Ie 2030 lecture 7 decision analysis
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IE 2030 Lecture 7 Decision Analysis. Expected Value Utility Decision Trees. 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

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IE 2030 Lecture 7 Decision Analysis

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Ie 2030 lecture 7 decision analysis

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

Topics TodayIE 2030 Lecture 7


Party example r howard

900

Clear

.6

Party Example (R. Howard)

Rain

.4

100

OUT

IN

600

Clear

.6

Rain

.4

500


Decision trees

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

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


Maximin and other payoff criteria

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

Never attribute to malice, what can be adequately explained by stupidity

Trust and Credibility


Risk aversion

Risk aversion

  • Choice of sure thing versus lottery

  • Size

  • Gain or loss

  • Expected value criterion

  • Utility


It is expensive to be poor

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

Decision Analysis: Value of Information (based on R. Howard’s notes)

900

out

Clear

.6

in

600

Rain

.4

100

out

in

500


Value of information

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


Forecast probabilities simple example

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

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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