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Session 6b

Session 6b. Overview. Decision Analysis Uncertain Future Events Perfect Information Partial Information The Return of Rev. Thomas Bayes.

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Session 6b

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  1. Session 6b

  2. Overview Decision Analysis • Uncertain Future Events • Perfect Information • Partial Information • The Return of Rev. Thomas Bayes Decision Models -- Prof. Juran

  3. Decision Models -- Prof. Juran

  4. Decision Models -- Prof. Juran

  5. Decision Models -- Prof. Juran

  6. Decision Models -- Prof. Juran

  7. Decision Models -- Prof. Juran

  8. Decision Models -- Prof. Juran

  9. Decision Models -- Prof. Juran

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  16. Each of the branches at the far right of the diagram is characterized by two elements: a probability and a payoff value. For example, the “Sell 100” branch has a probability of 0.05 and a payoff (in the case of having purchased 100 units of shoes) of $2,500 (see cell B8 in the payoff table). These entries are tedious, so we want to use copy-and-paste as much as possible. The payoffs will vary across the different purchase quantities, but the probabilities will not. Decision Models -- Prof. Juran

  17. Decision Models -- Prof. Juran

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  20. Decision Models -- Prof. Juran

  21. PrecisionTree uses “True” and “False” to indicate which branch of a decision node is optimal. Here, the best policy is to order 400 units and have an expected profit of $7,550. Decision Models -- Prof. Juran

  22. Example 2: TV Production Witkowski TV Productions is considering a pilot for a comedy series for a major television network. The network may reject the pilot and the series, or it may purchase the program for one or two years. Witkowski may decide to produce the pilot or transfer the rights for the series to a competitor for $100,000. Decision Models -- Prof. Juran

  23. Witkowski’s profits are summarized in the following profit ($1000s) payoff table: If the probability estimates for the states of nature are P(Reject) = 0.20, P(1 Year) = 0.30, and P(2 Years) = 0.50, what should Witkowski do? Decision Models -- Prof. Juran

  24. Decision Models -- Prof. Juran

  25. Value of Perfect Information Decision Models -- Prof. Juran

  26. Perfect information (if it were available) would be worth up to 125 - 100 = 25 thousand dollars to Witkowski. This is referred to as expected value of perfect information. Decision Models -- Prof. Juran

  27. For a consulting fee of $2,500, the O’Donnell agency will review the plans for the comedy series and indicate the overall chance of a favorable network reaction. Decision Models -- Prof. Juran

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  32. What should Witkowski’s strategy be? What is the expected value of this strategy? The best thing to do is to forget about O’Donnell and sell the rights for $100,000. Decision Models -- Prof. Juran

  33. What is the expected value of the O’Donnell agency’s sample information? Is the information worth the $2,500 fee? What is the efficiency of O’Donnell’s sample information? Decision Models -- Prof. Juran

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  35. Decision Models -- Prof. Juran

  36. ( ) ( ) ( ) ( ) ( ) ( ) + = + = 99 . 65 * 0 . 69 97 . 5 * 0 . 31 98 . 98 EV I P I EV I P I 1 1 2 2 Decision Alternative Expected Value Produce Pilot 99.65  Optimal Favorable O’Donnell Report Sell to Competitor 97.50 Produce Pilot - 4.20 Unfavorable O’Donnell Report Sell to Competitor 97.50  Optimal The overall expected value with sample information is: (EVwSI) (Note that we are assum ing here that we will always adopt the optimal strategy in light of whatever information O’Donnell provides.) Decision Models -- Prof. Juran

  37. Decision Models -- Prof. Juran

  38. Expected Value of Sample Information Decision Models -- Prof. Juran

  39. What is the expected value of the O’Donnell agency’s sample information? Is the information worth the $2,500 fee? If we pay O’Donnell the $2,500 fee, our overall expected value drops by $1,020. This implies that the O’Donnell report is worth We would be willing to pay up to (but no more than) $1,480 for the O’Donnell report. (This is one way to address the question, “How much should Witkowski be prepared to pay for the research study?”) Decision Models -- Prof. Juran

  40. Efficiency of Sample Information The efficiency of sample information is calculated using this formula: In other words, the market research project gives us information with less than 6% of the utility of having perfect information. Decision Models -- Prof. Juran

  41. Conclusions • Don’t buy the O’Donnell report • Sell the script to the competitor • Earn $100,000 Decision Models -- Prof. Juran

  42. Summary Decision Analysis • Uncertain Future Events • Perfect Information • Partial Information • The Return of Rev. Thomas Bayes Decision Models -- Prof. Juran

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