2420lecture09

2420lecture09 - Decision Analysis What is it? (to p2) What...

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1 Decision Analysis What is it? What is the objective? More example Tutorial: 8 th ed:: 5, 18, 26, 37 9 th ed: 3, 12, 17, 24 (to p2) (to p5) (to p50)
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2 What is it? It concerns with making a decision or an action based on a series of possible outcomes The possible outcomes are normally presented in a table format called “ Payoff Table” (to p3) (to p1)
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3 Payoff Table A payoff table consists of Columns: state of nature (ie events) Rows: choice of decision It corresponding entries are “payoff values” Example (to p4)
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4 Payoff Table (to p2)
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5 Objective Our objective here is to determine which which decision should be chosen based on the payoff table How to achieve it? Simple two-dimensional cases Posterior analysis with Bayesian rules (to p20) (to p1) (to p6)
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6 How to achieve it? The final decision could be based on one of the following criteria: 1) maximax, 2) maximin, 3) minimax regret, 4) Hurwicz, 5) equal likelihood Each one is better one? Ex 4 and 7 QM programs (to p7) (to p9) (to p11) (to p15) (to p16) (to p17) (to p18) (to p5)
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7 The Maximax Criterion Known as “optimistic” person, he/she will pick the decision that has the maximum of maximum payoffs . How to derive this decision? Example: (to p8)
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8 Procedural Steps: Step1: For each row (or decision), select its max values Step 2: Choose the decision that has the max value of Step1 Example: Max 50,000 100,00 0 30,000 100,000 max (to p3)
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9 The Maximin Criterion Known as the “pessimistic” person, she/he will select the decision that has the maximum of the minimum from the payoff table How to obtain it? Example Select this action (to p10)
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10 Procedural steps: Step 1: For each row (or decision), obtain its min values Step 2: Choose the decision that has the max value from step 1 Min 30,000 -40,000 10,000 (to p3)
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11 The Minimax: Regret Criterion Regret is the difference between the payoff from the best decision and all other decision payoffs. The decision maker attempts to avoid regret by selecting the decision alternative that minimizes the maximum regret. How to obtain it? Solution (to p12)
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12 Procedural steps: Step 1: Find out the max value for each column Step 2: Subtract value of step 1 to all entry of that column Step 3: Find out the max value for each row Step 4: Choose the decision that has smallest value of step 3 Step 1: Max 100,000 30,000 Example (to p13)
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13 (100,000 - 50,000) Step 2: Subtract value of step 1 to all entry of that column (30,000 - 30,000) Note: this is a regret table. (to p14)
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14 Max 50,000 70,000 70,000 Min Step 3: Find out the max value for each row Step 4: Choose the decision that has smallest value of step 3 Select this decision (to p3)
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15 Decision Making without Probabilities The Hurwicz Criterion - The Hurwicz criterion is a compromise between the max imax and max imin criterion. - A coefficient of optimism, α , is a measure of the decision maker’s optimism. - The Hurwicz criterion multiplies the best payoff by α and the worst payoff by 1- α ., for each decision, and the best result is selected.
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2420lecture09 - Decision Analysis What is it? (to p2) What...

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