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. 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

12. 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?

13. Value of 90% accurate forecast .9 clear 900 .1 rain out 100 in Predict Clear 5/8 600 clear .1 rain 500 900 Predict Rain 3/8 .1 clear out .9 rain 100 in .1 clear 600 .9 rain 500

14. Value of 90% accurate forecast .9 clear 900 820 .1 rain out 100 in Predict Clear 5/8 600 clear 590 .1 rain 500 900 Predict Rain 3/8 .1 clear 180 out .9 rain 100 in .1 clear 600 510 .9 rain 500

15. Value of 90% accurate forecast .9 clear 900 820 .1 rain out 100 820 in Predict Clear 5/8 600 clear 590 .1 rain 500 900 Predict Rain 3/8 .1 clear 180 out .9 rain 510 100 in .1 clear 600 510 .9 rain 500

16. Expected Value of 90% accurate forecast • If you had the forecast, expected value of party scenario is • (5/8)820 + (3/8)510 = 703.75 • If you had no forecast, expected value=580 • Expected value of forecast = 123.75 • Compare with perfect info value 160

17. 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

18. IE 2030 Lecture 9 • PERT intro • Project 1a recap • What is a model? • Quiz • Homework: problems not questions; drawing cpm networks

19. WHAT IS A MODEL?

20. Alberti, Brunelleschi Process Flow Diagram Map Graphs: Euler, MARTA Light as Particles Light as Waves How flies move in a straight line How fish form ellipsoidal schools Why great whales are in danger of extinction Why there aren’t enough big classrooms at Georgia Tech Model: Abstraction, Representation

21. Abstraction

22. Abstraction • Infinitely many models of the same reality • Often a model is created for a purpose • a good model discards the irrelevant • a good model retains what is crucial • Often we believe we understand something better after modeling it • We trust a model if it gives accurate predictions (qualitative or quantitative) • Words are mental models. Reality?

23. Example: Why Few Large Classrooms at Georgia Tech ? • Benefit of large room to ISyE: 110 • Benefit of large room 1/2 time: 100 • Benefit of 2 small rooms to ISyE: 150 • Benefit of 1 small room: 75 • 110 < 150 Build small rooms • Assume 2 Schools like ISyE • 100+ 75 > 150 Build a large room

24. QUIZ: SHORT ANSWERS • WHY ISN’T THE STROH BREWERY CLASSIFIED AS A PURE CONTINUOUS FLOW PROCESS? • WHAT MAKES IT POSSIBLE FOR THE PACKAGING PORTION OF THE PROCESS TO RUN SMOOTHLY, DESPITE THE HYBRID NATURE OF THE WHOLE SYSTEM?