1. Chapter 3
Decision Analysis

2. Decision Theory
Decision theory is the analytic and systematic approach for making the best decision.

3. Features of Decision Making
Decision making is for __________.
a. past b. future c. both past and future
A decision is about a (an) _________.
status b. action c. condition
The process of making decision is a process of __________.
producing b. manufacturing c. creating
d. cooking e. selecting f. fabricating

4. Components in Decision Making (1 of 2)
Alternatives of a decision
A list of choices, one of which will be selected as the decision by the decision maker.
States of Nature
Possible conditions that may actually occur in the future, which will affect the outcome of your decision but are beyond your control.

5. Components in Decision Making (2 of 2)
Payoffs
a payoff is the outcome of a decision alternative under a state of nature. The larger the payoff the better.
The decision alternatives, states of nature and payoffs are organized in a decision table.

6. Decision Table for the Thompson Lumber Example
Decision Alternatives
States of Nature
Favorable Market
Unfavorable Market
Build a large plant
$200,000
-$180,000
Build a small plant
$100,000
-$20,000
Doing nothing $0

7. Types of Decision Making
Decision making under certainty
The outcome of a decision alternative is known (i.e., there is only one state of nature.)
Decision making under risk
The outcome of a decision alternative is not known, but its probability is known.
Decision making under uncertainty
The outcome of a decision alternative is not known, and even its probability is not known.

8. Decision Making under Uncertainty
The outcome of a decision alternative is not known, and even its probability is not known.
A few criteria (approaches) are available for the decision makers to select according to their preferences and personalities.

9. Criterion 1: Maximax (Optimistic)
Step 1. Pick maximum payoff of each alternative.
Step 2. Pick maximum of those maximums in Step 1; its corresponding alternative is the decision.
“Best of bests”.

10. Maximax Decision for Thompson Lumber
States of Nature Row
Decision Favorable Unfavorable Maximum
Alternatives market market
Large plant ,000 –180, ,000
Small plant ,000 –20, ,000
Do nothing
Max(Row max’s) = Max(200,000, 100,000, 0) = 200,000.
So, the decision is ‘Large plant’.

11. For Whom? MaxiMax is an approach for:
Risk taker who tends not to give up attractive opportunities regardless of possible failures, or
Optimistic decision maker in whose eyes future is bright.

12. Criterion 2: Maximin (Pessimistic)
Step 1. Pick minimum payoff of each alternative
Step 2. Pick the maximum of those minimums in Step 1, its corresponding alternative is the decision
“Best of worsts”

13. Maximin Decision for Thompson Lumber
States of Nature Row
Decision Favorable Unfavorable Minimum
Alternatives market market payoffs
Large plant ,000 –180, –180,000
Small plant ,000 –20,000 –20,000
Do nothing
Max(Row Min’s) = Max(–180,000, –20,000, 0) = 0.
So, the decision is ‘do nothing’.

14. For Whom? MaxiMin is an approach for:
Risk averter who tends to avoid bad outcomes despite of some possible attractive outcomes; or
Pessimistic decision maker in whose eyes future is obscure.

15. Criterion 3: Hurwicz (Realism)
Step 1. Calculate Hurwicz value for each alternative
Step 2. Pick the alternative of largest Hurwicz value as the decision.

16. Hurwicz Value Hurwicz value of an alternative
= (row max)() + (row min)(1-)
where  (01) is called coefficient of realism.

17. Decision by Hurwicz Value for Thompson Lumber
=0.8
States of Nature
Decision Favorable Unfavorable Hurwicz
Alternatives market market values
Large plant ,000 –180, ,000
Small plant , –20, ,000
Do nothing
Max(Hurwicz values) = Max(124,000,76,000,0) = 124,000.
So, the decision is ‘large plant’.

18. For Whom?
Hurwicz method can be used by decision makers with different preferences on risks.
For a person who tends to take risk, a larger  is used;
For a person who tends to be conservative, a smaller  is used.
What if  = 1?
What if  = 0?

19. Criterion 4: Equally Likely
Step 1. Calculate the average payoff for each alternative.
Step 2. The alternative with highest average if the decision.

20. Decision by Equally Likely for Thompson Lumber
States of Nature Row
Decision Favorable Unfavorable Average
Alternatives market market
Large plant ,000 –180, ,000
Small plant , –20, ,000
Do nothing
Max(Row avg’s) = Max(10,000, 40,000, 0) = 40,000.
So, the decision is ‘small plant’.

21. For Whom?
Equally Likely method is for the decision maker who does not have particular preference on taking or avoiding risks.

22. Criterion 5: Minimax Regret
Step 1. Construct a ‘regret table’,
Step 2. Pick maximum regret of each row in regret table,
Step 3. Pick minimum of those maximums in Step 2, its corresponding alternative is the decision.

23. Regret
Regret is amount you give up due to not picking the best alternative in a given state of nature.
Regret = Opportunity cost = Opportunity loss

24. Payoff Table for Thompson Lumber and Column Maximums
States of Nature
Decision Favorable Unfavorable
Alternatives market market
Large plant $200,000 -$180,000
Small plant $100, $20,000
Doing nothing $ $0
Column Max $200, $0

25. Regret Table for Thompson Lumber
States of Nature
Decision Favorable Unfavorable
Alternatives market market
Large plant $0 $180,000
Small plant $100, $20,000
Doing nothing $200, $0

26. Minimax Regret Decision for Thompson Lumber
Regret Table
States of Nature
Decision Favorable Unfavorable Row
Alternatives market market Maximum
Large plant , ,000
Small plant , , ,000
Do nothing , ,000
Min(Row max’s) = Min{180,000, 100,000, 200,000}
= 100,000.
So, the minimax regret decision is ‘small plant’.

