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Decision Analysis

Decision Analysis. OPS 370. Decision Theory. A. B. a. b. c. d. e. Decision Theory. A. a. b. c. . Decision Theory. Steps: 1. A. B. 2. A. 3. 4. 5. Payoff Table. Shows Expected Payoffs for Various States of Nature. Decision Environments. A. a. B. a. C.

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Decision Analysis

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  1. Decision Analysis OPS 370

  2. Decision Theory • A. • B. • a. • b. • c. • d. • e.

  3. Decision Theory • A. • a. • b. • c.

  4. Decision Theory • Steps: • 1. • A. • B. • 2. • A. • 3. • 4. • 5.

  5. Payoff Table • Shows Expected Payoffs for Various States of Nature

  6. Decision Environments • A. • a. • B. • a. • C. • a.

  7. Decision Making • A. • a. • b.

  8. Decision Making • Under Uncertainty • Four Decision Criteria • 1. • A. • B. • 2. • A. • B.

  9. Decision Making • Under Uncertainty • 3. • A. • B. • 4. • A. • B.

  10. Example • Maximin • Indoor  • Drive-In  • Both  • Choose “Best of Worst” 

  11. Example • Maximax • Indoor  • Drive-In  • Both  • Choose “Best of Best” 

  12. Example • Laplace • Indoor  • Drive-In  • Both  • Choose

  13. Decision Making • Minimax Regret • Criterion for Decision Making Under Uncertainty • A. • B.

  14. Decision Making

  15. Decision Making • A. • Indoor  • Drive-In  • Both  • B. • a.

  16. Decision Making • Under Risk • A. • B. • a. • b.

  17. Decision Making • Under Risk • Expected Payoffs: • Indoor: • Drive-In: (0.3)(700) + (0.5)(1500) + (0.2)(1250) = • Both: (0.3)(-2000) + (0.5)(-1000) + (0.2)(3000) = • Select

  18. Expected Value of Perfect Info • A. • B.

  19. Expected Value of Perfect Info • Steps: • 1. • 2. • 3. • Example • A. • a. • B. • C.

  20. Expected Value of Perfect Info • NOTE: • A.

  21. Decision Trees • Visual tool to represent a decision model • Squares: - Decisions • Circles: - Uncertain Events (Subject to Probability) • Branches: Potential Actions or Results • Some Branches are Terminal (End)  Terminal Branches Have Payoffs (Payoffs Should Reflect All Costs/Revenues)

  22. Decision Trees • Simple Example Terminal Branches $0 No $49 Buy Raffle Ticket? Win (0.01) Yes ($1 to Buy) Lose (0.99) -$1 Decision Uncertain Event

  23. Decision Trees • Build Decision Trees from LEFT to RIGHT • Solve Decision Trees from RIGHT to LEFT • Determine Expected Values at Chance Nodes • Choose “Best” Expected Value at Decision Nodes • Identify “Best” Path of Decisions

  24. Decision Trees • Simple Example $0 No $49 Buy Raffle Ticket? Win (0.01) Yes ($1 to Buy) Lose (0.99) -$1 Expected Value = (0.01)(49) + (0.99)(-1) = 0.49 – 0.99 = -0.5

  25. Decision Trees • Simple Example • Should You Buy a Raffle Ticket? • NO! Your Expected Value is Negative $0 No Buy Raffle Ticket? Yes -$0.5

  26. Decision Trees • More Complex Example

  27. Decision Trees Settle Now ($?) Settle? Wait

  28. Decision Trees Settle Now ($?) Opp Wins (0.5) Settle? Wait Opp Loses (0.5) $0

  29. Decision Trees Settle Now ($?) Opp Sues (0.8) Opp Wins (0.5) Settle? No Suit(0.2) Wait Opp Loses (0.5) $0

  30. Decision Trees Settle ($8) Settle Now ($?) Contest Opp Sues (0.8) Contest Settlement Opp Wins (0.5) Settle? No Suit(0.2) $0 Wait Opp Loses (0.5) $0

  31. Decision Trees We Win (0.3) ($0) Settle ($8) Settle Now ($?) Contest Opp Sues (0.8) We Lose (0.7) ($10) Contest Settlement Opp Wins (0.5) Settle? No Suit(0.2) Low (0.4) ($5) $0 Wait Opp Loses (0.5) $0 Win (0.6) ($15)

  32. Decision Trees We Win (0.3) ($0) Settle ($8) Settle Now ($?) Contest Opp Sues (0.8) We Lose (0.7) ($10) Contest Settlement EV = (0.3)(0) + (0.7)(10) = 7 Opp Wins (0.5) Settle? No Suit(0.2) Low (0.4) ($5) $0 Wait Opp Loses (0.5) $0 Win (0.6) ($15) EV = (0.4)(5) + (0.6)(15) = 11

  33. Decision Trees Settle ($8) Settle Now ($?) Contest $7 Opp Sues (0.8) Contest Settlement Opp Wins (0.5) Settle? No Suit(0.2) $0 Wait $11 Opp Loses (0.5) $0

  34. Decision Trees Settle Now ($?) $7 Opp Sues (0.8) Opp Wins (0.5) Settle? No Suit(0.2) $0 Wait Opp Loses (0.5) $0

  35. Decision Trees Settle Now ($?) $7 Opp Sues (0.8) Opp Wins (0.5) Settle? No Suit(0.2) $0 EV = (0.8)(7) + (0.2)(0) = 5.6 Wait Opp Loses (0.5) $0

  36. Decision Trees Settle Now ($?) $5.6 Opp Wins (0.5) Settle? Wait Opp Loses (0.5) $0

  37. Decision Trees Settle Now ($?) $5.6 Settle? Opp Wins (0.5) Wait Opp Loses (0.5) $0 EV = (0.5)(5.6) + (0.5)(0) = 2.8

  38. Decision Trees Settle Now ($?) Settle? $2.8 Wait

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