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Chapter 14

Chapter 14. Decision Analysis – Part 2. Introduction Review. Payoff Table development Decision Analysis under Uncertainty. Decision Criteria (Risk). Expected Monetary Value (EMV) Select alternative with highest expected payoff Maximum Likelihood

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Chapter 14

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  1. Chapter 14 Decision Analysis – Part 2

  2. Introduction Review • Payoff Table development • Decision Analysis under Uncertainty

  3. Decision Criteria (Risk) • Expected Monetary Value (EMV) • Select alternative with highest expected payoff • Maximum Likelihood • Select best of payoffs that are most likely to occur • Dominance Models

  4. Expected Monetary Value • Sum of weighted payoffs associated with a specific alternative EMV (Alt) =  [ CP (Alt|Statei)P(Statei)] i

  5. Payoff Table Probabilities of =Demand Levels; sum = 1 .1 .2 .1 .4 .2 Demand Stock

  6. EMV Calculations EMV5 = .1(20) + .2(10) + .1(0) + .4(-10) + .2(-20) = EMV10 = .1(5) + .2(40) + .1(30) + .4(20) + .2(10) = EMV15 = .1(-10) + .2(25) + .1(60) + .4(50) + .2(40) = EMV20 = .1(-25) + .2(10) + .1(45) + .4(80) + .2(70) = EMV25 = .1(-40) + .2(-5) + .1(30) + .4(65) + .2(100) = EMV (Alt) =  [ CP (Alt|Statei)P(Statei)] i

  7. Payoff Table Demand Stock

  8. Value of Perfect Information • How much would it be worth to us to know the state of nature ahead of time (would we change our decision)? • Specifically, how much additional profit could we make if we knew exactly what demand would be?

  9. Value of Perfect Information • EPPI = Expected Payoff Under Perfect Information • EPPP = Expected Payoff with Perfect Prediction • EPUC = Expected Payoff Under Certainty

  10. Payoff Table If we knew demand would be 5 shirts, how much would we stock? 10? 15? 20? 25? .1 .2 .1 .4 .2 Demand Stock

  11. Expected Payoff Under Perfect Information = = This is the maximum we could expect to make if we always knew ahead of time what the demand was going to be. EPPI =  CP* (State i) P (State i) i

  12. Expected Value of Perfect Information • EVPI is the expected value of having perfect information; i.e. – it is the amount we would make over and above what we could make on our own without perfect information EVPI = EPPI – EMV*

  13. Expected Value of Perfect Information EVPI = EPPI – EMV* EVPI = This is how much perfect information would be worth to us. It’s also the maximum amount we would be willing to pay for perfect information.

  14. Decision Tree • Visual display of the decision at hand • Allows for sequential decision making • Steps: • For each set of state branches, find the EMV for the decision branch. • Compare the EMVs across all decisions and select the best decision based on the highest EMV.

  15. D=5 (.1) 20 D=10 (.2) 10 D=15 (.1) 0 D=20 (.4) -10 D=25 (.2) -20 Stock 5 D=5 (.1) 5 D=10 (.2) 40 D=15 (.1) 30 D=20 (.4) 20 D=25 (.2) 10 Decision node Stock 10 State node D=5 (.1) -10 D=10 (.2) 25 D=15 (.1) 60 D=20 (.4) 50 D=25 (.2) 40 Stock 15

  16. D=5 (.1) -25 D=10 (.2) 10 D=15 (.1) 45 D=20 (.4) 80 D=25 (.2) 70 Stock 20 D=5 (.1) -40 D=10 (.2) -5 D=15 (.1) 30 D=20 (.4) 65 D=25 (.2) 100 Stock 25

  17. D=5 (.1) 20 D=10 (.2) 10 D=15 (.1) 0 D=20 (.4) -10 D=25 (.2) -20 Stock 5 EMV= D=5 (.1) 5 D=10 (.2) 40 D=15 (.1) 30 D=20 (.4) 20 D=25 (.2) 10 Stock 10 EMV= D=5 (.1) -10 D=10 (.2) 25 D=15 (.1) 60 D=20 (.4) 50 D=25 (.2) 40 Stock 15 EMV=

