# Decision Analysis and Probability Tree

Problems: 9-13, 15, 16, 18, 19, 20

Scenario 15-1

An investor is considering 4 investments, A, B, C and leaving his money in the bank. The payoff from each investment is a function of the economic climate over the next 2 years. The economy can expand or decline. The following payoff matrix has been developed for the decision problem.

A B C D

1 Payoff Matrix

2

3 Economy

4 Investment Decline Expand

5 A 0 85

6 B 25 65

7 C 40 30

8 Bank 10 10

Payoffs

____ 9. Refer to Scenario 15-1. What decision should be made according to the maximin decision rule?

a. A

b. B

c. C

d. Bank

____ 10. Refer to Scenario 15-1. What decision should be made according to the minimax regret decision rule?

a. A

b. B

c. C

d. Bank

Scenario 15-2

An investor is considering 4 investments, A, B, C and leaving his money in the bank. The payoff from each investment is a function of the economic climate over the next 2 years. The economy can expand or decline. The following payoff matrix has been developed for the decision problem.

A B C D E F G H

1 Payoff Matrix Regret Matrix

2

3 Economy Economy

4 Investment Decline Expand Investment Decline Expand

5 A 0 85 A

6 B 25 65 B

7 C 40 30 C

8 Bank 10 10 Bank

____ 11. Refer to Scenario 15-2. What formula should go in cell F5 of the Regret Matrix to compute the regret value?

a. =B$5-MAX(B$5:B$8)

b. =MAX(B$5:B$8)-MAX(B5)

c. =MAX(B$5:B$8)-MIN(B$5:B$8)

d. =MAX(B$5:B$8)-B5

____ 12. Expected regret is also called

a. EMV.

b. EOL.

c. EPA.

d. EOQ.

Scenario 15-3

An investor is considering 4 investments, A, B, C and leaving his money in the bank. The payoff from each investment is a function of the economic climate over the next 2 years. The economy can expand or decline. The following payoff matrix has been developed for the decision problem. The investor has estimated the probability of a declining economy at 70% and an expanding economy at 30%.

A B C D

1 Payoff Matrix

2

3 Economy

4 Investment Decline Expand EMV

5 A -10 90

6 B 20 50

7 C 40 45

8 Bank 15 20

9

10 Probability 0.7 0.3

Payoffs

____ 13. Refer to Scenario 15-3. What decision should be made according to the expected monetary value decision rule?

a. A

b. B

c. C

d. Bank

Scenario 15-5

An investor is considering 4 investments, A, B, C, D. The payoff from each investment is a function of the economic climate over the next 2 years. The economy can expand or decline. The following decision tree has been developed for the problem. The investor has estimated the probability of a declining economy at 40% and an expanding economy at 60%.

____ 15. Refer to Scenario 15-5. What is the correct decision for this investor based on an expected monetary value criteria?

a. A

b. B

c. C

d. D

____ 16. Refer to Scenario 15-5. What is the expected monetary value for the investor's problem?

a. 32

b. 36

c. 38

d. 42

Scenario 15-6

A company is planning a plant expansion. They can build a large or small plant. The payoffs for the plant depend on the level of consumer demand for the company's products. The company believes that there is an 69% chance that demand for their products will be high and a 31% chance that it will be low. The company can pay a market research firm to survey consumer attitudes towards the company's products. There is a 63% chance that the customers will like the products and a 37% chance that they won't. The payoff matrix and costs of the two plants are listed below. The company believes that if the survey is favorable there is a 92% chance that demand will be high for the products. If the survey is unfavorable there is only a 30% chance that the demand will be high. The following decision tree has been built for this problem. The company has computed that the expected monetary value of the best decision without sample information is 154.35 million. The company has developed the following conditional probability table for their decision problem.

A B C D

1

2 Joint Probabilities

3 High Demand Low Demand Total

4 Favorable Response 0.58 0.05 0.63

5 Unfavorable

Response 0.11 0.26 0.37

6 Total 0.69 0.31 1.00

7

8

9 Conditional Probability

10 For A Given Survey Response

11 High Demand Low Demand

12 Favorable Response 0.92 0.08

13 Unfavorable Response 0.30 0.70

14

15 Conditional Probability

16 For A Given Demand Level

17 High Demand Low Demand

18 Favorable Response 0.84 0.16

19 Unfavorable Response 0.16 0.84

____ 18. Refer to Scenario 15-6. What formula should go in cell C13 of the probability table?

a. =C5/$D4

b. =C5/C$6

c. =C5/$D5

d. =C4/$D4

Scenario 15-7

A decision maker is faced with two alternatives. The decision maker has determined that she is indifferent between the two alternatives when p=0.45.

Alternative 1: Receive $82,000 with certainty

Alternative 2: Receive $143,000 with probability p and lose $15,000 with probability (1-p).

____ 19. Refer to Scenario 15-7. What is the decision maker's certainty equivalent for this problem?

a. -$15,000

b. $82,000

c. $56,100

d. $82,000

____ 20. What is the formula for the weighted average score for alternative j when using a multi-criteria scoring model?

a.

b.

c.

d.

#### Solution Summary

The solution is comprised of a detailed explanation of the various aspects of Decision Analysis. This step-by-step calculation of these complicated topics provides students with a clear perspective of Decision Tree, Maximin Criterion, Minimax Regret Criterion, Regret Matrix, Expected Regret, Expected Value Criterion, Certainity Equivalent, etc.