Decision Analysis Introduction Chapter 6

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Decision Analysis Introduction Chapter 6
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What kinds of problems ?

• Decision Alternatives (what ifs) are known
• States of Nature and their probabilities are
  known (ex. rainy 20, partly cloudy 50, sunny
  20)
• Outcomes, (referred to as Payoffs) are
  computable under different possible scenarios
  each is a combination of a decision alternative
  and a state of nature

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Decision Analysis Basic Terms

• Decision Alternatives
• States of Nature (eg. Condition of economy or
  weather)
• Payoffs ( outcome of a choice assuming a state
  of nature)
• Criteria (i.e. Expected Value)

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Decision Analysis Conditions

• Certainty
• Decision Maker knows with certainty what the
  state of nature will be - only one possible state
  of nature
• Ignorance
• Decision Maker knows all possible states of
  nature, but does not know probability of
  occurrence
• Risk
• Decision Maker knows all possible states of
  nature, and can assign probability of occurrence
  for each state this will be our focus

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Decision Making Under Certainty
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Decision Making Under Ignorance Payoff Table
Kelly Construction Payoff Table (Prob. 8-17)
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Decision Making Under Ignorance

• Which alternative will we choose?
• Maximax
• Select the strategy with the highest possible
  return
• Maximin
• Select the strategy with the smallest possible
  loss

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Maximax The Optimistic Point of View

• Select the best of the best strategy
• Evaluates each decision by the maximum possible
  return associated with that decision (Note if
  cost data is used, the minimum return is best)
• The decision that yields the maximum of these
  maximum returns (maximax) is then selected
• For risk takers
• Doesnt consider the down side risk
• Ignores the possible losses from the selected
  alternative

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Maximax Example
Kelly Construction
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Maximin The Pessimistic Point of View

• Select the best of the worst strategy
• Evaluates each decision by the minimum possible
  return associated with the decision
• The decision that yields the maximum value of the
  minimum returns (maximin) is selected
• For risk averse decision makers
• A protect strategy
• Worst case scenario the focus

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Maximin
Kelly Construction
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Decision Making Under Risk

• Expected Return (ER)
• Select the alternative with the highest expected
  return
• Use a weighted average of the possible returns
  for each alternative, with probabilities used as
  weights
• Also referred to as Expected Value (EV) or
  Expected Monetary Value (EMV)

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Expected Return
Note that we now have probabilities for each
state of nature
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Expected Value of Perfect Information

• EVPI measures how much better you could do on
  this decision if you could always know when each
  state of nature would occur, where
• EVUPI Expected Value Under Perfect Information
  (also called EVwPI, the EV with perfect
  information, or EVC, the EV under certainty)
• EVUII Expected Value of the best action with
  imperfect information (also called EVBest )
• EVPI EVUPI EVUII
• EVPI tells you how much you are willing to pay
  for perfect information (or is the upper limit
  for what you would pay for additional imperfect
  information!)

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Expected Value of Perfect Information
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Using Excel to Calculate EVPI Formulas View
Kelly Construction