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## Chapter 3 Fundamentals of Decision Theory Models

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**Chapter 3**Fundamentals of Decision Theory Models 3-1**Learning Objectives**Students will be able to: • List the steps of the decision-making process • Describe the types of decision-making environments • Use probability values to make decisions under risk • Make decisions under uncertainty, where there is risk but probability values are not known • Use computers to solve basic decision-making problems 3-2**Chapter Outline**3.1 Introduction 3.2 The Six Steps in Decision Theory 3.3 Types of Decision-Making Environments 3.4 Decision Making Under Risk 3.5 Decision Making Under Uncertainty 3.6 Marginal Analysis with a Large Number of Alternatives and States of Nature 3-3**Introduction**• Decision theory is an analytical and systematic way to tackle problems • A good decision is based on logic. 3-4**The Six Steps in Decision Theory**• Clearly define the problem at hand • List the possible alternatives • Identify the possible outcomes • List the payoff or profit of each combination of alternatives and outcomes • Select one of the mathematical decision theory models • Apply the model and make your decision 3-5**Types of Decision-Making Environments**• Type 1: Decision-making under certainty • decision-maker knows with certainty the consequences of every alternative or decision choice • Type 2: Decision-making under risk • The decision-maker does know the probabilities of the various outcomes • Decision-making under uncertainty • The decision-maker does not know the probabilities of the various outcomes 3-7**Decision-Making Under Risk**Expected Monetary Value 3-10**Expected Value of Perfect Information (EVPI)**• EVPI places an upper bound on what one would pay for additional information • EVPI is the expected value with perfect information minus the maximum EMV 3-12**Expected Value of Perfect Information**• EVPI = EV|PI - maximum EMV 3-14**Expected Value of Perfect Information**EVPI = expected value with perfect information - max(EMV) = $200,000*0.50 + 0*0.50 - $40,000 = $60,000 3-16**Expected Opportunity Loss**• EOL is the cost of not picking the best solution • EOL = Expected Regret 3-17**Sensitivity Analysis**EMV(Large Plant) = $200,000P - (1-P)$180,000 EMV(Small Plant) = $100,000P - $20,000(1-P) EMV(Do Nothing) = $0P + 0(1-P) 3-21**Sensitivity Analysis - continued**250000 200000 Point 1 Point 2 150000 Small Plant 100000 50000 EMV Values 0 -50000 0 0.2 0.4 0.6 0.8 1 -100000 Large Plant EMV -150000 -200000 Values of P 3-22**Decision Making Under Uncertainty**• Maximax • Maximin • Equally likely (Laplace) • Criterion of Realism • Minimax 3-23**Decision Making Under Uncertainty**Maximax - Choose the alternative with the maximum output 3-24**Decision Making Under Uncertainty**Maximin - Choose the alternative with the maximum minimum output 3-25**Decision Making Under Uncertainty**Equally likely (Laplace) - Assume all states of nature to be equally likely, choose maximum Average 3-26**Decision Making Under Uncertainty**Criterion of Realism (Hurwicz): CR = *(row max) + (1-)*(row min) 3-27**Decision Making Under Uncertainty**Minimax - choose the alternative with the minimum maximum Opportunity Loss 3-28**Marginal Analysis**• P= probability that demand is greater that or equal to a given supply • 1-P = probability that demand will be less than supply • MP = marginal profit • ML = marginal loss • Optimal decision rule is: P*MP (1-P)*ML • or 3-29**Marginal Analysis -Discrete Distributions**Steps using Discrete Distributions: • Determine the value forP • Construct a probability table and add a cumulative probability column • Keep ordering inventory as long as the probability of selling at least one additional unit is greater than P 3-30**Café du Donut Example continued**Marginal profit = selling price - cost = $6 - $4 = $2 Marginal loss = cost Therefore: 3-32**Café du Donut Example continued**Daily Sales Probability of Probability that Sales (Cartons) Sales at this Level Will Be at this Level or Greater ³ 4 0.05 1.00 0.66 ³ 5 0.15 0.95 0.66 ³ 6 0.15 0. 80 0.66 7 0.20 0.65 8 0.25 0.45 9 0.10 0.20 10 0.10 0.10 1.00 3-33**Marginal AnalysisNormal Distribution**• = average or mean sales • = standard deviation of sales • MP = marginal profit • ML = Marginal loss 3-34**Marginal Analysis -Discrete Distributions**ML = P + ML MP * - m X = Z s • Steps using Normal Distributions: • Determine the value forP. • Locate P on the normal distribution. For a given area under the curve, we find Zfrom thestandard Normal table. • Using we can now solve for X* 3-35**Joe’s Newsstand Example A**• ML = 4 • MP = 6 • = Average demand = 50 papers per day • = Standard deviation of demand = 10 3-36**Joe’s Newsstand Example A - continued**Step 1: Step 2: Look in the Normal table for P = 0.6 (i.e., 1 – 0.4) . 3-37**Joe’s Newsstand Example B**• ML = 8 • MP = 2 • = Average demand = 100 papers per day • = Standard deviation of demand = 10 3-39**Joe’s Newsstand Example B - continued**• Step 1: • Step 2: Z = -0.84 for an areaof 0.80 and or: 3-40