  18. D=5 (.1) -25 D=10 (.2) 10 D=15 (.1) 45 D=20 (.4) 80 D=25 (.2) 70 Stock 20 EMV= D=5 (.1) -40 D=10 (.2) -5 D=15 (.1) 30 D=20 (.4) 65 D=25 (.2) 100 Stock 25 EMV=

  19. Sequential Decision Making • Decision trees are very useful when there are multiple decisions to be made and they follow a sequence in time. There are also usually multiple sets of states. CP Decision 1 State 1 CP State 1 Decision 2 Decision 1 State 2 State 2 CP CP State 1 State 1 CP CP Decision 1 Decision 2 State 2 State 2 Decision 2 CP State 1 CP CP Decision 1 CP Decision 3 State 2 Decision 2 CP

  20. Sequential Decision Example • Suppose that you are trying to decide which of three companies to invest in: Company A, B, or C. If you choose A, there is a 50/50 chance of going broke or earning $50,000. If you go broke with A, you then have three choices: accept a debt of $2,000; embezzle $35,000 of company money (not that we would EVER do this) and leave the country; or file for personal bankruptcy at the hands of a court-appointed trustee.

  21. Invest in A Invest in B Invest in C

  22. Sequential Decision Example • Suppose that you are trying to decide which of three companies to invest in: Company A, B, or C. If you choose A, there is a 50/50 chance of going broke or earning $50,000. If you go broke with A, you then have three choices: accept a debt of $2,000; embezzle $35,000 of company money (not that we would EVER do this) and leave the country; or file for personal bankruptcy at the hands of a court-appointed trustee.

  23. Debt Embezzle Go Broke(.5) Invest in A Bankrupt Earn $$(.5) $50,000 Invest in B Invest in C

  24. Sequential Decision Example • If you embezzle money and leave the country, there is a 95% chance of being extradited and fined $10,000. If you file for personal bankruptcy, there is a 95% chance that your debts will be wiped out and a 5% chance that you will have to pay back $4,000.

  25. Debt -$2K Extrad(.95) -$10K Go Broke(.5) Embezzle A Not(.05) $35K Earn $$(.5) Bankrupt Pay back(.05) -$4K B $50,000 Wiped out(.95) $ 0 C

  26. Sequential Decision Example • If you choose Company B, there is an 80 percent chance of earning $25,000. If Business B fails, you still have the option of either settling for $500 or taking a stock option in the company that will be worth $50,000 with probability 0.1 or zero with probability 0.9.

  27. A Earn $$(.8) B $25000 Settle B fails(.2) $500 Earn(.1) Stock option $ 50000 C Not(.9) $ 0

  28. Sequential Decision Example • Finally if you choose Company C, you will either earn $10,000 with probability 0.6, or be in debt for $1,000 with probability 0.4.

  29. A B Earn $$(.6) $10000 C Debt(.4) -$1000

  30. Sequential Decision Example • Solve by folding back the tree • Trees are drawn from left to right; they are folded back from right to left. • For each set of state branches, find the EMV for the connected decision. • For each set of decisions, select the one with the highest EMV and carry the EMV* forward (to the left)

  31. Debt Extrad(.95) -$10000 Go Broke(.5) Embezzle A Not(.05) $35000 Earn $$(.5) Bankrupt Pay back(.05) $50000 -$4000 Earn $$(.8) B $25000 Wiped out(.95) Settle B fails(.2) $500 $ 0 Earn(.1) Stock option Earn $$(.6) $50000 $10000 C Not(.9) Debt(.4) -$1000 $ 0

  32. Sequential Decision Example • After you fold back the tree and determine the best initial decision, then state the complete optimal sequence of decisions: Invest in Company A. If you go broke, then file for bankruptcy. Otherwise enjoy the $50,000!!

  33. For Next Class • Continue reading Chapter 14 (thru page 27) • Do remaining homeworks

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