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)

600

500

Clear

.6

Rain.4

900

100

Clear

.6

Rain.4

OUT

IN

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)

Clear

.6

Rain.4

out

in

outin

900

600

100

500

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

Clear

5/8PredictRain3/8

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

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?