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Stevenson and Ozgur First Edition Introduction to Management Science with Spreadsheets McGraw-Hill/Irwin Copyright © 2007 by The McGraw-Hill Companies,

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Presentation on theme: "Stevenson and Ozgur First Edition Introduction to Management Science with Spreadsheets McGraw-Hill/Irwin Copyright © 2007 by The McGraw-Hill Companies,"— Presentation transcript:

1 Stevenson and Ozgur First Edition Introduction to Management Science with Spreadsheets McGraw-Hill/Irwin Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter 11 Decision Theory Part 3 Probabilistic Decision Models

2 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–2 Learning Objectives 1.Outline the characteristics of a decision theory approach to decision making. 2.Describe and give examples of decisions under certainty, risk, and complete uncertainty. 3.Make decisions using maximin, maximax, minimax regret, Hurwicz, equally likely, and expected value criteria and use Excel to solve problems involving these techniques. 4.Use Excel to solve decision-making problems under risk using the expected value criterion. After completing this chapter, you should be able to:

3 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–3 Learning Objectives (cont’d) 5.Develop decision trees that consist of a combination of decision alternatives and events. 6.Use TreePlan to develop decision trees with Excel. 7.Determine if acquiring additional information in a decision problem will be worth the cost. 8.Calculate revised probabilities manually and with Excel. 9.Analyze the sensitivity of decisions to probability estimates. 10.Describe how utilities can be used in lieu of monetary value in making decisions. After completing this chapter, you should be able to:

4 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–4 Decision Theory Decision theory problems are characterized by the following: 1.A list of alternatives. 2.A list of possible future states of nature. 3.Payoffs associated with each alternative/state of nature combination. 4.An assessment of the degree of certainty of possible future events. 5.A decision criterion.

5 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–5 Example 11-1 Suppose that a real estate developer must decide on a plan for developing a certain piece of property. After careful consideration, the developer has ruled out “do nothing” and is left with the following list of acceptable alternatives: 1. Residential proposal. 2. Commercial proposal #1. 3. Commercial proposal #2. Suppose that the developer views the possibilities as 1. No shopping center. 2. Medium-sized shopping center. 3. Large shopping center.

6 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–6 Table 11–1General Format of a Decision Table

7 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–7 Table 11–2 Payoff Table for Real Estate Developer

8 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–8 Table 11–3If It Is Known That No Shopping Center Will be Built, Only the First Column Payoffs Would Be Relevant Decision Making under Certainty

9 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–9 Decision Making under Complete Uncertainty Approaches to decision making under complete uncertainty: 1.Maximin 2.Maximax. 3.Minimax regret. 4.Hurwicz 5.Equal likelihood

10 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–10 Table 11–4Maximin Solution for Real Estate Problem Maximin The maximin strategy is a conservative one; it consists of identifying the worst (minimum) payoff for each alternative and then selecting the alternative that has the best (maximum) of the worst payoffs. In effect, the decision maker is setting a floor for the potential payoff; the actual payoff cannot be less than this amount.

11 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–11 Table 11–5Maximax Solution for Real Estate Problem Maximax The maximax approach is the opposite of the previous one: The best payoff for each alternative is identified, and the alternative with the maximum of these is the designated decision.

12 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–12 Table 11–6Payoff Table with Similar Maximum Payoffs Minimax Regret An approach that takes all payoffs into account. To use this approach, it is necessary to develop an opportunity loss table that reflects the difference between each payoff and the best possible payoff in a column (i.e., given a state of nature). Hence, opportunity loss amounts are found by identifying the best payoff in a column and then subtracting each of the other values in the column from that payoff.

13 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–13 Table 11–7Opportunity Loss Table for Real Estate Problem

14 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–14 Table 11–8Identifying the Minimax Regret Alternative

15 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–15 Table 11–9Minimax Regret Can Lead in a Poor Decision

16 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–16 The Hurwicz (Realism) Criterion (Weighted Average or Realism Criterion) The approach offers the decision maker a compromise between the maximax and the maximin criteria. –Requires the decision maker to specify a degree of optimism, in the form of a coefficient of optimism α, with possible values of α ranging from 0 to 1.00. –The closer the selected value of α is to 1.00, the more optimistic the decision maker is, and the closer the value of α is to 0, the more pessimistic the decision maker is.

17 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–17 Table 11–10Equal Likelihood Criterion

18 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–18 Table 11–11Summary of Methods for Decision Making under Complete Uncertainty

19 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–19 Exhibit 11-1Using Excel to Make Decisions under Complete Uncertainty

20 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–20 Decision Making under Risk Decision making under partial uncertainty –Distinguished by the present of probabilities for the occurrence of the various states of nature under partial uncertainty. –The term risk is often used in conjunction with partial uncertainty. Sources of probabilities –Subjective estimates –Expert opinions –Historical frequencies

21 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–21 Table 11–12Real Estate Payoff Table with Probabilities Expected Monetary Value (EMV) approach Provides the decision maker with a value that represents an average payoff for each alternative. The best alternative is, then, the one that has the highest expected monetary value. The average or expected payoff of each alternative is a weighted average: the state of nature probabilities are used to weight the respective payoffs.

