1. LECTURE TWELVE
Decision-Making
UNDER UNCERTAINITY

2. Introduction
Decision analysis provides a framework and methodology for rational decision making when the outcomes are uncertain.
Example: A company plans to determine the best location to startup a new plant from a choice of several locations. Each location offers a different cost scenario. Decision Analysis techniques can be used to determine the best decision.

3. Payoff Table
States of Nature refer to future events which may occur and the values in a Payoff Table refer to either Profit or Cost. Example: s1, s2 & s3 could refer to possible scenarios (i.e. Moderate, Strong & Weak market demand)
States of Nature
s s s3 d
Decisions d d

4. Simple Decision Making without Probabilities
Three commonly used criteria for decision making when probability information regarding the likelihood of the states of nature is unavailable are:
the Optimistic approach (Maximax or Minimin)
the Conservative approach (Maximin or Minimax)
the Minimax Regret approach.

5. Optimistic Approach
The optimistic approach would be used by an optimistic decision maker.
The decision with the largest possible payoff is chosen.
If the payoff table was in terms of costs, the decision with the lowest cost would be chosen.

6. Example: Optimistic Approach
Consider the following problem with three decision alternatives and three states of nature with the following payoff table representing profits:
States of Nature
s s s3 d
Decisions d d

7. Example: Optimistic Approach
The Optimistic Approach is to make decision based on the maximum of the largest profits. For each decision, d, the largest profits are identified (i.e. 4, -1 & 5)
Formula Spreadsheet

8. Example: Optimistic Approach
Solution Spreadsheet

9. Conservative Approach
The conservative approach would be used by a conservative decision maker.
For each decision the minimum payoff is listed and then the decision corresponding to the maximum of these minimum payoffs is selected.
If the payoff was in terms of costs, the maximum costs would be determined for each decision and then the decision corresponding to the minimum of these maximum costs is selected.

10. Example: Conservative Approach
Based on the same table with three decision alternatives and three states of nature with the following payoff table representing profits:
States of Nature
s s s3 d
Decisions d d

11. Example: Conservative Approach
Formula Spreadsheet

12. Example: Conservative Approach
Solution Spreadsheet

13. Minimax Regret Approach
The minimax regret approach requires the construction of a regret table or an opportunity loss table.
This is done by calculating for each state of nature the difference between each payoff and the largest payoff for that state of nature.
Then, using this regret table, the maximum regret for each possible decision is listed.
The decision chosen is the one corresponding to the minimum of the maximum regrets.

14. Example: Minimax Regret Approach
Compute a regret table by subtracting each payoff in a column from the largest payoff in that column. Add a Max Regret Col and make decision based on the Minimum of Maximum Regret. Example: 4, 0, 1 is subtracted by 4 giving OL 0, 4, 3, etc.
s1 OL s2 OL s3 OL Max Regret d d d

15. Example: Minimax Regret Approach
Formula Spreadsheet

16. Example: Minimax Regret Approach
Solution Spreadsheet

17. Decision Making with Probabilities
Expected Value Approach
If probabilities regarding the states of nature is available, we may use the expected value (EV) approach. Decision is based on maximising EV.
The expected value (EV) of decision alternative di is defined as:
where: N = the number of states of nature
P(sj ) = the probability of state of nature sj
Vij = the payoff corresponding to decision alternative di and state of nature sj

18. Example: Expected Value Approach
ABC Restaurant
Average Number of Customers Per Hour
s1 = s2 = s3 = 120
Model A $10, $15, $14,000
Model B $ 8, $18, $12,000
Model C $ 6, $16, $21,000
Probability
Given s1, s2 & s3 have the probabilities: 0.4, 0.2 & 0.4

19. Example: Expected Value Approach
Formula Spreadsheet

20. Example: Expected Value Approach
Solution Spreadsheet

21. Expected Value of Perfect Information
The expected value of perfect information (EVPI) is the increase in the expected profit that would result if one knew with certainty which state of nature would occur.
EVPI = EVwPI – Max EV where EVwPI = ∑ Pi * Max Vi where Vi is the payoffs and EVwPI = Expected Value with Perfect Information

22. Expected Value of Perfect Information
Spreadsheet

23. Decision Tree Payoffs 10,000 2 15,000 d1 14,000 8,000 d2 1 3 18,000 d3
Average Number of Customers Per Hour
s1 = s2 = s3 = 120
Model A $10, $15, $14,000
Model B $ 8, $18, $12,000
Model C $ 6, $16, $21,000
Probabilities
Payoffs s1 .4
10,000 s2 .2 2
15,000 s3 .4 d1
14,000 .4 s1
8,000 d2 1 3 s2 .2
18,000 d3 s3 .4
12,000 s1 .4
6,000 4 s2 .2
16,000 s3 .4
21,000

24. Decision Tree d1 2 Model A Model B d2
Choose the model with largest EV, Model C.
EMV = .4(10,000) + .2(15,000) + .4(14,000)
= $12,600 d1 2
Model A
EMV = .4(8,000) + .2(18,000) + .4(12,000)
= $11,600
Model B d2 1 3 d3
EMV = .4(6,000) + .2(16,000) + .4(21,000)
= $14,000
Model C 4

25. Decision Tree with Tree Plan
Open ‘tree164e.xla’ and enable Macro first.

26. Decision Tree with Tree Plan

27. Decision Tree with Tree Plan

28. Decision Tree with Tree Plan

29. TOM BROWN INVESTMENT DECISION
Tom Brown has inherited $1000.
He has to decide how to invest the money for one year.
A broker has suggested five potential investments.
Gold
Junk Bond
Growth Stock
Certificate of Deposit
Stock Option Hedge

30. TOM BROWN
The return on each investment depends on the (uncertain) market behavior during the year.
Tom would build a payoff table to help make the investment decision

31. The Payoff Table DJA is down more than 800 points
DJA moves within
[-300,+300]
DJA is up
[+300,+1000]
DJA is up more than1000 points

32. Task Evaluate each investment alternative using: Maximax approach
Maximin approach
Minimax Regret approach
EV approach
And construct Decision Tree for EV approach
Calculate EVPI

33. QUESTIONS

34. Review Questions:
1. What is meant by ‘decision-making under uncertainty’? 2. Why should sequential decisions be considered differently from a series of separate decisions? 3. How can you identify the best decisions in a decision tree?