1. DECISION THEORY & DECISION TREE
Components of Decision Making
Decision Making Under Uncertainty (Without Probabilities)
Decision Making Under Risk (With Probabilities)
Decision Analysis with Additional Information
Utility

2. The Six Steps in Decision Theory
Clearly define the problem at hand
List the possible alternatives
Identify the possible outcomes
List the payoff or profit of each combination of alternatives and outcomes
Select one of the mathematical decision theory models
Apply the model and make your decision

3. 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.
Payoff Table

4. Types of Decision-Making Environments
Type 1: Decision-making under certainty
decision-maker knows with certainty the consequences of every alternative or decision choice
Decision-making under uncertainty (without probability)
The decision-maker does not know the probabilities of the various outcomes
Type 2: Decision-making under risk (with probability)
The decision-maker does know the probabilities of the various outcomes

5. Decision Analysis Decision Making without Probabilities
Decision situation: An investor wants to decide which of the three property to buy.
Decision-Making Criteria:
Maximax, Maximin, Minimax, Minimax Regret, Hurwicz,
Equal Likelihood (Laplace)
Payoff Table for the Real Estate Investments

6. Decision Making without Probabilities The Maximax Criterion
In the maximax criterion the decision maker selects the decision that will result in the maximum of maximum payoffs; an optimistic criterion.
Payoff Table Illustrating a Maximax Decision

7. Decision Making without Probabilities The Maximin Criterion
In the maximin criterion the decision maker selects the decision that will reflect the maximum of the minimum payoffs; a pessimistic criterion.
Payoff Table Illustrating a Maximin Decision

8. Decision Making without Probabilities The Minimax Regret Criterion
Regret is the difference between the payoff from the best decision and all other decision payoffs.
The decision maker attempts to avoid regret by selecting the decision alternative that minimizes the maximum regret.
Regret Table Illustrating the Minimax Regret Decision

9. Decision Making without Probabilities The 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

10. Decision Making without Probabilities The 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

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 liklihood Apartment building

12. Decision Making without Probabilities Solutions with QM for Windows (1 of 2)

13. Decision Making without Probabilities Solutions with QM for Windows (2 of 2)

14. Decision Making under Risk (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

15. 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

16. Decision Making with Probabilities Solution of Expected Value Problems with QM for Windows

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.

18. Decision Making with Probabilities EVPI Example
Decision with perfect information: $100,000(.60) + 30,000(.40) = $72, Decision without perfect information: EV(office) = $100,000(.60) - 40,000(.40) = $44, EVPI = $72, ,000 = $28, EOL(office) = $0(.60) + 70,000(.4) = $28,000

19. Decision Making with Probabilities EVPI with QM for Windows

20. Decision Making with Probabilities Decision Trees
A decision tree is a diagram consisting of decision nodes (represented as squares), probability nodes (circles), and decision alternatives (branches).