Question

Free-Response Questions Directions: Show all work. Indicate clearly the methods you use. You will be graded on method as well as accuracy. 1) Consider the following risk profiles for two decision strategies: A and B. The payoffs are given in tens of thousands of dollars (18p.) A Payoff 4 11 14 18 Probability 0.20 0.30 0.20 0.30 В Рayoff 4 11 14 18 Probability 0.20 0.20 0.30 0.30 Determine each of the following statements as True or False A stochastically dominates B B stochastically dominates A. A deterministically dominates B. B deterministically dominates A. Neither A nor B stochastically dominates the other. Neither A nor B deterministically dominates the other. 2) The executives of a particular company are considering the national launch of a new product The launch will be either a "success" (resulting in a payoff of $8 million) or a "failure" (resulting in a loss of $2 million). The initial estimates of the probabilities of success and failure are 0.80 and 0.20, respectively The company has the opportunity to contract with a marketing firm in order to conduct a study determine whether or not the product will be a success. (40p.) a) What would be the maximum amount that the company should pay this marketing firm for the study, assuming that the study would be a perfect indicator of the success of the product? (EVPI) b) Assume that, for the company, data have been gathered as to the accuracy of studies made by the marketing firm. These data indicate the following conditional probabilities: P(study forecasts successlproduct is a success)-0.95, P(study forecasts failurelproduct is a failure)-0.90. What is the maximum amount that should be paid for this (imperfect) marketing study? (EVSI) 3) The president of Pegasus Corporation is trying to decide which of three candidates (denoted as candidates A, B, and C) to hire as the firm's new vice president of marketing The primary criteria the president is considering are each candidate's leadership ability, interpersonal skills, and administrative ability. After carefully considering their qualifications, the president used AHP to create the following pairwise comparison matrices for the three candidates on the various criteria: (42p.) Leadership Ability A B C 3 4 A 1 1/3 1/4 1 C 1/2 Interpersonal Skills Values of RI for use in AHP A RI (Random Index) 1 1/2 1 1/8 3 2 0.00 2 8 1/3 1 0.58 Administrative Ability 0.90 4 A C 1.12 5 1/8 1/3 1 A B 1/5 5 1 8 3 C Next, the president of Pegasus considered the relative importance of the three criteria. This resulted in the following pairwise comparison matrix: Criteria Administrative Аbility Interpersonal Skills Leadership Аbility 1/4 1/2 1/3 1 Leadership Ability Interpersonal Skills Administrative Ability 1 2 4 a) Use AHP to compute scores for each candidate on each of the three criteria and to compute weights for each of the criteria. b) Was the president consistent in making pairwise comparisons? (Check only for Leadership Ah) e) Compute the weighted average score for each candidate. Which candidate should be selected according to your results? BC

Answer 1

Answer: 1) Astochastically dominates B = False A stochastically dominates B =True A deterministically dominates B=False B deterministically dominates A=False Neither A nor B stochastically dominates the other False Neither A nor B deterministically dominates the other-True

3)

Calculation for leadership is given as below, Firstly write down the whole data and take the sum of it column-wise. The screenshots are given as below A C D E Pairwise Comparisons 2 3 X Y Z 3.000 4 1.000 4.000 2.000 Y 0.333 1.000 6 0.250 0.500 1.000 A C D E 1 Pairwise Comparisons 2 3 X Y Z 4 X 1.000 3.000 4.000 Y 0.333 1.000 2.000 6 7 0.250 0.500 1.000 7 Sum 1.583 4.500 7.00 X N N N L CO

Now, divide the each value by the sum of its column's value. The screenshot is given as below, =C4/C$7 C11 A C 1 Pairwise Comparisons 2 3 X Y Z 4.000 X 1.000 3.000 Y 0.333 1.000 2.000 6 7 0.250 0.500 1.000 7 Sum 1.583 4,500 7.00 Normalized Comparisons 9 10 X Z 11 X 0.632 0.667 0.571 12 Y 0.211 0.222 0.286 0.158 13 7 0.111 0.143 LO CO CO O

After this calculate the price scores by using the AVERAGE( ) function of excel. The screenshot is given as below, =AVERAGE(C11:E11) F11 A B C E 1 Pairwise Comparisons 2 3 X Y 7 4 1.000 3.000 4.000 Y 0.333 1.000 2.000 6 0.250 0.500 1.000 7 Sum 1.583 4.500 7.00 8 Normalized Comparisons 9 Price 10 X Y Scores 11 X 0.632 0.667 0.571 0.623 0.211 12 Y 0.222 0.286 0.239 0.111 13 Z 0.158 0.143 0.137 X N N oN co o

