Air’s ability to meet its control limits?  Explain your answer.

 

 

 

 

 

 

 

 

d)  Now, the airline industry’s standards for flights that are not on-time are expressed in the form of upper and lower specification limits.  These upper and lower limits are 0.126 and 0.040 respectively.  What would you conclude about Alabama Air’s ability to meet the industry standards?  Explain your answer.    

 

 

10.  (26 points)

 

The Wizard Tax Service is analyzing its operations during the month prior to the April 15 tax filing date.  There is currently only one tax preparer at Wizard.  On the basis of past data, it has been estimated that customers arrive according to a Poisson process with an average time between arrivals of 12 minutes.  When the tax return is being completed, the customer is at the tax preparer’s desk working with the preparer and this is considered the service time.  The time to complete a return for a customer is exponentially distributed with a mean time of 10 minutes.  Customers are processed in the order of arrival.  Based on this information, answer the following questions.

 

a)  On average and measured from when a customer arrives at Wizard, how much time does the customer spend at the tax service, whether waiting to have the tax preparer work on his return or having his tax return completed?

 

 

b)  What is the average number of customers at the tax service, whether waiting for the tax preparer or having the return prepared?

 

 

c)  An arriving customer will not wait if there are at least three others waiting for the tax preparer to start preparing their returns.  What is the probability that the arriving customer will not wait?

 

 

 

 

d)  Wizard is considering adding a second tax preparer.  This tax preparer will also complete returns following an exponential distribution with a mean time of 10 minutes.  As a result of adding the second tax preparer, the arrival rate increases to a customer arriving every 8 minutes following a Poisson arrival process.  Suppose the cost of the first preparer is $50 per hour and the cost of the second preparer is only $40 per hour.   Also, the cost of a customer while waiting for a tax preparer to start preparing the return is $125 per hour.  What is the cost of each option (the single tax preparer and the two tax preparer options)?  

 

 

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Due By (Pacific Time) 01/17/2015 10:21 pm
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