Please show all work as it was solved to these 10 questions. I need it completed and emailed to me at 8:00pm Eastern Standard Time today, April 20, 2013.
1. (26 points)
a) A fast-food restaurant serves hamburgers, cheeseburgers, and chicken sandwiches. The restaurant counts a cheeseburger as equivalent to 1.25 hamburgers and chicken sandwiches as 0.8 hamburger. Output is measured in the number of units produced. Current employment is five full-time employees (each working a 40-hour week).
· In week one, if the restaurant sold 700 hamburgers, 900 cheeseburgers, and 500 chicken sandwiches in one week, what is its labor productivity?
· Suppose you want to increase the productivity you just calculated by 10%. To do this, you can only increase the number of hamburgers while keeping the number of cheeseburgers, chicken sandwiches, conversion rates and labor hours the same. How many hamburgers would you need to make to achieve this goal? Leave the units in decimal form as follows x.xx.
· In week two, what would its productivity have been if it had sold the same number of sandwiches (2,100) but the mix was 700 of each type?
· What would be the percentage change in productivity from week one to week two?
b) Burger Doodle is a fast-food restaurant that processes an average of 700 food orders each day. The average cost of each order is $6.16. Four percent of the orders are incorrect and only 10 percent of those defective orders can be and are corrected with additional food items at an average cost of $1.75. The remaining defective orders have to be thrown out.
Consider the output as the number of correct food orders, what is the multifactor productivity value for Burger Doodle based on the information provided here.
2. (20 points)
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 three forecasting methods to see which method provides a better forecast for the occupancy rate.
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%)
You are asked to forecast the Occupancy Rate for Year 9. Although you believe there might be a linear regression relationship, your boss has told you to only consider the following three forecasting methods:
· 3-period moving average
· 3-period weighted moving average with the following given weights of 0.6 and 0.3 for the most recent and next most recent periods, and the remaining weight (s) consistent with this method as we have used in class, and
· exponential smoothing with α = 0.3 and the forecast for Year 4 for the Occupancy Rate is 86.0.
a) What is the forecast from each of these methods for Year 9?
b) Which forecasting method provides the better forecast for Year 9? Why? Your selection criteria must be based on one of the numerical evaluation methods we have used on the homework this term using the forecast results for Year 5 through Year 8.
c) Based on your analysis in b), would you recommend using the forecasting method and the resulting forecast that you selected in b)? Identify the key factors, including key one(s) presented in class, that should be considered in making this decision.
3. (24 points)
ABC’s production line of the Widget gadget has a fixed cost of $200,000 and the variable cost is $5 per unit.
a) If the company sells the first 10,000 units at a price of $20 and then sells all additional units at $15 per unit, what is the break-even point?
b) Suppose that the company is considering outsourcing this to DEF company. If so, it will save the fixed and variable costs per unit. If the cost of outsourcing is $13 per unit, over what range would each of the production options (in-house and outsourcing) be preferred? Assume that the price per unit will remain the same whether it produces the product internally or outsources it.
c) Suppose that the company has determined that its demand is going to be 10,000 units. What is the outsourcing cost per unit that makes the two production alternatives equal to each other? Assume that the price per unit will remain the same whether it produces the product internally or outsources it.
d) Johndoe Company is interested in buying the Widget gadget from ABC. Johndoe Company is open to letting ABC manufacture them in-house or outsource them under certain conditions. Johndoe will only buy the outsourced if ABC reduces the selling price to $18 per unit. Also, if ABC does outsource this, Johndoe will only buy 8,000 units. On the other hand, if ABC produces the product internally, Johndoe will be willing to pay $20 per unit for all the products and Johndoe will buy 12,000 widgits. Economically, which option (produce internally or outsource) is better for ABC?
4. (16 points)
a) What is a poka-yoke? A typical word processing software package (such as Word, WordPerfect, etc.) is loaded with poka-yokes. List any two of these. Briefly explain your selections.
b) 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.