27. For Whom?
MiniMax Regret is an approach for the decision maker who hates the feeling of having regrets.

28. Decision Making under Risk
The outcome of a decision alternative is not known, but its probability is known.

29. Max EMV Approach Step 1. Calculate EMV for each alternative.
Step 2. Pick the alternative with highest EMV as the decision.

30. EMV – expected monetary value
EMV of an alternative is the expected value of possible payoffs of that alternative.
EMV
n=number of states of nature
P(Xi)=probability of the i-th state of nature
Xi=payoff of the alternative under the i-th state of nature

31. Example of Thompson Lumber
States of Nature
Decision Favorable Unfavorable
Alternatives market market EMV
Large plant $200, $180, ,000
Small plant $100, $20, ,000
Doing nothing $ $

32. Minimum EOL Approach Step 1. Generate the opportunity loss table.
Step 2. Calculate the expected value (EOL) for each alternative in the opportunity loss table.
Step 3. Pick up the alternative with the minimum EOL.

33. Opportunity Loss Table
Opportunity loss = Regret = Opp. cost
Opportunity loss table = Regret Table

34. Payoff Table for the Thompson Lumber Example
Decision Alternatives
States of Nature
Favorable Market
Unfavorable Market
Build a large plant
$200,000
-$180,000
Build a small plant
$100,000
-$20,000
Doing nothing $0

35. Opportunity Loss table and EOL for Thompson Lumber
States of Nature
Decision Favorable Unfavorable
Alternatives market market EOL
Large plant $0 $180,000
Small plant $100, $20,000
Doing nothing $200, $0

36. Expected Value of Perfect Information (EVPI)
It is value of additional information for better decision making.
It is an upper bound on how much to pay for the additional information.

37. Calculating EVPI EVPI = (Exp. payoff with perfect information) –
(Exp. payoff without perfect information)
= EVwPI – EVw/oPI

38. EVw/oPI
EVw/oPI is the average payoff you expect to get based only on the information given in the decision table without the help of additional information.
EVw/oPI = Max (EMV)

39. EVw/oPI = Maximum EMV States of Nature Decision Favorable Unfavorable
Alternatives market market EMV
Large plant $200, $180, ,000
Small plant $100, $20, ,000
Doing nothing $ $
Since Max EMV = 40,000,
EVw/oPI = 40,000.

40. EVwPI
EVwPI is the average payoff you can get if following the perfect information about the state of nature in the future.
EVwPI
where n=number of states of nature
bi=best payoff of i-th state of nature
Pi=probability of i-th state of nature

41. EVwPI for the Example of Thompson
States of Nature
Decision Favorable Unfavorable
Alternatives market market EMV
Large plant $200, $180, ,000
Small plant $100, $20, ,000
Doing nothing $ $
bi $200, $0
EVwPI = 200,000*0.5+0*0.5 = 100,000

42. EVPI for Thompson Lumber
EVwPI = 200,000* *0.50 = $100,000
EVw/oPI = Maximum EMV = $40,000
EVPI = EVwPI – EVw/oPI
= $100,000 – $40,000
= $60,000

43. EVPI is a Benchmark in Purchasing Additional Information
EVPI is the maximum $ amount the decision maker would pay to purchase the additional information about the states of nature (from a consulting firm, for example).

44. What if Information Is Not Perfect?
In most cases, information about future is not “perfect”. We need to discount EVwPI properly in those cases.
If you have 80% of confidence on the information, then
Expected Value of Additional Information = EVAI
= EVwPI * 80% - EVw/oPI

45. Maximum EMV, Minimum EOL, and EVPI
The decision selected by the Maximum EMV approach is always the same as the decision selected by the Minimum EOL approach. (why?)
The value of EVPI is equal to the value of minimum EOL. (why?)

46. An Example You can play the game for many times.
Someone offers you perfect information about “landing” at the price of $65 per time. Do you take it? If not, how much would you pay?
(See the handout of class work)
Land on ‘Head’
Land on ‘Tail’
Guess ‘Head’
$100
- $60
Guess ‘Tail’
- $80
$150

47. In the Tossing Coin Example
EMV for “guess Head” = $20.
EMV for “guess Tail” = $35* (Max EMV).
EOL for “guess Head” = $105
EOL for “guess Tail” = $90* (Min EOL)
EVwPI = $125, EVw/oPI=$35
EVPI = $90

48. Maximum average payoff per game$
Maximum average payoff per game
125
regret
EOL
regret
EOL
average
payoff
EMV 35
average
payoff
EMV
Alt. 2,
Guess “Tail” 20
Alt. 1,
Guess “Head”
Alternatives

49. How to Set Up a Decision Table
A decision table is set up by the decision maker.
Determine decision alternatives and states of nature.
Determine the payoffs of each alternative under the states of nature.
See case “Garden Salad” in class work.