Decision Analysis

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Chapter 14 Decision Analysis
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Decision Making

• Many decision making occur under condition of
  uncertainty
• Decision situations
• Probability cannot be assigned to future
  occurrence
• Probability cannot be assigned to future
  occurrence

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Chapter Topics

• Components of Decision Making
• Decision themselves
• State of nature actual event that may occur in
  the future
• Payoff payoffs from different decisions given
  the various states of nature

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Decision making Tools

• Decision Making without Probabilities
• Decision-Making Criteria maximax, maximin,
  minimax, Hurwicz, and equal likelihood
• Decision Making with Probabilities
• Expected Value
• Expected opportunity loss
• Expected value of perfect information (EVPI)
• Decision Tree
• Some Other Decision Analysis Tools

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Decision Making without Probabilities

• Maximax Selects the decision that will result in
  the maximum of maximum payoffs (optimistic
  criterion)
• Example
• Maximin Selects the decision that will reflect
  the maximum of the minimum payoffs (pessimistic
  criterion)
• Example
• Hurwicz criterion compromise between the maximax
  and maximin criterion
• Multiplies the best payoff by ? and the worst
  payoff by 1- ?
• ?, coefficient of optimism, is a measure of the
  decision makers optimism
• Example
• Equal Likelihood ( or Laplace) Multiplies the
  decision payoff for each state of nature by an
  equal weight

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Decision Making with Probabilities

• Expected value Computed by multiplying each
  decision outcome by the probability of its
  occurrence
• Example
• Expected opportunity loss Expected value of the
  regret for each decision
• Example
• Expected value of perfect information (EVPI)
  Maximum amount a decision maker would pay for
  additional information
• EVPI (Expected value given perfect information)
  (Expected value without perfect information)
• EVPIthe expected opportunity loss (EOL) for the
  best alternative
• Example

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Expected Opportunity loss (EOL)

• Select the maximum payoff under each state of
  nature and then subtract all other payoffs under
  respective state of nature
• Good Condition Bad Condition
• 100,000-50,00050000 30,000-30,0000
• 100,000-100,0000 30,000-(-40,000)70,000
• 100,000-30,00070,000 30,000-10,00020,000
• Represent the regret that the decision maker
  would experience if a decision were made that
  resulted in less than the maximum payoff
• Assume DM is able to estimate a 0.6 that good
  will prevail and a 0.4 that poor will prevail
• EOL(A)50,000(.6)(0)(0.4) 30,000
• EOL(B)0(.6)(70000)(0.4) 28000 best
• EOL(C)70,000(.6)(20000)(0.4) 50,000

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Expected Value of Perfect Information

• Possible to purchase additional information
  regarding the future
• DM should not pay more than what he/she earns
  from his investment
• Thus there is a maximum value for it
• Computed as the expected value of perfect
  information (EVPI)
• If the DM knows for sure that good condition will
  prevail, he goes after B (100,000)
• If the DM knows for sure that poor condition will
  prevail, he goes after A (30,000)

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Expected Value of Perfect Information (EVPI)

• Also the probabilities tell us about the
  likelihood of good or poor condition (0.6 and
  0.4)
• Means that each state of nature will occur only a
  certain portion of the time
• Thus, each decision outcomes must be weighted
  (100,000)(0.6)(30,000)(0.4)72,000
• 72,000 is the expected value of the decision,
  given perfect information, not the EVPI
• EVPI is computed by subtracting the expected
  value (EV) without perfect information (44000)
  from the expected value given perfect information
  72,000
• EVPI72,000-44,00028,000
• Maximum amount that DM would pay for additional
  information, but usually pays less

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Decision Making with Probabilities-Cont.

• Decision Trees A diagram consisting of decision
  nodes (squares), probability nodes (circles), and
  decision alternatives (branches)
• Example
• Sequential decision tree Used to illustrate a
  situation requiring a series of decisions
• Example
• Bayesian analysis uses additional information to
  change the marginal probability of an event
• Uses conditional probability- probability that an
  event will occur given that another event has
  already occurred
• Uses also posterior probability altered marginal
  probability of an event based on additional
  information
• Example

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Decision Analysis Example

• Determine the best decision using the 5 criteria
• Determine best decision with probabilities
  assuming .70 probability of good conditions, .30
  of poor conditions. Use expected value and
  expected opportunity loss criteria.
• Compute expected value of perfect information.
• Develop a decision tree with expected value at
  the nodes
• Given following, P(P?g) .70, P(N?g) .30,
  P(P?p) 20, P(N?p) .80, determine posteria
  probabilities using Bayes rule
• Perform a decision tree analysis using the
  posterior probability obtained in part e