5. (22 points)
Blackburn Engineering, a parts reseller in Nashville, is currently considering using one of three suppliers. For a specific part, Blackburn’s upper specification limit (USL) is 8.8 centimeters (cm) and its lower specification limit (LSL) is 6.5 centimeters (cm).
a) The first supplier, ABC, can adjust its mean but cannot reduce its standard deviation. Its standard deviation is 0.3 cm. What is the range (lower and upper limits) for the mean of the process if ABC wants its process capability index (C_{pk}) to satisfy at least Blackburn’s minimum acceptable value of 1.33?
b) The second supplier, DEF, cannot adjust the mean of its process which is currently 7.5 cm. However it can improve its standard deviation if necessary. What is the maximum standard deviation (σ) allowed if DEF wants its process capability index (C_{pk}) to be at least the minimum acceptable value of 1.33?
c) The third supplier, GEF has a process whose standard deviation is 0.6 cm and the mean of its process is 7.3 cm. Answer the following:
6. (17 points)
A company manufactures stamped steel products. With global competition increasing, the company is looking at options for it to be in a more competitive position. There are three possible market conditions that can develop. There can be high market demand with a probability of 0.4, there can be medium market demand with a probability of 0.5, or there can be a low market demand with a probability of 0.1. It is currently looking at three options. It can automate now (referred to as the Automate Now decision), form an Alliance or delay the decision (referred to as Delayed Decision) for two years. If the company decides to Automate Now, the present value of the returns (this means that the returns are expressed in terms of today’s dollars) are $4.0 million if there is high market demand, $2.6 million if there is medium market demand, and $2 million if there is low market demand. The company could also form an Alliance with one of its suppliers. In this case, the present value of the returns for high, medium, and low market demand are $3 million, $2.8 million and $1 million respectively.
The company can also delay this situation for two years (referred to as Delayed Decision). At that point the company would either automate then or outsource. If it automates then (referred to as Automates Later), the expected return for this decision is $2.5 million. If it Outsources Later at that time, the expected return is $3.3 million.
a) Draw the appropriate decision tree for this company and using an expected value approach, what decision should the company make. Provide your supporting work.
b) Now, consider only the Automate Now and Delayed Decision options. Let everything else be the same except for the return for the high market demand for the Automate Now option. What would this return have to be so that the Automate Now and Delayed Decision options are equal?
7. (13 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.
Critical Success Factor |
Factor Weight |
Kansas City |
Atlanta |
Cost per computer |
0.50 |
$3,900 |
$4,300 |
Cost of living |
0.10 |
1.2 |
1.4 |
Labor availability |
0.10 |
1.4 |
1.4 |
Union activities |
0.15 |
0.8 |
1.2 |
Proximity to similar industries |
0.10 |
1.4 |
1.0 |
Local transportation systems |
0.05 |
1.4 |
1.8 |
The non-economic scores are on a 0 to 2.0 basis with 2.0 being best and it is possible to achieve the 2.0 score.
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 |
Labor availability |
1.0 |
Union activities |
1.1 |
Proximity to similar industries |
1.0 |
Local transportation systems |
1.2 |
Given the information provided in the problem, what would you conclude about the cost of the computer from Omaha that would let Omaha 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?
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?
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. (29 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 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. What is the probability that the arriving customer will not wait?
The following information is for parts d) and e). 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 the adding the second tax preparer, the arrival rate increases to a customer arriving every 8 minutes following a Poisson arrival process.
d) 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)?
e) Suppose the servers in the two server model are complaining about their hourly pay ($50 per hour and $40 per hour respectively for the first and second servers). How much could Wizard afford to pay the two servers in total (combined) to be indifferent between the one server and two server options? For the single server scenario, assume that the server will continue to receive the $50 hourly pay. The pay only changes for the two server model.
Subject | Business |
Due By (Pacific Time) | 04/20/2013 02:47 pm |
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