Presentation on theme: "Decision Theory Models Decision Tree & Utility Theory"— Presentation transcript:
1 Decision Theory Models Decision Tree & Utility Theory Kusdhianto SetiawanGadjah Mada University
2 Introduction What is a good decision? Based on logicIs rational model applied by all people in making logical decision?What is rational model?Types of Decision-Making EnvironmentUnder Certainty: tahu semua konsekuensinyaUnder Risk: tahu probabilitas dari outcomesUnder Uncertainty: tidak tahu probabilitas dari outcomes
3 Decision Making Under Risk Risky choice = Gamble that can yield various outcomes with different probabilities?Psychophysical Analysis relevant?Daniel Bernoully (1978):people are generally averse to risk and risk aversion decreases with increasing wealth.People do not evaluate prospects by the expectation of their monetary outcomes, but rather by the expectation of subjective value of these outcome
4 Von Neumann & Morgenstein (1947) – Concept of Rationality Preference of rational decision making should follow:Transitivity, if A is preferred to B and B is preferred to C, then A is preferred to C.Substitution, if A is preferred to B, then an even chance to get A or C is preferred to an even chance to get B or C).Dominance, if prospect A is at least as good as prospect B in every respect and better than B in at least one respect, then A should be preferred to B.Invariance, preference order between prospects should not depend on the manner in which they are described.
5 Expected Monetary Value EMV is the weighted sum of possible payoffs for each alternative (prospect)EMV (alternative i) =(payoff of first state of nature) x (probability of first state of nature)+ (payoff of 2nd state of nature) x (probability of 2nd state of nature)+ ……… + (payoff of last state of nature) x (probability of last stateof nature).What does EMV means?Nilai moneter (uang) yang akan kita terima secara rata-rata jika mengambil keputusan dalam kondisi tertentu (state of nature) berulang kali.
6 EMV Continued John Thompson Case Alternative State of Nature EMV Fav. MktUnf. MktConstruct a large plant10.000Construct a small plant40.000Do NothingProbabilities0.5
7 Expected Value of Perfect Information (EVPI) EVPI merupakan harga dari perfect information, misal: jasa konsultan yang diharapkan akan memberikan informasi paling benar (harga tertinggi yang mungkin kita bayar).EVPI = expected value with perfect information (EVwPI)– maximum EMVEVwPI = (best outcome for the 1st SoN) x (P(1st SoN)) + …. + (best outcomes of last SoN) x (P(last SoN)).
8 Opportunity Lossmaximizing EMV = minimizing expected opportunity loss (EOL)AlternativeState of NatureEOLFav. MktUnf. MktConstruct a large plant–0 – ( )90.000Construct a small plant–0 – ( )60.000Do Nothing– 00- 0Probabilities0.5
9 Sensitivity AnalysisSA investigaes how our decision might change with different input data.EMV(large p) = P – (1-P)= P –EMV(small p) = P – (1-P)= P –EMV(do nothing) = 0P + 0(1-P) = 0
10 Sensitivity Analysis EMV Values EMV Large Plant EMV Small Plant EMV Do Nothing0.1670.62Probability of Favourable Market
11 Decision Making Under Uncertainty Maximax (Optimistic Approach)Maximin (Pessimistic Approach)Equally Likely (Laplace)Criterion of Realism (Hurwicz Criterion)Minimax (based on opportunity loss)
12 Marginal Analysis: Discrete Distribution Example: Café’ du DonutBuying price from the producer: $4/cartoonSelling price to customer: $6/cartoon, thenMarginal Profit (MP) = 6 – 4 = $2/cartoonMarginal Loss (ML) = $4, letsP = probability that demand ≥ supply (or the probability of selling at least one additional unit)1 – P = probability that demand will be less than supply.
13 The Optimal Decision Rule P(MP) ≥ (1 - P)(ML)or P(MP) + P(ML) ≥ MLor P(MP + ML) ≥ MLor P ≥ ML/(MP+ML), meaning that:as long as the probability of selling one more unit (P) is greater than or equal to ML/(MP + ML), we would stock additional unit.
14 Café’ Du Donut Case P ≥ ML/(MP+ML) = 4/(4+2) = 4/6 P ≥ 0.66 Daily SalesP that sales will be at this levelP that Sales will be at this level or greater40.051 ≥ 0.6650.150.95 ≥ 0.6660.8 ≥ 0.6670.200.6580.250.4590.10.210P ≥ ML/(MP+ML) = 4/(4+2) = 4/6P ≥ 0.66
15 Marginal Analysis with Normal Distribution Data RequirementThe average or mean for the product, μThe standard deviation of sales, σThe Marginal ProfitThe Marginal LossStepsDetermine P = ML/(MP+ML)Locate P on the Normal Distribution, and find Z for a given area under the curve, then find X*Z = (X* - m)/s
16 Chicago Tribune Distributor Case Average Sales/day = 50 papersStandard Deviation = 10 papersMarginal Profit = 6 centsMarginal Loss = 4 centsDetermine Stocking Policy!Step 1P = ML/(ML+MP)=4/(4+6)=0.4Step 2= 0.6 … look at the z table, and find for zZ = 0.25 standard deviation from the mean0.25 = (X*- 50)/10 X*=10(0.25) + 50 = 52.3 or 53 papersDecision: The distributor should order 53 paper daily.