09 QM Lecture Note B

# 09 QM Lecture Note B - Lecture Note B: Decision Analysis GG...

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42 Lecture Note B: Decision Analysis GG Hegde Evaluating and choosing among alternatives List all possible alternatives (Choices) and possible outcomes for each alternative( Chances) Identify the payoff for each alternative & outcome combination Based on a given criterion, choose the best decision Decisions Under Uncertainity :Probabilities of the possible outcomes are not known Optimistic Pessimistic Minimax regret Decisions Under Uncertainity: Probabilities of the possible outcomes are known ( decision trees approach) Expected Value approach: Expected Value with No Information (EV with No Info) Expected Value with Perfect Information( EV with PI) Expected Value of PI, EVPI= EV with PI- EV with No Info Sample Information(SI): Revising the probabilities, & computing Expected value with SI, EV with SI. Expected value of SI, EVSI= EV with SI- EV with No Info Efficiency= EVSI/EVPI

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43 Ex.1: Real Estate Co. Decisions: States of Nature(Chance events): Pay off- Table: s1 s2 D1 200 -180 D2 100 -20 Prob 0.5 0.5 (prior) Draw decision trees and compute EV with No Info, EV with PI. (a)EV with No Info = 40 (b)EV with PI= 100
44 ( c) s1 s2 D1 200 -180 D2 100 -20 Prob(prior) 0.5 0.5 Market Research Information: Sample Information(SI): Revising the probabilities, & computing Expected value with SI(EV with SI): Market survey: Favorable or Unfavorable Prior probabilities are the probability values before new information Revised probabilities are obtained by combining the prior probabilities with the new information. Market Research Firm provides(conditional info): Fav or Unfav report P(Fav/s1)=0.700, P(Unfav/s2)=0.800 Decision tree with SI: EV with SI= 59.2 116.4, 73.6, -77.4, 12.4 Decision Starategy: Effiiency=

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46 s1 s2 D1 200 -180 D2 100 -20 Prob 0.5 0.5 (prior) Market Research Firm provides(conditional info): Fav or Unfav report P(Fav/s1)=0.700, P(Unfav/s2)=0.800 Revising the probabilities

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47 Probabilities are not known s1 s2 D1 200 -180 D2 100 -20 Optimistic: Assume the best payoff will occur for each alternative & Choose best of the best Pessimistic : Assume the worst payoff will occur for each alternative, choose the best of the worst Regret or opportunity loss measures “how much better we could have done” Regret = (best payoff) – (actual payoff) Choices s1 s2 D1 200 - 180 D2 100 -20 Best Regret or opportunity loss “ table
48 Ex.2 :Lumber Company(LC): Choices: Build a large plant(D1) or Build a small plant(D2) Chances: High Demand(s1) , Moderate Demand(s2), Low demand(s3) Output: Payoff Table( in millions): s1 s2 s3 Large Plant(D1 ): \$200 \$100 -\$120 Small Plant(D2): \$90 \$50 -\$20 Probabilities are not known Optimistic: Pessimistic :

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## 09 QM Lecture Note B - Lecture Note B: Decision Analysis GG...

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