Transcript IE 2030 Lecture 7 Decision Analysis

IE 2030 Lecture 7
Decision Analysis
Expected Value
Utility
Decision Trees
Topics Today
• Introduction to PERT
• Decision tree example:
party planning
• Concepts:
– Uncertainty
– Minimax Criterion
– Expected Value
Criterion
– Risk Aversion
IE 2030 Lecture 7
– Risk Neutral, Risk
Averse, Risk Seeking
– Utility
– Outcome and
Decision
– Decision Tree
– Value of information
– Sensitivity analysis
Party Example (R. Howard)
900
100
600
500
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? Probability of regret
– Decisions vs. Outcomes
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)
900
600
100
500
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
• 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?