Models for Decision


Models for Decision
POST 1
BUSI48O15 Models for Decision
Full Time 2015 MBA
SUMMATIVE ASSIGNMENT
Attached below are three mini cases. Write a report to answer the questions in the mini-cases. You should structure your report in three sections, as follows:
1) Linear regression (30 marks).
2) Linear programming (30 marks).
3) Simulation (40 marks).
Where diagrams are used these should normally be included in the main body of your work. If they are located in the appendix they will not have a role in the assessment – examiners are under no obligation to read appendices.
In your report you should describe the formulas you used and critically present the results you obtained. You do not need to attach excel files with your submission.
Continued
BUSI48O15 Models for Decision Full Time 2015 MBA
© 2016
Page 2
Master of Business Administration
MINI CASE 1 ON LINEAR REGRESSION1
Dixie Showtime Movie Theathers, Inc., owns and operates a chain of cinemas in several markets in the southern United States. The owners would like to estimate weekly gross revenues as a function of advertising expenditures. Data (in hundreds of dollars) for a sample of eight markets for a recent week follow:
Market
Weekly Gross Revenue ($100s)
Television Advertising ($100s)
Newspaper Advertising ($100s)
Mobile
101.3
5.0
1.5
Shreveport
51.9
3.0
3.0
Jackson
74.8
4.0
1.5
Birmingham
126.2
4.3
4.3
Little Rock
137.8
3.6
4.0
Biloxi
101.4
3.5
2.3
New Orleans
237.8
5.0
8.4
Baton Rouge
219.6
6.9
5.8
1) Develop an estimated regression equation with the amount of television advertising as the independent variable. Test for a significant relationship between television advertising and weekly gross revenue at the 0.05 level of significance. What is the interpretation of this relationship? How much variation in the sample values of weekly gross revenues does this model explain?
2) Develop an estimated regression equation with both television and advertising and newspaper advertising as the independent variables. Is the overall regression statistically significant at the 0.05 level of significance? If so, then test whether each of the regression parameters
,
, and
is equal to zero at the 0.05 level of significance. What are the correct interpretations of the estimated regression parameters? Are these interpretations reasonable? How much variation in the sample values of weekly gross revenues does this model explain?
3) Given the results obtained, what should your next step be? Explain. What are the managerial implications of these results?
1 Source: Camm et al., 2015. Essentials of Business Analytics. First Edition. Stamford, CT, USA: CENGAGE Learning, p. 187.
BUSI48O15 Models for Decision Full Time 2015 MBA
© 2016
Page 3
Master of Business Administration
MINI CASE 2 ON LINEAR PROGRAMMING2
Round Tree Manor is a hotel that provides two types of rooms with three rental classes: “Super Saver”, “Deluxe”, and “Business”. The profit per night for each type of room and rental class is as follows:
Rental class
Room
Super Saver
Deluxe
Business
Type I
$30
$35

Type II
$20
$30
$40
Type I rooms do not have wireless Internet access and are not available for the Business rental class. Round Tree’s management makes a forecast of the demand by rental class for each night in the future. A linear programming model developed to maximise profit is used to determine how many reservations to accept for each rental class. The demand forecast for a particular night is 130 rentals in the “Super Saver” class, 60 rentals in the “Deluxe” class, and 50 rentals in the “Business” class. Round Tree has 100 Type I rooms and 120 Type II rooms.
1) Use linear programming to determine how many reservations to accept in each rental class and how the reservations should be allocated to room types. Is the demand by any rental class not satisfied? Explain.
2) The management is considering offering a free breakfast to anyone upgrading from a “Super Saver” reservation to “Deluxe” class. If the cost of the breakfast to Round Tree is $5, should this incentive be offered?
3) With a little work, an unused office area could be converted to a rental room. If the conversion cost is the same for both types of rooms, would you recommend converting the office to Type I or Type II room? Why?
4) Could the linear programming model be modified to plan for the allocation of rental demand for the next night? What information would be needed and how would the model change?
2 Source: Camm et al., 2015. Essentials of Business Analytics. First Edition. Stamford, CT, USA: CENGAGE Learning, p. 391.
