1. Decision Analysis
Chapter 12

2. Chapter Topics Components of Decision Making
Decision Making without Probabilities
Decision Making with Probabilities
Decision Analysis with Additional Information
Utility
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3. Components of Decision Making
Decision Analysis
Components of Decision Making
A state of nature is an actual event that may occur in the future.
A payoff table is a means of organizing a decision situation, presenting the payoffs from different decisions given the various states of nature.
Table Payoff Table
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4. Decision Analysis Decision Making Without Probabilities
Figure 12.1
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5. Decision Making without Probabilities
Decision Analysis
Decision Making without Probabilities
Decision-Making Criteria
maximax maximin
minimax regret Hurwicz equal likelihood
Table 12.2
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6. Table 12.3 Payoff Table Illustrating a Maximax Decision
Decision Making without Probabilities
Maximax Criterion
In the maximax criterion the decision maker selects the decision that will result in the maximum of maximum payoffs; an optimistic criterion.
Table Payoff Table Illustrating a Maximax Decision
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7. Table 12.4 Payoff Table Illustrating a Maximin Decision
Decision Making without Probabilities
Maximin Criterion
In the maximin criterion the decision maker selects the decision that will reflect the maximum of the minimum payoffs; a pessimistic criterion.
Table Payoff Table Illustrating a Maximin Decision
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8. Decision Making without Probabilities Hurwicz Criterion
The Hurwicz criterion is a compromise between the maximax and maximin criterion.
A coefficient of optimism, , is a measure of the decision maker’s optimism.
The Hurwicz criterion multiplies the best payoff by  and the worst payoff by (1- ), for each decision, and the best result is selected.
Decision Values
Apartment building $50,000(.4) + 30,000(.6) = 38,000
Office building $100,000(.4) - 40,000(.6) = 16,000
Warehouse $30,000(.4) + 10,000(.6) = 18,000
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9. Table 12.6 Regret Table Illustrating the Minimax Regret Decision
Decision Making without Probabilities
Minimax Regret Criterion
Regret is the difference between the payoff from the best decision and all other decision payoffs (opportunity cost).
The decision maker attempts to avoid regret by selecting the decision alternative that minimizes the maximum regret.
Table Regret Table Illustrating the Minimax Regret Decision
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10. Decision Making without Probabilities Equal Likelihood Criterion
The equal likelihood (or Laplace) criterion multiplies the decision payoff for each state of nature by an equal weight, thus assuming that the states of nature are equally likely to occur.
Decision Values
Apartment building $50,000(.5) + 30,000(.5) = 40,000
Office building $100,000(.5) - 40,000(.5) = 30,000
Warehouse $30,000(.5) + 10,000(.5) = 20,000
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11. Decision Making without Probabilities Summary of Criteria Results
A dominant decision is one that has a better payoff than another decision under each state of nature.
The appropriate criterion is dependent on the “risk” personality and philosophy of the decision maker.
Criterion Decision (Purchase)
Maximax Office building
Maximin Apartment building
Minimax regret Apartment building
Hurwicz Apartment building
Equal likelihood Apartment building
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12. Decision Making without Probabilities
Solution with QM for Windows (1 of 3)
Exhibit 12.1
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13. Decision Making without Probabilities
Solution with QM for Windows (2 of 3)
Exhibit 12.2
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14. Decision Making without Probabilities
Solution with QM for Windows (3 of 3)
Exhibit 12.3
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15. Decision Making with Probabilities Expected Value
Expected value is computed by multiplying each decision outcome under each state of nature by the probability of its occurrence.
EV(Apartment) = $50,000(.6) + 30,000(.4) = 42,000
EV(Office) = $100,000(.6) - 40,000(.4) = 44,000
EV(Warehouse) = $30,000(.6) + 10,000(.4) = 22,000
Table 12.7
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16. Decision Making with Probabilities Expected Opportunity Loss
The expected opportunity loss is the expected value of the regret for each decision.
The expected value and expected opportunity loss criterion result in the same decision.
EOL(Apartment) = $50,000(.6) + 0(.4) = 30,000
EOL(Office) = $0(.6) + 70,000(.4) = 28,000
EOL(Warehouse) = $70,000(.6) + 20,000(.4) = 50,000
Table 12.8
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17. Decision Making with Probabilities
Expected Value of Perfect Information
The expected value of perfect information (EVPI) is the maximum amount a decision maker would pay for additional information.
EVPI equals the expected value given perfect information minus the expected value without perfect information.
EVPI equals the expected opportunity loss (EOL) for the best decision.
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18. Table 12.9 Payoff Table with Decisions, Given Perfect Information
Decision Making with Probabilities
EVPI Example (1 of 2)
Table Payoff Table with Decisions, Given Perfect Information
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19. Decision Making with Probabilities EVPI Example (2 of 2)
EV of Decision with perfect information:
$100,000(.60) + 30,000(.40) = $72,000
EV of Decision without this perfect information:
EV(office) = $100,000(.60) - 40,000(.40) = $44,000
EVPI = $72, ,000 = $28,000
EOL(office) = $0(.60) + 70,000(.4) = $28,000
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20. Table 12.10 Payoff Table for Real Estate Investment Example
Decision Making with Probabilities
Decision Trees (1 of 4)
A decision tree is a diagram consisting of decision nodes (represented as squares), probability nodes (circles), and decision alternatives (branches).