22 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–22 Approaches to Incorporating Probabilities in the Decision Making Process Expected Monetary Value (EMV) approach –Provides the decision maker with a value that represents an average payoff for each alternative. Expected Opportunity Loss (EOL) –The opportunity losses for each alternative are weighted by the probabilities of their respective states of nature to compute a long-run average opportunity loss, and the alternative with the smallest expected loss is selected as the best choice. Expected Value of Perfect Information (EVPI) –A measure of the difference between the certain payoff that could be realized under a condition of certainty and the expected payoff under a condition involving risk.

23 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–23 Exhibit 11-2Using Excel to Make Decisions under Risk

24 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–24 Figure 11–1Decision Tree Format Decision trees are used by decision makers to obtain a visual portrayal of decision alternatives and their possible consequences.

25 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–25 Figure 11–2Decision Tree for Real Estate Developer Problem

26 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–26 Figure 11–3Real Estate Problem with a Second Possible Decision

27 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–27 Exhibit 11–3Initial TreePlan Dialog Box

28 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–28 Exhibit 11–4Decision Tree Initially Developed by TreePlan

29 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–29 Exhibit 11–5TreePlan Dialog Box to Add Branches, Decision Nodes, or Events

30 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–30 Exhibit 11–6Modified Decision Tree with Three Branches

31 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–31 Exhibit 11–7TreePlan Dialog Box to Add or Change Decision Nodes or Events

32 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–32 Exhibit 11–8Modified Decision Tree with Three Branches and the Added Event Node with Three Nodes

33 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–33 Exhibit 11–9Excel Solution to the Real Estate Developer Decision Tree Problem

34 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–34 Figure 11–4Sequential Decision Tree for Unicom Inc. (Example 11-3, part a)

35 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–35 Exhibit 11–10Excel Solution to the Unicom Inc. Sequential Decision Tree Problem

36 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–36 Figure 11–5Conceptual Portrayal of Market Test Example

37 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–37 Test Market Payoffs

38 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–38 Figure 11–6Summary of Analysis of Market Test Example

39 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–39 Table 11–13Reliability of Market Test

40 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–40 Table 11–14Probability Calculations Given the Market Test Indicates a Strong Market

41 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–41 Table 11–15Probability Calculations Given the Market Test Indicates a Weak Market Conditional probabilities express the reliability of the sampling device (e.g., market test) given the condition of actual market type.

42 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–42 Exhibit 11–11Calculation of the Revised Probabilities for the Market Test Example

43 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–43 Figure 11–7Format of Graph for Sensitivity Analysis Sensitivity Analysis enables decision makers to identify a range of probabilities over which a particular alternative would be optimal.

44 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–44 Figure 11–8The Expected Value Line for Alternative a.

45 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–45 Figure 11–9Example of Finding the Expected Value for Alternative a when P(#2) Is.50

46 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–46 Figure 11–10All Three Alternatives Are Plotted on a Single Graph

47 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–47 Figure 11–11The Line with the Highest Expected Profit Is Optimal for a Given Value of P(#2)

48 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–48 UtilityUtility Utility (of a payoff) –A measure of the personal satisfaction associated with a payoff. Risk –A decision problem in which the states of nature have probabilities associated with their occurrence. Risk Averters –Individuals that avoid taking risks. The decision maker has less utility for greater risk. Risk Takers –Individuals that like taking risks and that have a greater utility for the potential winnings even though their chances of winning are very low.

49 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–49 Figure 11–12Converting P(#2) Ranges into P(#1) Ranges

50 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–50 Exhibit 11–12Solved Problem 1: Decision Making under Complete Uncertainty—A Profit Maximization Problem (Part f)

51 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–51 Exhibit 11–13Solved Problem 2: Decision Making under Complete Uncertainty—A Cost Minimization Problem (part f)

52 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–52 Exhibit 11–14Calculation of the Revised Probabilities and Expected Value of Perfect Information for Solved Problem 3 (part c)

53 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–53 Exhibit 11–15Calculation of the Revised Probabilities for Solved Problem 5 (part c)

54 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–54 Exhibit 11–16TreePlan Dialog Box to Add Branches, Decision Nodes, or Events Exhibit 11–17TreePlan Dialog Box to Add or Change Decision Nodes or Events

55 Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 11–55 Exhibit 11–18Decision Tree for Solved Problem 5 (part c)


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