IE 2030 Lecture 7 Decision Analysis
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Transcript of IE 2030 Lecture 7 Decision Analysis
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IE 2030 Lecture 7Decision Analysis
Expected Value
Utility
Decision Trees
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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
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Party Example (R. Howard)
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Rain.4
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OUT
IN
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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
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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 regretProbability of regret
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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
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Never attribute to malice, what can be adequately explained by
stupidity
Trust and Credibility
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Risk aversion
• Choice of sure thing versus lottery
• Size
• Gain or loss
• Expected value criterion
• Utility
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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?
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Decision Analysis: Value of Information (based on R. Howard’s notes)
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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
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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?
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Value of 90% accurate forecast
Predict
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5/8PredictRain3/8
outin
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.9 clear
.1 rain
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Value of 90% accurate forecast
Predict
Clear
5/8PredictRain3/8
820
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180
510
outin
out
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.9 clear
.1 rain
clear
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Value of 90% accurate forecast
820
510
Predict
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5/8PredictRain3/8
820
590
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510
outoutin
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iinn
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100
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.9 clear
.1 rain
clear
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.1 clear
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.1 clear
.9 rain
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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
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Value of Information
• Expected value of a clairvoyantclairvoyant (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
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IE 2030 Lecture 9
• PERT intro
• Project 1a recap
• What is a model?
• Quiz
• Homework: problems not questions; drawing cpm networks
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WHAT IS A MODEL?
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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
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Abstraction
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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?
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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
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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?