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Chapter 3

Chapter 3. Fundamentals of Decision Theory Models. Decision Theory. Decision theory is the analytic and systematic methodology for making the best decision. Features of Decision Making. Decision making is for __________. a. past b. future c. both past and future

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Chapter 3

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  1. Chapter 3 Fundamentals of Decision Theory Models

  2. Decision Theory • Decision theory is the analytic and systematic methodology for making the best decision.

  3. Features of Decision Making • Decision making is for __________. a. past b. future c. both past and future • A decision is about a (an) _________. • status b. action c. condition • The process of making decision is a process of __________. • producing b. manufacturing c. creating d. cooking e. selecting f. fabricating

  4. Components in Decision Making (1 of 2) • Alternatives of a decision • A list of choices, one of which will be selected as the decision by the decision maker. • States of Nature • Possible conditions that may actually occur in the future, which will affect the outcome of your decision but are beyond your control.

  5. Components in Decision Making (2 of 2) • Payoffs • a payoff is the outcome of a decision alternative under a state of nature. The larger the payoff the better. • The decision alternatives, states of nature and payoffs are organized in a decision table.

  6. Decision Table for the Thompson Lumber Example States of Nature DecisionFavorable Unfavorable Alternativesmarket market Large plant $200,000 -$180,000 Small plant $100,000 -$20,000 Doing nothing $0 $0

  7. Types of Decision Making • Decision making under certainty • The outcome of a decision alternative is known (i.e., there is only one state of nature.) • Decision making under risk • The outcome of a decision alternative is not known, but its probability is known. • Decision making under uncertainty • The outcome of a decision alternative is not known, and even its probability is not known.

  8. Decision Table for the Thompson Lumber Example States of Nature DecisionFavorable Unfavorable Alternativesmarket market Large plant $200,000 -$180,000 Small plant $100,000 -$20,000 Doing nothing $0 $0

  9. Decision Making under Uncertainty • The outcome of a decision alternative is not known, and even its probability is not known. • A few criteria (approaches) are available for the decision makers to select according to their preferences and personalities.

  10. Criterion 1: Maximax • Pick the maximum of the maximum payoffs of the decision alternatives. • “Best of bests”.

  11. Maximax Decision for Thompson Lumber States of Nature Row Decision Favorable Unfavorable Maximum Alternatives market market Large plant 200,000 –180,000 200,000 Small plant 100,000 –20,000 100,000 Do nothing 0 0 0 Max(Row max’s) = Max(200,000, 100,000, 0) = 200,000. So, the decision is ‘Large plant’.

  12. For Whom? • MaxiMax is an approach for: • Risk taker who tends not to give up attractive opportunities regardless of possible failures, or • Optimistic decision maker in whose eyes future is bright.

  13. Criterion 2: Maximin • Pick the maximum of the minimum payoffs of the decision alternatives. • “Best of worsts”

  14. Maximin Decision for Thompson Lumber States of Nature Row Decision Favorable Unfavorable Minimum Alternatives market market payoffs Large plant 200,000 –180,000 –180,000 Small plant 100,000 –20,000 –20,000 Do nothing 0 0 0 Max(Row Min’s) = Max(–180,000, –20,000, 0) = 0. So, the decision is ‘do nothing’.

  15. For Whom? • MaxiMin is an approach for: • Risk averter who tends to avoid bad outcomes despite of some possible attractive outcomes; or • Pessimistic decision maker in whose eyes future is obscure.

  16. Criterion 3: Hurwicz (Realism) • Pick the maximum of the Hurwicz values of decision alternatives. • Hurwicz value of a decision alternative = weighted average of the best and worst payoffs of the alternative = (row max payoff)() + (row min payoff)(1-) where  (01) is called coefficient of realism.

  17. Leonid Hurwicz 1917-2008

  18. Decision by Hurwicz Valuefor Thompson Lumber =0.8 States of Nature Decision Favorable Unfavorable Hurwicz Alternatives market market values Large plant 200,000 –180,000 124,000 Small plant 100,000 –20,000 76,000 Do nothing 0 0 0 Max(Hurwicz values) = Max(124,000,76,000,0) = 124,000. So, the decision is ‘large plant’.

  19. For Whom? • Hurwicz method can be used by decision makers with different preferences on risks. • For a person who tends to take risk, a larger  is used; • For a person who tends to be conservative, a smaller  is used. • What if  = 1? • What if  = 0?

  20. Criterion 4: Equally Likely • Pick the maximum of the average payoffs of decision alternatives. • Average payoff: • Sum of the payoffs of a row divided by number of states of natures.

  21. Decision by Equally Likelyfor Thompson Lumber States of Nature Row Decision Favorable Unfavorable Average Alternatives market market Large plant 200,000 –180,000 10,000 Small plant 100,000 –20,000 40,000 Do nothing 0 0 0 Max(Row avg’s) = Max(10,000, 40,000, 0) = 40,000. So, the decision is ‘small plant’.

  22. For Whom? • Equally Likely method is for the decision maker who does not have particular preference on taking or avoiding risks.

  23. Criterion 5: Minimax Regret • Pick the minimum of (the maximum regrets of alternatives). • Step 1. Construct a ‘regret table’, • Step 2. Find ‘row maximums’, • Step 3. Find Min{Row maximums}.

