Presentation is loading. Please wait.

Presentation is loading. Please wait.

12-1 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Decision Analysis Chapter 12.

Similar presentations


Presentation on theme: "12-1 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Decision Analysis Chapter 12."— Presentation transcript:

1 12-1 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Decision Analysis Chapter 12

2 12-2 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall ■Components of Decision Making ■Decision Making without Probabilities ■Decision Making with Probabilities ■Decision Analysis with Additional Information ■Utility Chapter Topics

3 12-3 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall  Previous chapters used an assumption of certainty with regards to problem parameters.  This chapter relaxes the certainty assumption  Two categories of decision situations:  Probabilities can be assigned to future occurrences  Probabilities cannot be assigned to future occurrences Decision Analysis Overview

4 12-4 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Table 12.1 Payoff table ■A state of nature is an actual event that may occur in the future. ■A payoff table is a means of organizing a decision situation, presenting the payoffs from different decisions given the various states of nature. Decision Analysis Components of Decision Making

5 12-5 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Decision Analysis Decision Making Without Probabilities Figure 12.1 Decision situation with real estate investment alternatives

6 12-6 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Decision-Making Criteria maximaxmaximinminimax minimax regretHurwiczequal likelihood Decision Analysis Decision Making without Probabilities Table 12.2 Payoff table for the real estate investments

7 12-7 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Table 12.3 Payoff table illustrating a maximax decision In the maximax criterion the decision maker selects the decision that will result in the maximum of maximum payoffs; an optimistic criterion. Decision Making without Probabilities Maximax Criterion

8 12-8 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Table 12.4 Payoff table illustrating a maximin decision In the maximin criterion the decision maker selects the decision that will reflect the maximum of the minimum payoffs; a pessimistic criterion. Decision Making without Probabilities Maximin Criterion

9 12-9 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Table 12.5 Regret table  Regret is the difference between the payoff from the best decision and all other decision payoffs.  Example: under the Good Economic Conditions state of nature, the best payoff is $100,000. The manager’s regret for choosing the Warehouse alternative is $100,000-$30,000=$70,000 Decision Making without Probabilities Minimax Regret Criterion

10 12-10 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Table 12.6 Regret table illustrating the minimax regret decision  The manager calculates regrets for all alternatives under each state of nature. Then the manager identifies the maximum regret for each alternative.  Finally, the manager attempts to avoid regret by selecting the decision alternative that minimizes the maximum regret. Decision Making without Probabilities Minimax Regret Criterion

11 12-11 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall  The Hurwicz criterion is a compromise between the maximax and maximin criteria.  A coefficient of optimism, , is a measure of the decision maker’s optimism.  The Hurwicz criterion multiplies the best payoff by  and the worst payoff by 1- , for each decision, and the best result is selected. Here,  = 0.4. Decision Making without Probabilities Hurwicz Criterion DecisionValues Apartment building$50,000(.4) + 30,000(.6) = 38,000 Office building$100,000(.4) - 40,000(.6) = 16,000 Warehouse$30,000(.4) + 10,000(.6) = 18,000

12 12-12 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall The equal likelihood ( or Laplace) criterion multiplies the decision payoff for each state of nature by an equal weight, thus assuming that the states of nature are equally likely to occur. Decision Making without Probabilities Equal Likelihood Criterion DecisionValues Apartment building$50,000(.5) + 30,000(.5) = 40,000 Office building$100,000(.5) - 40,000(.5) = 30,000 Warehouse$30,000(.5) + 10,000(.5) = 20,000

13 12-13 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall ■A dominant decision is one that has a better payoff than another decision under each state of nature. ■The appropriate criterion is dependent on the “risk” personality and philosophy of the decision maker. Criterion Decision (Purchase) MaximaxOffice building MaximinApartment building Minimax regretApartment building HurwiczApartment building Equal likelihoodApartment building Decision Making without Probabilities Summary of Criteria Results

14 12-14 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Exhibit 12.1 Decision Making without Probabilities Solution with QM for Windows (1 of 3)

