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Decision Theory Models Decision Tree & Utility Theory

Decision Theory Models Decision Tree & Utility Theory. Kusdhianto Setiawan Gadjah Mada University. Introduction. What is a good decision? Based on logic Is rational model applied by all people in making logical decision? What is rational model? Types of Decision-Making Environment

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Decision Theory Models Decision Tree & Utility Theory

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  1. Decision Theory ModelsDecision Tree & Utility Theory Kusdhianto Setiawan Gadjah Mada University

  2. Introduction • What is a good decision? • Based on logic • Is rational model applied by all people in making logical decision? • What is rational model? • Types of Decision-Making Environment • Under Certainty: tahu semua konsekuensinya • Under Risk: tahu probabilitas dari outcomes • Under 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 state of 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

  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 EMV • EVwPI = (best outcome for the 1st SoN) x (P(1st SoN)) + …. + (best outcomes of last SoN) x (P(last SoN)).

  8. Opportunity Loss • maximizing EMV = minimizing expected opportunity loss (EOL)

  9. Sensitivity Analysis • SA investigaes how our decision might change with different input data. • EMV(large p) = 200.000P – 180.000(1-P) = 380.000P – 180.000 • EMV(small p) = 100.000P – 20.000(1-P) = 120.000P – 20.000 • EMV(do nothing) = 0P + 0(1-P) = 0

  10. Sensitivity Analysis EMV Values EMV Large Plant EMV Small Plant EMV Do Nothing 0.62 0.167 -20.000 Probability of Favourable Market -180.000

  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 Donut Buying price from the producer: $4/cartoon Selling price to customer: $6/cartoon, then Marginal Profit (MP) = 6 – 4 = $2/cartoon Marginal Loss (ML) = $4, lets P = 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) ≥ ML or P(MP + ML) ≥ ML or 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

  15. Marginal Analysis with Normal Distribution • Data Requirement • The average or mean for the product, μ • The standard deviation of sales, σ • The Marginal Profit • The Marginal Loss • Steps • Determine 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 papers • Standard Deviation = 10 papers • Marginal Profit = 6 cents • Marginal Loss = 4 cents • Determine Stocking Policy! Step 1 P = ML/(ML+MP)=4/(4+6)=0.4 Step 2 1 - 0.4 = 0.6 … look at the z table, and find for z Z = 0.25 standard deviation from the mean 0.25 = (X*- 50)/10  X*=10(0.25) + 50 = 52.3 or 53 papers Decision: The distributor should order 53 paper daily.

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