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

2. Topics Today IE 2030 Lecture 7 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

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

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) Clear.6 Rain.4 out in out in 900 600 100 500

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 Predict Clear 5/8 Predict Rain 3/8 out in out in 900 600 100 500 900 100 600 500.9 clear.1 rain clear.1 rain.1 clear.9 rain. 1 clear.9 rain

14. Value of 90% accurate forecast Predict Clear 5/8 Predict Rain 3/8 820 590 180 510 out in out in 900 600 100 500 900 100 600 500.9 clear.1 rain clear.1 rain.1 clear.9 rain. 1 clear.9 rain

15. Value of 90% accurate forecast 820 510 Predict Clear 5/8 Predict Rain 3/8 820 590 180 510 out in out inininin 900 600 100 500 900 100 600 500.9 clear.1 rain clear.1 rain.1 clear.9 rain. 1 clear.9 rain

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 clairvoyantExpected 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. Model: Abstraction, Representation 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

21. Abstraction

22. 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 < 150Build small rooms Assume 2 Schools like ISyE 100+ 75 > 150Build 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?