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Chapter 14

Chapter 14. Decision Analysis – Part 3. Restaurant Decision.

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Chapter 14

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  1. Chapter 14 Decision Analysis – Part 3

  2. Restaurant Decision • A company plans to open a restaurant/bar in Newark. It is considering 3 locations, A, B and C. Location A is furthest from campus, B is next closest and C is adjacent to the campus. The closer to campus, the greater the chance the restaurant will NOT get a liquor license– which will greatly impact revenues. The company plans to request a special vote to obtain a license. The vote could be favorable or unfavorable.

  3. Restaurant Decision • The following payoff table shows the potential revenue for each location given the vote outcome:

  4. Restaurant Decision • If the company has determined that the likelihood of a favorable vote is .55 and unfavorable is .45, then EMVs could be calculated as follows: EMVA = 60(.55) + 50(.45) = EMVB = 80(.55) + 30(.45) = EMVC = 100(.55) + 0(.45) =

  5. Restaurant Decision - EVPI • If the company has determined that the likelihood of a favorable vote is .55 and unfavorable is .45, then the EVPI could be calculated as follows: • EVPI = EPPI – EMV • EVPI = (100)(.55) + (50)(.45) – 57.5 = • EVPI =

  6. Sensitivity Analysis • In many cases, probabilities and payoffs are based on subjective assessments and can vary over time. • Sensitivity analysis can be used to determine how changes to these inputs impact your decision • If a small change in one of the inputs causes a change in the recommended decision alternative, extra effort and care should be taken in estimating the input value. The inverse is true as well!

  7. Sensitivity Analysis Example • Assume a reversal of the likelihoods from our restaurant example: Favorable = .45, Unfavorable = .55. • Now EMVs could be calculated as follows: • EMVA = 60(.45) + 50(.55) = • EMVB = 80(.45) + 30(.55) = • EMVC = 100(.45) + 0(.55) =

  8. Sensitivity Analysis Example • When likelihood of Favorable is larger, choose B; smaller, choose A. Question is: up to what point? • In the situation with 2 states of nature, can determine ranges using the following formula: P(S2) = 1- P(S1) = 1-P

  9. Sensitivity Analysis Example EV(A) = P(S1)(60) + P(S2)(50) = p(60) + (1-p)(50) = 60p + 50 – 50p = 10p +50 Use the same process for each alternative: EV(B) = 50p+30 EV(C) = 100p

  10. Sensitivity Analysis Example • Can use these equations to graph the EMVs across varying likelihoods to determine ranges of optimal selections • Identify graphing coordinates for each by setting p equal to extreme likelihoods: p = 1 and p = 0

  11. Sensitivity Analysis Example EV Alt B = highest EV Alt C = highest EV 120 100 80 60 40 20 0 -20 Alt A = highest EV EVC EVB EVA .2 .4 .6 .8 1.0 p How do you determine the points where you would change your mind?

  12. Sensitivity Analysis Example • Set equations equal to determine points of intersection EVA = EVB = 10p+50 = 50p+30 = .50 EVB = EVC = 50p+30 = 100p = .60 Conclusion: If likelihood for Favorable Vote is: <50% - Choose location A 50% - 60% - Choose location B 60%+ - Choose location C

  13. Sensitivity Analysis Example • Can also use sensitivity analysis to test payoff values • Identify “best” and 2nd best alternatives • Best: Choice B with EMV of 57.5 • 2nd Best: Choice A with EMV of 55.5 • Can state that Choice B will remain optimal as long as EVB≥ 55.5 Up to what point will this be true?

  14. Sensitivity Analysis Example • Let F = the payoff of decision B when a favorable vote is encountered • Let U = the payoff of decision B when an unfavorable vote is encountered EVB = .55F + .45U = .55F + .45U ≤ 55.5 = .55F + .45(30) = 55.5 .55F + 13.5 = 55.5 .55F = 42 F = 76.4 What does this # mean to you?

  15. Sensitivity Analysis Example • Let F = the payoff of decision B when a favorable vote is encountered • Let U = the payoff of decision B when an unfavorable vote is encountered EVB = .55F + .45U = .55F + .45U ≤ 55.5 = .55(80) + .45U = 55.5 44 + .45U= 55.5 .45U = 11.5 U = 25.5 What does this # mean to you?

  16. Reviewing Our Decision • Have alternatives  • Have payoff information  • Have initial assumptions re: likelihoods  • Have EVPI information– can decide whether or not to get new information to revise or update our assumptions  What happens if our new information changes our initial assumptions?

  17. New Information • Prior to deciding on a location, the company must decide whether to conduct a lobbying effort among the Newark authorities. The outcome of the lobbying effort can be positive or negative with the following likelihoods: P(positive lobbying effort) = .75 P(negative lobbying effort) = .25

  18. New Information • If the lobbying effort is positive, the company has determined that the likelihood for a favorable vote would increase– with new likelihoods as follows: P(Favorable vote given a positive lobbying effort) = .95 P(Unfavorable vote given a positive lobbying effort) = .05

  19. New Information • If the lobbying effort is negative, the company has determined that the likelihood for a favorable vote would decrease– with new likelihoods as follows: P(Favorable vote given a negative lobbying effort) = .35 P(Unfavorable vote given a negative lobbying effort) = .65

  20. New Information • If NO lobbying effort is conducted, the PRIOR probabilities are still applicable: P(favorable) = .55 P(unfavorable) = .45

  21. Decision Strategy with New Information • Can now create a new decision tree that reflects the alternate courses of action and revised (posterior) probabilities and SOLVE LET’S GO TO THE BOARD

  22. Fav .95 60 50 80 30 100 0 A Unfav .05 Positive .75 B Fav .95 Unfav .05 C Fav .95 Lobby Effort Unfav .05 Fav .35 60 50 80 30 100 0 A Unfav .65 B Fav .35 Unfav .65 Negative .25 C Fav .35 Unfav .65

  23. Fav .55 60 50 80 30 100 0 A Unfav .45 B Fav .55 Unfav .45 No Lobby Effort C Fav .55 Unfav .45

  24. Fav .95 60 50 80 30 100 0 A Unfav .05 Positive .75 B Fav .95 Unfav .05 C Fav .95 Lobby Effort Unfav .05 Fav .35 60 50 80 30 100 0 A Unfav .65 B Fav .35 Unfav .65 Negative .25 C Fav .35 Unfav .65

  25. Fav .55 60 50 80 30 100 0 A Unfav .45 B Fav .55 Unfav .45 No Lobby Effort C Fav .55 Unfav .45

  26. Expected Value of Sample Information • If we chose to do the lobbying effort, the EV = $84.625 • If we chose NOT to do the lobbying effort, the EV = 57.5 • The difference between these EVs is the Expected Value of Sample Information: EVSI = | EVwSI – EVwoSI |

  27. Expected Value of Sample Information EVSI = | EVwSI – EVwoSI | EVSI = 84.625 – 57.5 = 27.125 Conducting the lobbying effort adds $27,125 to the location decision EV.

  28. Efficiency of Sample Information • Since we can’t be sure that the sample information will yield us PERFECT information, it’s helpful to consider the efficiency of the information we do receive. • Assuming that perfect information yields an efficiency of 100%, we can calculate: • Efficiency = (EVSI / EVPI) x 100

  29. Efficiency of Sample Information Efficiency = (EVSI / EVPI) x 100 = 27.125 x 100 = 135% 20 This value means that the lobbying effort is 135% as efficient as perfect information– so we would definitely want to pursue it!

  30. For Next Class • Read balance of Chapter 14 (Bayes Theorem) and Utility Theory

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