  24. Regret • Regret is the opportunity cost of not picking the best decision. • Regret = Opportunity cost = Opportunity loss • For a specific state of nature SN: Regret of a decision = (the maximum payoff under SN) – (payoff of the decision under SN)

  25. For Whom? • MiniMax Regret is an approach for the decision maker who hates the feeling of having regrets.

  26. Payoff Tablefor Thompson LumberandColumn Maximums States of Nature DecisionFavorable Unfavorable Alternativesmarket market Large plant $200,000 -$180,000 Small plant $100,000 -$20,000 Doing nothing $0 $0 Column Max $200,000 $0

  27. Regret Tablefor Thompson Lumber States of Nature DecisionFavorable Unfavorable Alternativesmarket market Large plant $0 $180,000 Small plant $100,000 $20,000 Doing nothing $200,000 $0

  28. Minimax Regret Decision for Thompson Lumber (Based on the Regret Table) States of Nature Row Decision Favorable Unfavorable Maximum Alternatives market market Large plant 0 180,000 180,000 Small plant 100,000 20,000 100,000 Do nothing 200,000 0 200,000 Min(Row max’s) = Min{180,000, 100,000, 200,000} = 100,000. So, the minimax regret decision is ‘small plant’.

  29. Decision Making under Risk • The outcome of a decision alternative is not known, but its probability is known. • The alternative with the maximum EMV, expected monetary values, is selected. • EMV is the expected value of an alternative.

  30. Max EMV Approach • EMV of an alternative is the expected value of possible payoffs of that alternative. • EMV n=number of states of nature Pi=probability of the i-th state of nature Vi=payoff of the alternative under the i-th state of nature

  31. Example of Thompson Lumber (see Table 3.9, p.77) States of Nature DecisionFavorable Unfavorable Alternativesmarket market EMV 0.50.5 Large plant $200,000 -$180,000 10,000 Small plant $100,000 -$20,000 40,000 Doing nothing $0 $0 0

  32. Minimum EOL Approach Step 1. Generate the opportunity loss table. Step 2. Calculate the expected opportunity loss (EOL) for each alternative. Step 3. Pick up the alternative with the minimum EOL.

  33. Opportunity Loss Table • Opportunity loss = Regret = Opp. cost • Opportunity loss table = Regret Table

  34. Payoff Tablefor Thompson Lumber States of Nature DecisionFavorable Unfavorable Alternativesmarket market EMV 0.50.5 Large plant $200,000 -$180,000 Small plant $100,000 -$20,000 Doing nothing $0 $0

  35. Opportunity Loss Table for Example of Thompson States of Nature DecisionFavorable Unfavorable Alternativesmarket market Large plant $0 $180,000 Small plant $100,000 $20,000 Doing nothing $200,000 $0

  36. Expected Opportunity Loss (EOL) • EOL is the expected value of the opportunity losses (regrets) of a decision alternative.

  37. Opportunity Loss table and EOLfor Thompson Lumber States of Nature DecisionFavorable Unfavorable Alternativesmarket market EOL 0.5 0.5 Large plant $0 $180,000 Small plant $100,000 $20,000 Doing nothing $200,000 $0

  38. Expected Value of Perfect Information (EVPI) • It is value of additional information for better decision making. • It is an upper bound on how much to pay for the additional information.

  39. An Example • You can play the game for many times. • What is your rational strategy of “guessing”? • Someone offers you perfect information about “landing” at $65 per time. Do you take it? If not, how much would you pay?

  40. Calculating EVPI • EVPI = (Exp. payoff with perfect information) – (Exp. payoff without perfect information) = EVwPI – EVw/oPI

  41. EVw/oPI • EVw/oPI is the average payoff you expect to get based only on the information given in the decision table without the help of additional information. • EVw/oPI = Max (EMV)

  42. EVw/oPI = Maximum EMV States of Nature DecisionFavorable Unfavorable Alternativesmarket market EMV 0.50.5 Large plant $200,000 -$180,000 10,000 Small plant $100,000 -$20,000 40,000 Doing nothing $0 $0 0 Since Max EMV = 40,000, EVw/oPI = 40,000.

  43. EVwPI • EVwPI is the average payoff you can get if following the perfect information about the state of nature in the future. • EVwPI where n=number of states of nature bi=best payoff of i-th state of nature Pi=probability of i-th state of nature

  44. EVwPI for the Example of Thompson States of Nature DecisionFavorable Unfavorable Alternativesmarket market EMV 0.5 0.5 Large plant $200,000 -$180,000 10,000 Small plant $100,000 -$20,000 40,000 Doing nothing $0 $0 0 bi $200,000 $0 EVwPI = 200,000*0.5+0*0.5 = 100,000

  45. EVPI for Thompson Lumber • EVwPI = 200,000*0.5 + 0*0.50 = $100,000 • EVw/oPI = Maximum EMV = $40,000 • EVPI = EVwPI – EVw/oPI = $100,000 – $40,000 = $60,000

  46. Example Revisit (1) What is your strategy of “guessing?” Up to how much would you pay for a piece of information about result of “landing”?

  47. Example Revisit (2) • Decision alternatives in this problem are: • States of nature in this problem are:

  48. Example Revisit (3) • Decision making in this problem is to select an alternative. • To make a better decision, or select a better alternative, we need to look at the average payoff of each alternative.

  49. Example Revisit (4) • The average payoff of an alternative is the expected value of the payoffs of an alternative, which is also called EMV of an alternative.

  50. Example Revisit (5) • For alternative 1, Guess “Head”, EMV (or average payoff) is: • For alternative 2, Guess “Tail”, EMV (or average payoff) is:

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