Decision Analysis

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Decision Analysis

• Decision Making Under Uncertainty
• Techniques play an important role in business,
  government, everyday life, college football
  rankings
• How can a manager provide a rational methodology
  for decision making and analysis in the face of
  uncertainty?
• How does a manager chose among alternatives in an
  optimal fashion when those alternatives may be
  numerous and conflicting?

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Components of Decision Making

• State
• An actual event that may occur in the future
• Decision
• Options from which a decision maker can chose
• Outcomes
• The result of a combination of states and
  decisions

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Payoff Table

• A means to organize states, decisions, and
  outcomes e.g.,
• States
• Decisions a b
• 1 payoff 1a payoff 1b
• 2 payoff 2a payoff 2b

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Payoff Table Example

• An investor must decide among an apartment
  building, an office building, and a warehouse.
• States
• Decisions Good Bad
• Apartment 50,000 30,000
• Office 100,000 -40,000
• Warehouse 30,000 10,000

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Decision Criteria

• Maximax
• Maximin
• Minimax Regret
• Hurwicz
• Equal Likelihood

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Maximax

• Decision maker selects the decision that will
  result in the maximum of the maximum payoffs
• Decisions Good
• Apartment 50,000
• Office 100,000
• Warehouse 30,000
• Decision would be to purchase the office
• Decision completely ignores down side, loss of
  40,000
• Assumes a very optimistic future

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Maximin

• Decision maker selects the decision that will
  result in the maximum of the minimum payoffs
• Decisions Bad
• Apartment 30,000
• Office -40,000
• Warehouse 10,000
• Decision would be to purchase the apartment
• Decision is relatively conservative
• Assumes a very pessimistic future

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Minimax Regret

• Decision maker attempts to avoid regret by
  selecting the decision alternative that minimizes
  the maximum regret
• Select the maximum payoff under each state
• Good ----gt 100,000
• Bad ------gt 30,000
• Regret is then calculated as follows
• Good ----gt 100,000 - payoff for each decision
• Bad ------gt 30,000 - payoff for each decision

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Minimax Regret

• The calculations for the example
• States
• Decisions Good Bad
• Apartment 100,000 - 50,000 50,000
  30,000 - 30,000 0
• Office 100,000 - 100,000 0 30,000
  - (-40,000) 70,000
• Warehouse 100,000 - 30,000 70,000
  30,000 - 10,000 20,000
• Chose the decision which minimizes this regret
• Purchase the apartment building
• Decision maker experiences the least amount of
  regret

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Hurwicz Criterion

• A compromise between the maximax and maximin
  criterions
• Payoffs are weighted using a coefficient of
  optimism, ?
• A measure of the decision makers optimism
  regarding the outcome of the events
• 0 lt ? lt 1

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Hurwicz Criterion

• The ? is multiplied by the best payoff and (1-?)
  is multiplied by the worst payoff and these
  values are added together
• This criterion is a simple weighting scheme
• However, ? must be determined by the decision
  maker and is completely subjective
• The Hurwicz Criterion is completely subjective

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Hurwicz Criterion

• Given ? 0.4, then 1-? 0.6,
• Decisions Values
• Apartment 50,000(0.4) 30,000(0.6)
  38,000
• Office 100,000 (0.4) - 40,000(0.6) 16,000
• Warehouse 30,000 (0.4) 10,000(0.6)
  18,000
• Hurwicz criterion specifies selection
  corresponding to the maximum weighted average
• Apartment building

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Equal Likelihood or LaPlace

• Hurwicz Criterion when ? 0.5
• Decisions Values
• Apartment 50,000(0.5) 30,000(0.5)
  40,000
• Office 100,000 (0.5) - 40,000(0.5) 30,000
• Warehouse 30,000 (0.5) 10,000(0.5)
  20,000
• Equal likelihood criterion specifies selection
  corresponding to the maximum weighted average
• Apartment building

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Limitations of Weighting Methods

• Regardless of how a is determined it is a
  subjective measure, even with equal likelihood
• The degree of the decision makers optimism is
  reflected in ?
• Untrained decision makers generally choose ?
  incorrectly
• How would you choose ??

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Summary of Techniques

• Criterion Decision
• Maximax Office Building
• Maximin Apartment
• Minimax regret Apartment
• Hurwicz Apartment
• Equal Likelihood Apartment