BUSI48O15 Models for Decision Full Time 2015 MBA
© 2016
Page 4
Master of Business Administration
MINI CASE 3 ON SIMULATION3
OuRX, a retail pharmacy chain, is faced with the decision of how much flu vaccine to order for the next flu season. OuRX has to place a single order for the flu vaccine several months before the beginning of the season because it takes four to five months for the supplier to create the vaccine. OuRX wants to more closely examine the ordering decision because, over the past few years, the company has ordered too much vaccine and too little. OuRX pays a wholesale price of $12 per dose to obtain the flu vaccine from the supplier and then sells the flu shot to their customers at a retail price of $20. Based on industry trends as feedback from their marketing managers, OuRX has generated a rough estimate of flu vaccine demand at their retail pharmacies. OuRX is confident that demand will range from 800,000 doses to 4,500,000 doses. The following table lists probabilities for demand values within this range.
Demand
1,000,000
2,000,000
3,000,000
4,000,000
Probabilities
.05
.20
.50
.25
Because OuRX earns a profit on flu shots that it sells and it cannot sell more than its supply, the appropriate profit computation depends on whether demand exceeds the order quantity or vice versa. Similarly, the number of lost sales and excess doses depends on whether demand exceeds the order quantity and vice versa.
1) Construct a spreadsheet model that computes the net profit corresponding to a given level of demand and specified order quantity. Model demand is a random variable with Analytic Solver Platform custom general distribution.
2) Using simulation and optimisation, determine the order quantity that maximises expected profit. What is the probability of running out of flu vaccine at this order quantity?
3) How many doses does OuRX need to order so that the probability of running out of flu vaccine is only 25 percent? How much expected profit will OuRX lose if it orders this amount rather than the amount obtained from answering question 2?
3 Source: Camm et al., 2015. Essentials of Business Analytics. First Edition. Stamford, CT, USA: CENGAGE Learning, p. 532.
BUSI48O15 Models for Decision Full Time 2015 MBA
© 2016
Page 5
Master of Business Administration
Overall word limit 4,000 words maximum.
The word count should:
 Include all the text, including title, preface, introduction, in-text citations, quotations, footnotes and any other items not specifically excluded below.
 Exclude diagrams, tables (including tables/lists of contents and figures), equations, executive summary/abstract, acknowledgements, declaration, bibliography/list of references and appendices. However, it is not appropriate to use diagrams or tables merely as a way of circumventing the word limit. If a student uses a table or figure as a means of presenting his/her own words, then this is included in the word count.
Examiners will stop reading once the word limit has been reached, and work beyond this point will not be assessed. Checks of word counts will be carried out on submitted work, including any assignments or dissertations/business projects that appear to be clearly over-length. Checks may take place manually and/or with the aid of the word count provided via an electronic submission. Where a student has intentionally misrepresented their word count, the School may treat this as an offence under Section IV of the General Regulations of the University. Extreme cases may be viewed as dishonest practice under Section IV, 5 (a) (x) of the General Regulations.
Very occasionally it may be appropriate to present, in an appendix, material which does not properly belong in the main body of the assessment but which some students wish to provide for the sake of completeness. Any appendices will not have a role in the assessment – examiners are under no obligation to read appendices and they do not form part of the word count. Material that students wish to be assessed should always be included in the main body of the text.
YOUR COMPLETED ASSIGNMENT MUST BE SUBMITTED ELECTRONICALLY TO DUO NO LATER THAN 08.45AM, MONDAY 7Th MARCH 2016.
MARKING GUIDELINES
Performance in the summative assessment for this module is judged against the following criteria:
 Relevance to question(s)
 Organisation, structure and presentation
 Depth of understanding
BUSI48O15 Models for Decision Full Time 2015 MBA
© 2016
Page 6
Master of Business Administration
 Analysis and discussion
 Use of sources and referencing
 Overall conclusions
Assignments must be typed or word-processed using 1.5 line spacing and with margins of 2-3 cm. Pages should be numbered. The word count should include all the text (plus endnotes and footnotes), but exclude diagrams, tables, bibliography, references and appendices. Guidance on referencing can be found in your year handbook.
