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Quantitative Module A

Quantitative Module A. Decision-Making Tools. Announcements. Skip p. 725 – 727, A More Complex Decision Tree Assignment 1. Decision-making process. Decision Analysis. A structured approach to decision-making under uncertainty. Examples:

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Quantitative Module A

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  1. Quantitative Module A Decision-Making Tools

  2. Announcements • Skip p. 725 – 727, A More Complex Decision Tree • Assignment 1

  3. Decision-making process

  4. Decision Analysis A structured approach to decision-making under uncertainty. Examples: • Decide whether or not to bid on a piece of property. • Decide how much to produce of a seasonal product.

  5. Example: Graft Land Development Corp. Graft Land owns 5000 acres that are zoned to be developed as recreational home sites. Three development alternatives are being considered:  D1: Develop a small amount of acreage (500 acres) D2: Develop a med. amount of acreage (2500 acres) D3: Develop a large amount of acreage (5000 acres)

  6. Example: Graft Land Development Corp. Three possible states of nature that Graft anticipates as possibilities: S1: Low customer demand S2: Medium customer demand S3: High customer demand

  7. Payoff Table • Projected profit depends on the decision alternative and the state of nature that occurs. Table 1 Payoff Table for Graft Land (Entries in $1000’s) Which decision alternative would you choose?

  8. Decision theory models • Decision alternatives – this is a course of action that may be chosen by the decision maker. • States of nature – an occurrence that affects the outcome of the decision; decision maker has no control over the states of nature • Payoff – benefit that occurs when a specific decision is made and a specific state of nature occurs.

  9. Payoff Table Tools of Decision Theory

  10. Tools of Decision Theory • Decision Tree • Decision nodes -  • State-of-nature nodes - 

  11. States of Nature • Affect the outcome of a decision • Decision-maker has little or no control over which state will occur. • Must not overlap • Cover the entire range of possibilities that may occur

  12. Decision –Making without probabilities • Implied assumption – states of nature are equally likely to occur. • 3 approaches in text • Optimistic approach: Maximax • Conservative approach: Maximin • Equally likely

  13. Optimistic approach Determines the best possible outcome for Graft. Graft Payoff Table Max of row 3500 12500  25000 Max of maximums 25000 Find the maximum payoff for each decision alternative (row). Select the decision alternative with the maximum maximum – MAXIMAX.

  14. Conservative approach Determines the best of the worst possible outcome for Graft. Graft Payoff Table Min of row  2700 1000 -500 Max of minimums 2700 Find the minimum payoff for each decision alternative (row). Select the decision alternative with the maximum minimum - MAXIMIN

  15. Equally likely approach Graft Payoff Table Go to Excel Find the average payoff for each decision alternative (row). Select the decision alternative with the maximum average.

  16. Equally likely approach Deteremines the highest average outcome. Graft Payoff Table Average 3066.7  8633.3 8083.3 8633.3 Max of average Find the average payoff for each decision alternative (row). Select the decision alternative with the maximum average.

  17. Which is the best decision? • Must be decided in the context of the problem – manager’s decision

  18. Which is the best decision? • Sometimes the biggest benefit for the manager in modeling the decision problem is the PROCESS • Structure the problem • What will be decided? • What are the decision alternatives? • What states of nature will affect the outcome? • Calculate the payoff table

  19. Decision-making with probabilities What if Graft estimates the likelihood of each state of nature occurring. S1: Low customer demand P(S1) = 0.2 S2: Med. customer demand P(S2) = 0.5 S3: High customer demand P(S3) = 0.3 Would this change your decision?

  20. Would that change your decision? Graft Payoff Table

  21. Review Probability & Statistics • P(S1) – the probability of state of nature 1 • Expected value – a measure of the central location of a probability distribution.

  22. Expected-value Approach Graft Payoff Table Expected value Go to Excel Find the expected value of each decision alternative (row). Select the decision alternative with the maximum expected value.

  23. Expected-value Approach Represents the average best (with probabilities) outcome for Graft. Graft Payoff Table Expected value 3010  10170 7275 10170 Max of expected values – Max EV Find the expected value of each decision alternative (row). Select the decision alternative with the maximum expected value.

  24. EVwPI – Expected value under certainty What if we had a crystal ball and we knew with certainty which state of nature would occur? EVwPI – expected value WITH perfect information

  25. EVwPI Graft Payoff Table If S1  D1 If S2 D2 If S3 D3 EVwPI = 0.2(3500) + 0.5(12500) + 0.3(25000)

  26. EVwPI Graft Payoff Table If S1  D1 If S2 D2 If S3 D3 EVwPI = 14450

  27. EVPI • EVPI – expected value OF perfect information • How much would Graft be willing to pay for a crystal ball?

  28. EVPI • EVPI = EVwPI – Max EV = 14450 - 10170 = 4280 • If Graft could survey people in order to better assess the demand, they should pay no more than $4280 for the information (survey).

  29. Decision Trees • Graphical tool for a decision • Decision nodes -  • State-of-nature nodes -  • A map to all possible outcomes • Particularly useful when there is a sequence of decisions to be made.

  30. Decision Tree for Graft Land

  31. Hale’s TV Productions • Hale’s TV Productions (HTP) is considering producing a pilot for a comedy series. HTP hopes to convince a major television network to purchase the series. While the network may reject the pilot and the series, it may also purchase the program for 1 or 2 years. HTP may decide to produce the pilot or transfer the rights for the series to a competitor for $100,000. • What are the decision alternatives? • What are the states of nature?

  32. HTP Payoff Table

  33. HTP without probabilities

  34. HTP without probabilities

  35. HTP with Probabilities Assuming the probability estimates for the states of nature are: P(reject) = .2 P(1 yr) = .3 P(2 yr) = .5 What should the company do?

  36. HTP with probabilities • Draw the decision tree. • Determine all expected values and Max EV. • Determine EVwPI. • Determine EVPI. • What’s the maximum that HTP should be willing to spend on a survey?

  37. HTP Decision Tree, Expected Values and Max EV

  38. HTP Payoff Table and Expected Values

  39. HTP EVwPI and EVoPI EVPI = EVwPI – Max EV = 125 – 100 = 25

  40. Excel OM Spreadsheet

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