Table Payoff Table for Real Estate Investment Example
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21. Figure 12.2 Decision Tree for Real Estate Investment Example
Decision Making with Probabilities
Decision Trees (2 of 4)
Figure Decision Tree for Real Estate Investment Example
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22. Decision Making with Probabilities Decision Trees (3 of 4)
The expected value is computed at each probability node:
EV(node 2) = .60($50,000) + .40(30,000) = $42,000
EV(node 3) = .60($100,000) + .40(-40,000) = $44,000
EV(node 4) = .60($30,000) + .40(10,000) = $22,000
Branches with the greatest expected value are selected.
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23. Figure 12.3 Decision Tree with Expected Value at Probability Nodes
Decision Making with Probabilities
Decision Trees (4 of 4)
Figure Decision Tree with Expected Value at Probability Nodes
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24. Decision Making with Probabilities Decision Trees with QM for Windows
Exhibit 12.9
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25. Decision Making with Probabilities Sequential Decision Trees (1 of 4)
A sequential decision tree is used to illustrate a situation requiring a series of decisions.
Used where a payoff table, limited to a single decision, cannot be used.
Real estate investment example modified to encompass a ten-year period in which several decisions must be made:
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26. Decision Making with Probabilities Sequential Decision Trees (2 of 4)
Figure Sequential Decision Tree
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27. Decision Making with Probabilities Sequential Decision Trees (3 of 4)
Figure Sequential Decision Tree with Nodal Expected Values
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28. Decision Making with Probabilities Sequential Decision Trees (4 of 4)
Decision is to purchase land; highest net expected value ($1,160,000).
Payoff of the decision is $1,160,000.
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29. Sequential Decision Tree Analysis Solution with QM for Windows
Exhibit 12.14
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30. Decision Analysis with Additional Information Utility (1 of 2)
Table Payoff Table for Auto Insurance Example
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31. Decision Analysis with Additional Information Utility (2 of 2)
Expected Cost (insurance) = .992($500) (500) = $500
Expected Cost (no insurance) = .992($0) (10,000) = $80
Decision should be do not purchase insurance, but people almost always do purchase insurance.
Utility is a measure of personal satisfaction derived from money.
Utiles are units of subjective measures of utility.
Risk averters forgo a high expected value to avoid a low-probability disaster.
Risk takers take a chance on a very low-probability event in spite of a sure thing.
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32. Example Problem Solution (1 of 9)
Decision Analysis
Example Problem Solution (1 of 9)
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33. Example Problem Solution (2 of 9)
Decision Analysis
Example Problem Solution (2 of 9)
Determine the best decision without probabilities using the 5 criteria of the chapter.
Determine best decision with probabilities assuming .70 probability of good conditions, .30 of poor conditions. Use expected value and expected opportunity loss criteria.
Compute expected value of perfect information.
Develop a decision tree with expected value at the nodes.
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34. Example Problem Solution (3 of 9)
Decision Analysis
Example Problem Solution (3 of 9)
Step 1 (part a): Determine decisions without probabilities.
Maximax Decision: Maintain status quo
Decisions Maximum Payoffs
Expand $800,000
Status quo 1,300,000 (maximum)
Sell ,000
Maximin Decision: Expand
Decisions Minimum Payoffs
Expand $500,000 (maximum)
Status quo -150,000
Sell ,000
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35. Example Problem Solution (4 of 9)
Decision Analysis
Example Problem Solution (4 of 9)
Minimax Regret Decision: Expand
Decisions Maximum Regrets
Expand $500,000 (minimum)
Status quo 650,000
Sell ,000
Hurwicz ( = .3) Decision: Expand
Expand $800,000(.3) + 500,000(.7) = $590,000
Status quo $1,300,000(.3) - 150,000(.7) = $285,000
Sell $320,000(.3) + 320,000(.7) = $320,000
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36. Example Problem Solution (5 of 9)
Decision Analysis
Example Problem Solution (5 of 9)
Equal Likelihood Decision: Expand
Expand $800,000(.5) + 500,000(.5) = $650,000
Status quo $1,300,000(.5) - 150,000(.5) = $575,000
Sell $320,000(.5) + 320,000(.5) = $320,000
Step 2 (part b): Determine Decisions with EV and EOL.
Expected value decision: Maintain status quo
Expand $800,000(.7) + 500,000(.3) = $710,000
Status quo $1,300,000(.7) - 150,000(.3) = $865,000
Sell $320,000(.7) + 320,000(.3) = $320,000
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37. Example Problem Solution (6 of 9)
Decision Analysis
Example Problem Solution (6 of 9)
Expected opportunity loss decision: Maintain status quo
Expand $500,000(.7) + 0(.3) = $350,000
Status quo (.7) + 650,000(.3) = $195,000
Sell $980,000(.7) + 180,000(.3) = $740,000
Step 3 (part c): Compute EVPI.
EV given perfect information = 1,300,000(.7) + 500,000(.3) = $1,060,000
EV without perfect information = $1,300,000(.7) - 150,000(.3) = $865,000
EVPI = $1.060, ,000 = $195,000
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38. Example Problem Solution (7 of 9)
Decision Analysis
Example Problem Solution (7 of 9)
Step 4 (part d): Develop a decision tree.
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