You are required to submit an electronic copy of your assignment on DUO which will be put through the plagiarism detection service.
PLAGIARISM AND COLLUSION
Students suspected of plagiarism, either of published work or the work of other students, or of collusion will be dealt with according to School and University guidelinesBUSI48O15 Models for Decision
Full Time 2015 MBA
SUMMATIVE ASSIGNMENT
Attached below are three mini cases. Write a report to answer the questions in the mini-cases. You should structure your report in three sections, as follows:
1) Linear regression (30 marks).
2) Linear programming (30 marks).
3) Simulation (40 marks).
Where diagrams are used these should normally be included in the main body of your work. If they are located in the appendix they will not have a role in the assessment – examiners are under no obligation to read appendices.
In your report you should describe the formulas you used and critically present the results you obtained. You do not need to attach excel files with your submission.
Continued
BUSI48O15 Models for Decision Full Time 2015 MBA
© 2016
Page 2
Master of Business Administration
MINI CASE 1 ON LINEAR REGRESSION1
Dixie Showtime Movie Theathers, Inc., owns and operates a chain of cinemas in several markets in the southern United States. The owners would like to estimate weekly gross revenues as a function of advertising expenditures. Data (in hundreds of dollars) for a sample of eight markets for a recent week follow:
Market
Weekly Gross Revenue ($100s)
Television Advertising ($100s)
Newspaper Advertising ($100s)
Mobile
101.3
5.0
1.5
Shreveport
51.9
3.0
3.0
Jackson
74.8
4.0
1.5
Birmingham
126.2
4.3
4.3
Little Rock
137.8
3.6
4.0
Biloxi
101.4
3.5
2.3
New Orleans
237.8
5.0
8.4
Baton Rouge
219.6
6.9
5.8
1) Develop an estimated regression equation with the amount of television advertising as the independent variable. Test for a significant relationship between television advertising and weekly gross revenue at the 0.05 level of significance. What is the interpretation of this relationship? How much variation in the sample values of weekly gross revenues does this model explain?
2) Develop an estimated regression equation with both television and advertising and newspaper advertising as the independent variables. Is the overall regression statistically significant at the 0.05 level of significance? If so, then test whether each of the regression parameters
,
, and
is equal to zero at the 0.05 level of significance. What are the correct interpretations of the estimated regression parameters? Are these interpretations reasonable? How much variation in the sample values of weekly gross revenues does this model explain?
3) Given the results obtained, what should your next step be? Explain. What are the managerial implications of these results?
1 Source: Camm et al., 2015. Essentials of Business Analytics. First Edition. Stamford, CT, USA: CENGAGE Learning, p. 187.
BUSI48O15 Models for Decision Full Time 2015 MBA
© 2016
Page 3
Master of Business Administration
MINI CASE 2 ON LINEAR PROGRAMMING2
Round Tree Manor is a hotel that provides two types of rooms with three rental classes: “Super Saver”, “Deluxe”, and “Business”. The profit per night for each type of room and rental class is as follows:
Rental class
Room
Super Saver
Deluxe
Business
Type I
$30
$35

Type II
$20
$30
$40
Type I rooms do not have wireless Internet access and are not available for the Business rental class. Round Tree’s management makes a forecast of the demand by rental class for each night in the future. A linear programming model developed to maximise profit is used to determine how many reservations to accept for each rental class. The demand forecast for a particular night is 130 rentals in the “Super Saver” class, 60 rentals in the “Deluxe” class, and 50 rentals in the “Business” class. Round Tree has 100 Type I rooms and 120 Type II rooms.
1) Use linear programming to determine how many reservations to accept in each rental class and how the reservations should be allocated to room types. Is the demand by any rental class not satisfied? Explain.
2) The management is considering offering a free breakfast to anyone upgrading from a “Super Saver” reservation to “Deluxe” class. If the cost of the breakfast to Round Tree is $5, should this incentive be offered?