15 12-15 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Exhibit 12.2 Decision Making without Probabilities Solution with QM for Windows (2 of 3) Equal likelihood weight

16 12-16 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Exhibit 12.3 Decision Making without Probabilities Solution with QM for Windows (3 of 3)

17 12-17 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Decision Making without Probabilities Solution with Excel Exhibit 12.4 =MIN(C7,D7) =MAX(E7,E9) =MAX(C18,D18) =MAX(F7:F9) =MAX(C7:C9)-C9 =C7*C25+D7*C26 =C7*0.5+D7*0.5

18 12-18 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall  Expected value is computed by multiplying each decision outcome under each state of nature by the probability of its occurrence. EV(Apartment) = $50,000(.6) + 30,000(.4) = $42,000 EV(Office) = $100,000(.6) - 40,000(.4) = $44,000 EV(Warehouse) = $30,000(.6) + 10,000(.4) = $22,000 Table 12.7 Payoff table with probabilities for states of nature Decision Making with Probabilities Expected Value

19 12-19 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall ■The expected opportunity loss is the expected value of the regret for each decision. ■The expected value and expected opportunity loss criterion result in the same decision. EOL(Apartment) = $50,000(.6) + 0(.4) = 30,000 EOL(Office) = $0(.6) + 70,000(.4) = 28,000 EOL(Warehouse) = $70,000(.6) + 20,000(.4) = 50,000 Table 12.8 Regret table with probabilities for states of nature Decision Making with Probabilities Expected Opportunity Loss

20 12-20 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Exhibit 12.5 Expected Value Problems Solution with QM for Windows Expected values

21 12-21 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Exhibit 12.6 Expected Value Problems Solution with Excel and Excel QM (1 of 2) Expected value for apartment building

22 12-22 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Expected Value Problems Solution with Excel and Excel QM (2 of 2) Exhibit 12.7 Click on “Add-Ins” to access the “Excel QM” menu

23 12-23 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall ■The expected value of perfect information (EVPI) is the maximum amount a decision maker would pay for additional information. ■EVPI equals the expected value given perfect information minus the expected value without perfect information. ■EVPI equals the expected opportunity loss (EOL) for the best decision. Decision Making with Probabilities Expected Value of Perfect Information

24 12-24 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Table 12.9 Payoff table with decisions, given perfect information Decision Making with Probabilities EVPI Example (1 of 2)

25 12-25 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall ■Decision with perfect information: $100,000(.60) + 30,000(.40) = $72,000 ■Decision without perfect information: EV(office) = $100,000(.60) - 40,000(.40) = $44,000 EVPI = $72,000 - 44,000 = $28,000 EOL(office) = $0(.60) + 70,000(.4) = $28,000 Decision Making with Probabilities EVPI Example (2 of 2)

26 12-26 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Exhibit 12.8 Decision Making with Probabilities EVPI with QM for Windows The expected value, given perfect information, in Cell F12 =MAX(E7:E9) =F12-F11

27 12-27 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall A decision tree is a diagram consisting of decision nodes (represented as squares), probability nodes (circles), and decision alternatives (branches). Table 12.10 Payoff table for real estate investment example Decision Making with Probabilities Decision Trees (1 of 4)

28 12-28 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Figure 12.2 Decision tree for real estate investment example Decision Making with Probabilities Decision Trees (2 of 4)

29 12-29 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall ■The expected value is computed at each probability node: EV(node 2) =.60($50,000) +.40(30,000) = $42,000 EV(node 3) =.60($100,000) +.40(-40,000) = $44,000 EV(node 4) =.60($30,000) +.40(10,000) = $22,000 ■Branches with the greatest expected value are selected. Decision Making with Probabilities Decision Trees (3 of 4)

30 12-30 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Figure 12.3 Decision tree with expected value at probability nodes Decision Making with Probabilities Decision Trees (4 of 4)

31 12-31 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Decision Making with Probabilities Decision Trees with QM for Windows Exhibit 12.9 Select node to add from Number of branches from node 1 Add branches from node 1 to 2, 3, and 4

