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IE 2030 Lecture 7Decision Analysis
Expected Value
Utility
Decision Trees
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
Party Example (R. Howard)
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500
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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
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
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
Never attribute to malice, what can be adequately explained by
stupidity
Trust and Credibility
Risk aversion
• Choice of sure thing versus lottery
• Size
• Gain or loss
• Expected value criterion
• Utility
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?
Decision Analysis: Value of Information (based on R. Howard’s notes)
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outin
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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
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?
Value of 90% accurate forecast
Predict
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5/8PredictRain3/8
outin
out
in
900
600
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500900
100
600
500
.9 clear
.1 rain
clear
.1 rain
.1 clear
.9 rain
.1 clear
.9 rain
Value of 90% accurate forecast
Predict
Clear
5/8PredictRain3/8
820
590
180
510
outin
out
in
900
600
100
500900
100
600
500
.9 clear
.1 rain
clear
.1 rain
.1 clear
.9 rain
.1 clear
.9 rain
Value of 90% accurate forecast
820
510
Predict
Clear
5/8PredictRain3/8
820
590
180
510
outoutin
out
iinn
900
600
100
500900
100
600
500
.9 clear
.1 rain
clear
.1 rain
.1 clear
.9 rain
.1 clear
.9 rain
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
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
IE 2030 Lecture 9
• PERT intro
• Project 1a recap
• What is a model?
• Quiz
• Homework: problems not questions; drawing cpm networks
WHAT IS A MODEL?
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
Abstraction
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?
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
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?