Now, calculate the consistency measure by using the MMULT( ) function of excel. The screenshot is given as below fox =MMULT(C4:E4,$F$11:$F$13)/F11 G11 A C D F 1 Pairwise Comparisons 2 3 X Y 7 4 X 1.000 3.000 4.000 5 Y 0.333 1.000 2.000 0.500 4.500 6 Z 0.250 1.000 1.583 7 Sum 7.00 Normalized Comparisons Consistency Measure 3.034 9 Price Scores 10 X Y 7 X 11 0.632 0.667 0.571 0.623 12 Y 0.211 0.222 0.286 0.239 3.014 0.143 0.137 13 Z 0.158 0.111 3.007 4 4 N N

Finally calculate the consistency ratio by using the AVERAGE( ) function of excel. The screenshot is given as below, - AVERAGE(G11:G13) -3)/(2*0.58) G15 A C D E F G 1 Pairwise Comparisons 2 3 X Y Z 4 X 1.000 3.000 4.000 5 Y 0.333 1.000 2.000 6 7 0.250 0.500 1.000 7 Sum 1.583 4.500 7.00 Normalized Comparisons Consistency Measure Price 10 X Y Z Scores 0.632 0.211 11 0.667 0.571 0.623 3.034 3.014 12 Y 0.222 0.286 0.239 0.158 13 0.111 0.143 0.137 3.007 14 Consistency Ratio: 15 0.016 X N

Similarly do calculation for interpersonal skills. The only change is that change in formula of consistency easure. The changed formula of and whole calculated screenshot is given as m below, =(AVERAGE(G11:G13)-3)/2/0.58 G15 A C D E F G 1 Pairwise Comparisons 2 3 X Y Z 4 X 1.000 0.500 3.000 5 Y 2.000 1.000 8.000 7 0.333 0.125 1.000 1.625 12.000 7 Sum 3.333 Normalized Comparisons Support Consistency 10 X Y Z Score Measure 11 0.300 0.308 0.250 0.286 3.007 12 Y 0.600 0.615 0.667 0.627 3.018 13 7 0.100 0.077 0.083 0.087 3.002 14 Consistency Ratio: 15 0.008 N X N Nm O Nco o

Similarly do calculation for administrative skills. The only change is that change in formula of consistency measure. The changed formula of and whole calculated screenshot is given as below, (AVERAGE(G11:G13)-3)/2/0.58 G15 A C E F G 1 Pairwise Comparisons 2 3 X Y Z 4 X 1.000 0.200 0.125 5 Y 5.000 1.000 0.333 6 7 8.000 3.000 1.000 7 Sum 14.000 4.200 1.458 8 Normalized Comparisons Consistency 9 Ease 10 X Y Z Score Measure 11 0.071 0.048 0.086 0.068 3.008 12 Y 0.357 0.238 0.229 0.275 3.040 13 7 0.571 0.714 0.686 0.657 3.085 14 Consistency Ratio: 15 0.038 m X N

Similarly do calculation for criteria. The only change is that change in formula of consistency measure. The changed formula of and whole calculated screenshot is given as below, (AVERAGE(G11:G13)-3)/2/0.58 G15 A C D F G 1 Pairwise Comparisons 2 Leadership IP Skills 1.000 3 Admin Skills 4 Leadership 0.333 0.250 5 IP Skills 3.000 1.000 0.500 2.000 6 Admin Skillls 4.000 1.000 7 Sum 8.000 3.333 1.750 Normalized Comparisons Leadership IP Skills 0.125 Criterion Consistency Weight 0.123 9 10 Admin Skills Measure Leadership 3.006 11 0.100 0.143 0.286 12 IP Skills 0.375 0.300 0.320 3.019 Admin Skills 13 0.500 0.600 0.571 0.557 3.030 14 Consistency Ratio: 15 0.016

The table for the combination of each calculated values is given as below C D E F 1 2 Alternative Criterion 3 Criterion X Y Z Weights Leadership 4 0.623 0.239 0.137 0.123 5 IP Skills 0.286 0.627 0.087 0.320 6 Admin Skills 0.068 0.275 0.657 0.557 Weighted Avg Score: 1.000 7 0.206 0.383 0.411

b. On seeing the above calculation, it can be said that the president is consistent in making pairwise comparison

C. Again take the table of combination of each comparison, A C D E G 1 Alternative 2 Criterion Criterion X Y Z Weights 0.623 4 Leadership IP Skills 0.239 0.137 0.123 0.286 0.627 0.087 0.320 Admin Skills 0.068 0.275 0.657 0.557 Weighted Avg Score: 0.206 1.000 7 0.383 0.411 On seeing the above table it is clear that candidate Z should be selected as the weighted average score is the highest for it. N LO C

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