32 12-32 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Decision Making with Probabilities Decision Trees with Excel and TreePlan (1 of 4) Exhibit 12.10

33 12-33 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Exhibit 12.11 Decision Making with Probabilities Decision Trees with Excel and TreePlan (2 of 4) To create another branch, click “B5,” then the “Decision Tree” menu, and select “Add Branch” Invoke TreePlan from the “Add Ins” menu

34 12-34 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Exhibit 12.12 Decision Making with Probabilities Decision Trees with Excel and TreePlan (3 of 4) Click on cell “F3,” then “Decision Tree” Select “Change to Event Node” and add two new branches

35 12-35 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Decision Making with Probabilities Decision Trees with Excel and TreePlan (4 of 4) Exhibit 12.13 Add numerical dollar and probability values in these cells in column H These cells contain decision tree formulas; do not type in these cells in columns E and I

36 12-36 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Exhibit 12.14 Sequential Decision Tree Analysis Solution with QM for Windows Cell A16 contains the expected value of $44,000

37 12-37 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Decision Making with Probabilities Sequential Decision Trees (1 of 4) ■A sequential decision tree is used to illustrate a situation requiring a series of decisions. ■Used where a payoff table, limited to a single decision, cannot be used. ■The next slide shows the real estate investment example modified to encompass a ten-year period in which several decisions must be made.

38 12-38 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Figure 12.4 Sequential decision tree Decision Making with Probabilities Sequential Decision Trees (2 of 4)

39 12-39 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Decision Making with Probabilities Sequential Decision Trees (3 of 4) ■Expected value of apartment building is: $1,290,000-800,000 = $490,000 ■Expected value if land is purchased is: $1,360,000-200,000 = $1,160,000 ■The decision is to purchase land; it has the highest net expected value of $1,160,000.

40 12-40 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Figure 12.5 Sequential decision tree with nodal expected values Decision Making with Probabilities Sequential Decision Trees (4 of 4)

41 12-41 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Exhibit 12.15 Sequential Decision Tree Analysis Solution with Excel QM

42 12-42 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Exhibit 12.16 Sequential Decision Tree Analysis Solution with TreePlan

43 12-43 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall ■Bayesian analysis uses additional information to alter the marginal probability of the occurrence of an event. ■In the real estate investment example, using the expected value criterion, the best decision was to purchase the office building with an expected value of $444,000, and EVPI of $28,000. Table 12.11 Payoff table for real estate investment Decision Analysis with Additional Information Bayesian Analysis (1 of 3)

44 12-44 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall ■A conditional probability is the probability that an event will occur given that another event has already occurred. ■An economic analyst provides additional information for the real estate investment decision, forming conditional probabilities: g = good economic conditions p = poor economic conditions P = positive economic report N = negative economic report P(P  g) =.80P(N  G) =.20 P(P  p) =.10P(N  p) =.90 Decision Analysis with Additional Information Bayesian Analysis (2 of 3)

45 12-45 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall ■A posterior probability is the altered marginal probability of an event based on additional information. ■Prior probabilities for good or poor economic conditions in the real estate decision: P(g) =.60; P(p) =.40 ■Posterior probabilities by Bayes’ rule: (g  P) = P(P  G)P(g)/[P(P  g)P(g) + P(P  p)P(p)] = (.80)(.60)/[(.80)(.60) + (.10)(.40)] =.923 ■Posterior (revised) probabilities for decision: P(g  N) =.250P(p  P) =.077P(p  N) =.750 Decision Analysis with Additional Information Bayesian Analysis (3 of 3)

46 12-46 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Decision Analysis with Additional Information Decision Trees with Posterior Probabilities (1 of 4) Decision trees with posterior probabilities differ from earlier versions in that: ■Two new branches at the beginning of the tree represent report outcomes. ■Probabilities of each state of nature are posterior probabilities from Bayes’ rule.

