decision analysis a method for determining optimal strategies when faced with several decision...
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Decision Analysis A method for determining optimal strategies
when faced with several decision alternatives and an uncertain pattern of future events.
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The Decision Analysis Approach
Identify the decision alternatives - di
Identify possible future events - sj
mutually exclusive - only one state can occur exhaustive - one of the states must occur
Determine the payoff associated with each decision and each state of nature - Vij
Apply a decision criterion
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Types of Decision Making Situations
Decision making under certainty state of nature is known decision is to choose the alternative with the best
payoff
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Types of Decision Making Situations
Decision making under uncertainty The decision maker is unable or unwilling to
estimate probabilities Apply a common sense criterion
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Decision Making Under Uncertainty
Maximin Criterion (for profits) - pessimistic list minimum payoff for each alternative choose alternative with the largest minimum
payoff
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Decision Making Under Uncertainty
Maximax Criterion (for profits) - optimistic list maximum payoff for each alternative choose alternative with the largest maximum
payoff
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Decision Making Under Uncertainty
Minimax Regret Criterion calculate the regret for each alternative and each
state list the maximum regret for each alternative choose the alternative with the smallest maximum
regret
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Decision Making Under Uncertainty
Minimax Regret Criterion Regret - amount of loss due to making an incorrect
decision - opportunity cost
|| * ijjij VVR
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Types of Decision Making Situations
Decision making under risk Expected Value Criterion
compute expected value for each decision alternative
select alternative with “best” expected value
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Computing Expected Value Let:
P(sj)=probability of occurrence for state sj
and N=the total number of states
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Computing Expected Value
Since the states are mutually exclusive and exhaustive
jsP
sPsPsPsP
j
N
j
Nj
allfor 0)(
and
1)()()()(1
21
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Types of Decision Making Situations
Then the expected value of any decision di is
ij
N
j
ji VsPdEV )()(1
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Decision Trees A graphical representation of a decision
situation Most useful for sequential decisions
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Decision Making Under Risk:Another Criterion
Expected Regret Criterion Compute the regret table Compute the expected regret for each alternative Choose the alternative with the smallest expected
regret The expected regret criterion will always yield
the same decision as the expected value criterion.
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Expected Regret Criterion The expected regret for the preferred decision
is equal to the Expected Value of Perfect Information - EVPI
EVPI is the expected value of knowing which state will occur.
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EVPI – Alternative to Expected Regret
EVPI – Expected Value of Perfect Information EVwPI – Expected Value with Perfect
Information about the States of Nature EVwoPI – Expected Value without Perfect
Information about the States of Nature EVPI=|EVwPI-EVwoPI|
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Bayes Law
In this equation, P(B) is called the prior probability of B and P(B|A) is called the posterior, or sometimes the revised probability of B. The idea here is that we have some initial estimate of the probability of B, we get some additional information about whether A happens or not, and then we use Bayes Law to compute this revised probability of B.
)()|()()|()(
)()|()()|(
)()|()|(
BPBAPBPBAPAP
BPBAPBPBAP
BPBAPABP
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Expected Value of Sample Information – EVSI
EVSI – Expected Value of Sample Information EVwSI – Expected Value with Sample
Information about the States of Nature EVwoSI – Expected Value without Sample
Information about the States of Nature EVSI=|EVwSI-EVwoSI|
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Efficiency of Sample Information – E
Perfect Information has an efficiency rating of 100%, the efficiency rating E for sample information is computed as follows:
Note: Low efficiency ratings for sample information might lead the decision maker to look for other types of information
100EVPI
EVSIE
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Accounting for Risk in Decision Analysis
Mean-Variance
j
m
j
iiji pERrVar
1
)(2
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Accounting for Risk in Decision Analysis
Utility Theory replacing the payoffs with a unitless scale that
accounts for both the value of the payoff and the decision makers risk attitude
Risk Aversion A decision maker is risk averse if he/she would
prefer a certain x dollars to a risky alternative with ER=x dollars.
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Accounting for Risk in Decision Analysis
Direct assessment of utility Utility functions
parameter.
aversionrisk theis and payoff
theofamount theis where
1)(
exampleFor /
r
x
xU erx