3) With a little work, an unused office area could be converted to a rental room. If the conversion cost is the same for both types of rooms, would you recommend converting the office to Type I or Type II room? Why?
4) Could the linear programming model be modified to plan for the allocation of rental demand for the next night? What information would be needed and how would the model change?
2 Source: Camm et al., 2015. Essentials of Business Analytics. First Edition. Stamford, CT, USA: CENGAGE Learning, p. 391.
BUSI48O15 Models for Decision Full Time 2015 MBA
© 2016
Page 4
Master of Business Administration
MINI CASE 3 ON SIMULATION3
OuRX, a retail pharmacy chain, is faced with the decision of how much flu vaccine to order for the next flu season. OuRX has to place a single order for the flu vaccine several months before the beginning of the season because it takes four to five months for the supplier to create the vaccine. OuRX wants to more closely examine the ordering decision because, over the past few years, the company has ordered too much vaccine and too little. OuRX pays a wholesale price of $12 per dose to obtain the flu vaccine from the supplier and then sells the flu shot to their customers at a retail price of $20. Based on industry trends as feedback from their marketing managers, OuRX has generated a rough estimate of flu vaccine demand at their retail pharmacies. OuRX is confident that demand will range from 800,000 doses to 4,500,000 doses. The following table lists probabilities for demand values within this range.
Demand
1,000,000
2,000,000
3,000,000
4,000,000
Probabilities
.05
.20
.50
.25
Because OuRX earns a profit on flu shots that it sells and it cannot sell more than its supply, the appropriate profit computation depends on whether demand exceeds the order quantity or vice versa. Similarly, the number of lost sales and excess doses depends on whether demand exceeds the order quantity and vice versa.
1) Construct a spreadsheet model that computes the net profit corresponding to a given level of demand and specified order quantity. Model demand is a random variable with Analytic Solver Platform custom general distribution.
2) Using simulation and optimisation, determine the order quantity that maximises expected profit. What is the probability of running out of flu vaccine at this order quantity?
3) How many doses does OuRX need to order so that the probability of running out of flu vaccine is only 25 percent? How much expected profit will OuRX lose if it orders this amount rather than the amount obtained from answering question 2?
3 Source: Camm et al., 2015. Essentials of Business Analytics. First Edition. Stamford, CT, USA: CENGAGE Learning, p. 532.
BUSI48O15 Models for Decision Full Time 2015 MBA
© 2016
Page 5
Master of Business Administration
Overall word limit 4,000 words maximum.
The word count should:
 Include all the text, including title, preface, introduction, in-text citations, quotations, footnotes and any other items not specifically excluded below.
 Exclude diagrams, tables (including tables/lists of contents and figures), equations, executive summary/abstract, acknowledgements, declaration, bibliography/list of references and appendices. However, it is not appropriate to use diagrams or tables merely as a way of circumventing the word limit. If a student uses a table or figure as a means of presenting his/her own words, then this is included in the word count.
Examiners will stop reading once the word limit has been reached, and work beyond this point will not be assessed. Checks of word counts will be carried out on submitted work, including any assignments or dissertations/business projects that appear to be clearly over-length. Checks may take place manually and/or with the aid of the word count provided via an electronic submission. Where a student has intentionally misrepresented their word count, the School may treat this as an offence under Section IV of the General Regulations of the University. Extreme cases may be viewed as dishonest practice under Section IV, 5 (a) (x) of the General Regulations.
Very occasionally it may be appropriate to present, in an appendix, material which does not properly belong in the main body of the assessment but which some students wish to provide for the sake of completeness. Any appendices will not have a role in the assessment – examiners are under no obligation to read appendices and they do not form part of the word count. Material that students wish to be assessed should always be included in the main body of the text.
YOUR COMPLETED ASSIGNMENT MUST BE SUBMITTED ELECTRONICALLY TO DUO NO LATER THAN 08.45AM, MONDAY 7Th MARCH 2016.
MARKING GUIDELINES
Performance in the summative assessment for this module is judged against the following criteria:
 Relevance to question(s)
 Organisation, structure and presentation
 Depth of understanding
BUSI48O15 Models for Decision Full Time 2015 M


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