1. Decision Making without State Probabilities
This is called DMUU—Decision Making Under Uncertainty

2. Decision Criteria
No state probabilities??--Your model is one of UNCERTAINTY
Use UNCERTAINTY criteria
Got state probabilities??--Your model is one of RISK
Use RISK criteria
(probabilities—probability information)

3. UNCERTAINTY Criteria—used when we don’t know the state probabilities
Based on DM’s attitude toward the risk
Pessimist, also called maximin
Optimist, also called maximax
in-betweenist
Insufficient reason
Regrettist, also called minimax regret

4. RISK Criteria Based on expected or probabilistic considerations
Expected payoff or value
Expected regret

5. Other RISK-related measures
Expected payoff of perfect information
Expected value of perfect information
Expected payoff of sample (imperfect) information
Expected value of sample [imperfect) information

6. Scenario
Consider the needs of a program manager who must decide which among several projects to bid on.
Due to resource constraints only one of the projects can be bid on.
There are two future states—WIN the bid or LOSE the bid

7. The Payoff Table

8. Assume we don’t know the win/lose probabilities
So we have to use the UNCERTAINTY criteria
Pessimist criterion
Optimist criterion
Regrettist criterion
In-betweenist criterion
Insufficient reason criterion

9. PESSIMIST CRITERION
1) For each row, find the smallest payoff in the row and record that in a column to the right, labeled ROW MINIMUM
2) Examine the column to the right labeled ROW MINIMUM and pick the alternative with the largest payoff in that column.

10. Pessimist Criterion--best of all of the worst-case scenarios
Do Nothing
Winner is…

11. OPTIMIST CRITERION
1) For each row, find the largest payoff in the row and record that in a column to the right, labeled ROW MAXIMUM
2) Examine the column to the right labeled ROW MAXIMUM and pick the alternative with the largest payoff in that column.

12. Optimist Criterion--best of all of the best-case scenarios
Bid Project 2
Winner is…

13. IN-BETWEENIST CRITERION
1) For each row, combine the smallest payoff in the row with the largest payoff in the row using the formula:
*ROW MIN + (1 - )*ROW MAX
record that in a column to the right, labeled COMBINED;
2) Examine the column labeled COMBINED to the right and pick the alternative with the largest payoff in that column.

14. In-Betweenist Criterion—alpha = .5
Bid Project 2
Winner is…

15. REGRETTIST CRITERION 1) Form the regret table.
2) For each row in the regret table, find the largest regret number in the row and record that in a column to the right labeled ROW MAXIMUM.
3) Examine the column labeled ROW MAXIMUM to the right and pick the alternative with the smallest regret in that column.

16. Regret Criterion

17. Regret Table
The Winner is…
Bid Project 2

18. Two Environments Decision-making under uncertainty
When we don’t know the state probabilities
Optimist, pessimist, in-betweenist, insufficient reason, regrettist
Decision-making under risk
When we do know the state probabilities
Expected value or payoff
Expected regret

19. Decision Making under Risk
Criteria
Expected value or payoff
Expected regret
Measures
Expected payoff of perfect information
Expected value of perfect information
Expected payoff of sample information
Expected value of sample information

20. DMUR Criterion
DMUR (Decision-Making Under risk) Expected Value Criterion
1) For each row,calculate the product of the column probability with the payoff in that column and add up all of the products, recording the result in the column labeled EXPECTED VALUE to the right of the payoff table
2) Examine the column labeled EXPECTED VALUE to the right and pick the alternative with the largest payoff in that column.

21. DMUR--Expected Value
Do Project 2!

22. EXPECTED REGRET Criterion
1) Form the regret table
2) For each row calculated its expected regret by taking the product of each state probability with the regret number in that column, summing all such products
3) Pick the alternative (i.e., row) whose expected regret is smallest
This will always be the same alternative that gets chosen by the expected value or payoff criterion.

23. Expected Regret
Do Project 2
The Winner is…

24. Expected Value & Regret

25. Notes
For any alternative, the expected value and expected regret numbers sum to the expected payoff of perfect information.
The expected value and expected regret criteria always select the same alternative, because when the former is maximized, the latter is minimized.

26. Expected Payoff of Perfect Information, EPPI
Calculated by finding the largest payoff in each column and then taking the products with the column probabilities and summing these products
The EPPI is the best we could do if we had perfect information.
$70,000 for this problem

27. Expected Value of Perfect Information, EVPI
By definition, EVPI = EPPI - EV*
EVPI = $70,000 - $67,000 = $3,000
The EVPI is the value to us of the additional information
The value is the “best we could do with the additional information” minus the “best we could do without the additional information”

28. More Notes
The minimum expected regret is also the EXPECTED VALUE OF PERFECT INFORMATION—THE ABSOLUTE MAXIMUM WE WOULD BE WILLING TO PAY FOR ADDITIONAL INFORMATION.
PROOF??

30. RULE OF INSUFFICIENT REASON
1) For each row, add-up all of the payoffs in that row and record the result in a column to the right labeled ROW SUM.
2) Examine the column labeled ROW SUM to the right and pick the alternative with the largest payoff in that column.

31. Insufficient Reason
Winner is…
Bid Project 2