IE 2030 Lecture 7 Decision Analysis

1. IE 2030 Lecture 7Decision Analysis Expected Value Utility Decision Trees

2. Introduction to PERT Decision tree example: party planning Concepts: Uncertainty Minimax Criterion Expected Value Criterion Risk Aversion Risk Neutral, Risk Averse, Risk Seeking Utility Outcome and Decision Decision Tree Value of information Sensitivity analysis Topics Today IE 2030 Lecture 7

3. 900 Clear .6 Party Example (R. Howard) Rain .4 100 OUT IN 600 Clear .6 Rain .4 500

4. Decision Trees • Use different shapes for decisions and uncertain branchings • Compute from the leaves back to the root • Use expected values • When you make a decision, you know the history, the path from the root to the decision point

5. Minimax or Maximin Criterion • Choice to make worst possible outcome as good as possible • Usually gives poor decisions because excessively risk averse • Fearful people use this criterion • Are you afraid of being judged badly afterwards? • Decisions vs. Outcomes Probability of regret

6. Maximin and other Payoff Criteria • Who is your opponent? • An indifferent Nature… • use probability, consider expected value • A hostile or vengeful Fate... • Use Maximin, consider a psychiatrist • A self-interested person… • use game theory and economics • A hostile person who desires your failure... • use game theory, maximin, consider an intermediary or arbitrator

7. Never attribute to malice, what can be adequately explained by stupidity Trust and Credibility

8. Risk aversion • Choice of sure thing versus lottery • Size • Gain or loss • Expected value criterion • Utility

9. It is expensive to be poor • Companies don’t like to risk going out of business • Wealthier people can afford to gamble • get higher average returns • We model this by setting very low utility values on outcomes below “danger” threshholds • Can cause problems in environmental decisions. Is going bankrupt as bad as destroying the world’s ecology?

10. Decision Analysis: Value of Information (based on R. Howard’s notes) 900 out Clear .6 in 600 Rain .4 100 out in 500

11. Value of Information • Expected value of a clairvoyant (perfect information) is an upper bound on the value of any forecast • Analysis assumes your probabilities are correct • Must use conditional probability to find probabilities of imperfect forecasts

12. Forecast probabilities: simple example • Consistently 90% accurate forecast: whatever the forecast, it is correct w.p..9 • If it rains 50% of the time, forecast rain w.p. .5 • If it rains 90% of time, forecast rain w.p. 1 • If it rains 100% of time, consistent 90% accuracy is impossible • Many forecasts have inconsistent accuracy

13. Forecast probabilities: party example • Consistently 90% accurate forecast: whatever the forecast, it is correct w.p..9 • If it rains 40% of time, forecast rain w.p. q. • .9q + .1(1-q) = 0.4 • LHS = Prob(rain), calculated over event partition: {predict rain, don’t predict rain} • You must decide what to do for each possible forecast • What if the forecast were 0% accurate?