1 / 33

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

jory
Télécharger la présentation

Chapter 14

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related