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Quantitative Analysis for Management

Quantitative Analysis for Management. Chapter 3 Fundamentals of Decision Theory Models. 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

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Quantitative Analysis for Management

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  1. Quantitative Analysis for Management Chapter 3 Fundamentals of Decision Theory Models 3-1

  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 3-2

  3. 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 3-3

  4. Introduction • Decision theory is an analytical and systematic way to tackle problems • A good decision is based on logic. 3-4

  5. 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

  6. Decision Table for Thompson Lumber Favorable Market ($) Unfavorable Market ($) Construct a large plant 200,000 -180,000 Construct a small plant -20,000 100,000 Do nothing 0 0 3-6

  7. 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 knows the probabilities of the various outcomes • Decision-making under uncertainty • The decision-maker does not know the probabilities of the various outcomes 3-7

  8. Decision-Making Under Risk n = å EMV(Altern ative i) (Payoff * P(S )) j S j = j 1 = where j 1 to the number of states of nature, n Expected Monetary Value: 3-8

  9. Decision Table for Thompson Lumber Favorable Market ($) Unfavorable Market ($) Construct a large plant 200,000 -180,000 10,000 Construct a small plant 100,000 -20,000 40,000 Do nothing 0 0 0 0.50 0.50 EMV 3-9

  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 3-10

  11. Expected Value With Perfect Information (EV|PI) n = å EV | PI ( best outcome for state of nature j) * P(S ) j = 1 j = where j 1 to the number of states of nature, n 3-11

  12. Expected Value of Perfect Information • EVPI = EV|PI - maximum EMV 3-12

  13. Expected Value of Perfect Information Favorable Market ($) Unfavorable Market ($) Construct a large plant 200,000 Construct a small plant 40,000 Do nothing 0 0.50 0.50 EMV 3-13

  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 3-14

  15. Expected Opportunity Loss • EOL is the cost of not picking the best solution • EOL = Expected Regret We want to maximize EMV or minimize EOL 3-15

  16. Computing EOL - The Opportunity Loss Table 3-16

  17. The Opportunity Loss Table continued 3-17

  18. The Opportunity Loss Table continued 3-18

  19. 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) 3-19

  20. Sensitivity Analysis - continued EMV (Small Plant) EMV(Large Plant) 3-20

  21. Decision Making Under Uncertainty • Maximax • Maximin • Equally likely (Laplace) • Criterion of Realism • Minimax 3-21

  22. Decision Making Under Uncertainty Favorable Market ($) Unfavorable Market ($) 200,000 -180,000 Construct a large plant 100,000 -20,000 Construct a small plant 0 0 Do nothing Maximax - Choose the alternative with the maximum output 3-22

  23. Decision Making Under Uncertainty Favorable Market ($) Unfavorable Market ($) 200,000 -180,000 Construct a large plant 100,000 -20,000 Construct a small plant 0 0 Do nothing Maximin - Choose the alternative with the maximum minimum output 3-23

  24. Decision Making Under Uncertainty Favorable Market ($) Unfavorable Market ($) 200,000 -180,000 EMV Construct a large plant 10,000 100,000 -20,000 Construct a small plant 40,000 0 0 Do nothing 0 0.50 0.50 Equally likely (Laplace) - Assume all states of nature to be equally likely, choose maximum EMV 3-24

  25. Decision Making Under Uncertainty Favorable Market ($) Unfavorable Market ($) 200,000 -180,000 CR Construct a large plant 124,000 100,000 -20,000 Construct a small plant 76,000 0 0 0 Do nothing 0.50 0.50 Criterion of Realism (Hurwicz): CR = *(row max) + (1-)*(row min) 3-25

  26. Decision Making Under Uncertainty Favorable Market ($) Unfavorable Market ($) Max in row Construct a large plant 0 180,000 180,000 Construct a small plant 100,000 20,000 100,000 Do nothing 200,000 0 200,000 0.50 0.50 Minimax - choose the alternative with the minimum maximum Opportunity Loss 3-26

  27. Marginal Analysis • P = probability that demand is greater than 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 3-27

  28. 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 3-28

  29. Café du Donut Example 3-29

  30. Café du Donut Example continued ML ³ P + ML MP 4 4 = = = 0 66 . 4 + 2 6 • Marginal profit = selling price - cost = $6 - $4 = $2 • Marginal loss = cost • Therefore: 3-30

  31. Café du Donut Example continued 3-31

  32. Marginal AnalysisNormal Distribution •  = average or mean sales •  = standard deviation of sales • MP = marginal profit • ML = Marginal loss 3-32

  33. 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* 3-33

  34. Joe’s Newsstand Example A • ML = 4 • MP = 6 • = Average demand = 50 papers per day •  = Standard deviation of demand = 10 3-34

  35. Joe’s Newsstand Example A continued 4 ML = = = 0 40 P . + 4 + 6 ML MP * - 50 X 0 25 = 10 * = 10 0 25 + 50 = 52 5 53 X * . . or newspapers • Step 1: • Step 2: Look on the Normal table for P = 0.6 (i.e., 1 - .04)  Z = 0.25, and or: . 3-35

  36. Joe’s Newsstand Example A continued 3-36

  37. Joe’s Newsstand Example B • ML = 8 • MP = 2 •  = Average demand = 100 papers per day •  = Standard deviation of demand = 10 3-37

  38. Joe’s Newsstand Example B continued 8 ML = = = 0 80 P . + 8 + 2 ML MP * - 1000 X - 0 84 = 10 * = - 8 4 + 100 = 91 6 92 X . . or newspapers • Step 1: • Step 2: Z = -0.84 for an area of 0.80 and or: . 3-38

  39. Joe’s Newsstand Example B continued 3-39

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