1. Slides 8a: Introduction

2. Decision Analysis A set of alternative actions
We may chose whichever we please
A set of possible states of nature
Only one will be correct, but we don’t know in advance
A set of outcomes and a value for each
Each is a combination of an alternative action and a state of nature
Value can be monetary or otherwise

3. Decision Analysis Certainty Ignorance Risk
Decision Maker knows with certainty what the state of nature will be - only one possible state of nature
Ignorance
Decision Maker knows all possible states of nature, but does not know probability of occurrence
Risk
Decision Maker knows all possible states of nature, and can assign probability of occurrence for each state

4. Decision Making Under Certainty

5. Decision Making Under Ignorance – Payoff Table
Kelly Construction Payoff Table (Prob. 8-17)

6. Decision Making Under Ignorance
Maximax
Select the strategy with the highest possible return
Maximin
Select the strategy with the smallest possible loss
LaPlace-Bayes
All states of nature are equally likely to occur.
Select alternative with best average payoff

7. Maximax: The Optimistic Point of View
Select the “best of the best” strategy
Evaluates each decision by the maximum possible return associated with that decision (Note: if cost data is used, the minimum return is “best”)
The decision that yields the maximum of these maximum returns (maximax) is then selected
For “risk takers”
Doesn’t consider the “down side” risk
Ignores the possible losses from the selected alternative

8. Maximax Example
Kelly Construction

9. Maximin: The Pessimistic Point of View
Select the “best of the worst” strategy
Evaluates each decision by the minimum possible return associated with the decision
The decision that yields the maximum value of the minimum returns (maximin) is selected
For “risk averse” decision makers
A “protect” strategy
Worst case scenario the focus

10. Maximin
Kelly Construction

11. Decision Making Under Risk
Expected Return (ER)*
Select the alternative with the highest (long term) expected return
A weighted average of the possible returns for each alternative, with the probabilities used as weights
* Also referred to as Expected Value (EV) or Expected Monetary Value (EMV)
**Note that this amount will not be obtained in the short term, or if the decision is a one-time event!

12. Expected Return

13. Expected Value of Perfect Information
EVPI measures how much better you could do on this decision if you could always know when each state of nature would occur, where:
EVUPI = Expected Value Under Perfect Information (also called EVwPI, the EV with perfect information, or EVC, the EV “under certainty”)
EVUII = Expected Value of the best action with imperfect information (also called EVBest )
EVPI = EVUPI – EVUII
EVPI tells you how much you are willing to pay for perfect information (or is the upper limit for what you would pay for additional “imperfect” information!)

14. Expected Value of Perfect Information

15. Using Excel to Calculate EVPI: Formulas View
Kelly Construction

16. The Newsvendor Model
A newsvendor can buy the Wall Street Journal newspapers for 40 cents each and sell them for 75 cents.
However, he must buy the papers before he knows how many he can actually sell. If he buys more papers than he can sell, he disposes of the excess at no additional cost. If he does not buy enough papers, he loses potential sales now and possibly in the future.
Suppose that the loss of future sales is captured by a loss of goodwill cost of 50 cents per unsatisfied customer.

17. The demand distribution is as follows:
P0 = Prob{demand = 0} = 0.1
P1 = Prob{demand = 1} = 0.3
P2 = Prob{demand = 2} = 0.4
P3 = Prob{demand = 3} = 0.2
Each of these four values represent the states of nature. The number of papers ordered is the decision. The returns or payoffs are as follows:

18. State of Nature (Demand)
Decision
Payoff = 75(# papers sold) – 40(# papers ordered) – 50(unmet demand)
Where 75¢ = selling price
40¢ = cost of buying a paper
50¢ = cost of loss of goodwill

19. State of Nature (Demand)
Now, the ER is calculated for each decision:
ER0 = 0(0.1) – 50(0.3) – 100(0.4) – 150(0.2) = -85
ER1 = -40(0.1) + 35(0.3) – 15(0.4) – 65(0.2) = -12.5
ER2 = -80(0.1) – 5(0.3) + 70(0.4) + 20(0.2) = 22.5
ER3 = -120(0.1) – 45(0.3) + 30(0.4) – 105(0.2) = 7.5
State of Nature (Demand)
Decision ER
Prob
Of these four ER’s, choose the maximum,
and order 2 papers

20. ER(current) = 22.5 EVPI = 59.5 – 22.5 = 37.0 cents
State of Nature
Decision
Prob
ER(new) = 0(0.1) + 35(0.3) + 70(0.4) + 105(0.2)
= 59.5
ER(current) = 22.5
EVPI = 59.5 – 22.5 = 37.0 cents

21. Maximax Criterion: The Maximax criterion is an optimistic decision making criterion.
This method evaluates each decision by the maximum possible return associated with that decision.
The decision that yields the maximum of these maximum returns (maximax) is then selected.

22. Maximin Criterion: The Maximin criterion is an extremely conservative, or pessimistic, approach to making decisions.
Maximin evaluates each decision by the minimum possible return associated with the decision.
Then, the decision that yields the maximum value of the minimum returns (maximin) is selected.

23. So, using the 3 criteria, we made the following decisions regarding the newsvendor data:
Criteria Decision
Maximin Cash Flow Order 1 paper
Expected Return Order 2 papers
Maximax Cash Flow Order 3 papers

24. THE RATIONALE FOR UTILITY
Most people are risk-averse, which means they would feel that the loss of a certain amount of money would be more painful than the gain of
the same amount of money.
Utility functions in decision analysis measure the “attractiveness” of money.
Utility can be thought of as a measure of “satisfaction.”

25. Typical risk-averse utility function:
A gain in utility of 0.06
Utility
1.0
0.910
0.850
0.775
0.680
0.524
Dollars
Go from $400 to $500 results in

26. To illustrate, first suppose you have $100 and someone gives you an additional $100. Note that your utility increases by
U(200) – U(100) = – = 0.156
Now suppose you start with $400 and someone gives you an additional $100. Now your utility increases by
U(500) – U(400) = – = 0.060
This illustrates that an additional $100 is less attractive if you have $400 on hand than it is if you start with $100.

27. Utilities and Decisions under Risk
Summary:
Utility is a way to incorporate risk aversion into the expected return calculation.
Calculating a utility function is out of the scope of this course, but it can be calculated by a series of lottery questions (e.g., Would you prefer one million dollars or a 50% chance of earning five million?).