47 12-47 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Figure 12.6 Decision tree with posterior probabilities Decision Analysis with Additional Information Decision Trees with Posterior Probabilities (2 of 4)

48 12-48 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Decision Analysis with Additional Information Decision Trees with Posterior Probabilities (3 of 4) EV (apartment building) = $50,000(.923) + 30,000(.077) = $48,460 EV (strategy) = $89,220(.52) + 35,000(.48) = $63,194

49 12-49 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Figure 12.7 Decision tree analysis for real estate investment Decision Analysis with Additional Information Decision Trees with Posterior Probabilities (4 of 4)

50 12-50 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Table 12.12 Computation of posterior probabilities Decision Analysis with Additional Information Computing Posterior Probabilities with Tables

51 12-51 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Decision Analysis with Additional Information Computing Posterior Probabilities with Excel Exhibit 12.17

52 12-52 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall ■The expected value of sample information (EVSI) is the difference between the expected value with and without information: For example problem, EVSI = $63,194 - 44,000 = $19,194 ■The efficiency of sample information is the ratio of the expected value of sample information to the expected value of perfect information: efficiency = EVSI /EVPI = $19,194/ 28,000 =.68 Decision Analysis with Additional Information Expected Value of Sample Information

53 12-53 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Table 12.13 Payoff table for auto insurance example Decision Analysis with Additional Information Utility (1 of 2)

54 12-54 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Expected Cost (insurance) =.992($500) +.008(500) = $500 Expected Cost (no insurance) =.992($0) +.008(10,000) = $80 The decision should be do not purchase insurance, but people almost always do purchase insurance. ■Utility is a measure of personal satisfaction derived from money. ■Utiles are units of subjective measures of utility. ■Risk averters forgo a high expected value to avoid a low- probability disaster. ■Risk takers take a chance for a bonanza on a very low- probability event in lieu of a sure thing. Decision Analysis with Additional Information Utility (2 of 2)

55 12-55 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Decision Analysis Example Problem Solution (1 of 9) A corporate raider contemplates the future of a recent acquisition. Three alternatives are being considered in two states of nature. The payoff table is below.

56 12-56 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Decision Analysis Example Problem Solution (2 of 9) a.Determine the best decision without probabilities using the 5 criteria of the chapter. b.Determine best decision with probabilities assuming.70 probability of good conditions,.30 of poor conditions. Use expected value and expected opportunity loss criteria. c.Compute expected value of perfect information. d.Develop a decision tree with expected value at the nodes. e.Given the following, P(P  g) =.70, P(N  g) =.30, P(P  p) = 20, P(N  p) =.80, determine posterior probabilities using Bayes’ rule. f.Perform a decision tree analysis using the posterior probability obtained in part e.

57 12-57 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Step 1 (part a): Determine decisions without probabilities. Maximax Decision: Maintain status quo DecisionsMaximum Payoffs Expand $800,000 Status quo1,300,000 (maximum) Sell 320,000 Maximin Decision: Expand DecisionsMinimum Payoffs Expand$500,000 (maximum) Status quo-150,000 Sell 320,000 Decision Analysis Example Problem Solution (3 of 9)

58 12-58 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Minimax Regret Decision: Expand DecisionsMaximum Regrets Expand$500,000 (minimum) Status quo650,000 Sell 980,000 Hurwicz (  =.3) Decision: Expand Expand $800,000(.3) + 500,000(.7) = $590,000 Status quo$1,300,000(.3) - 150,000(.7) = $285,000 Sell $320,000(.3) + 320,000(.7) = $320,000 Decision Analysis Example Problem Solution (4 of 9)

59 12-59 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Equal Likelihood Decision: Expand Expand $800,000(.5) + 500,000(.5) = $650,000 Status quo $1,300,000(.5) - 150,000(.5) = $575,000 Sell $320,000(.5) + 320,000(.5) = $320,000 Step 2 (part b): Determine Decisions with EV and EOL. Expected value decision: Maintain status quo Expand $800,000(.7) + 500,000(.3) = $710,000 Status quo $1,300,000(.7) - 150,000(.3) = $865,000 Sell $320,000(.7) + 320,000(.3) = $320,000 Decision Analysis Example Problem Solution (5 of 9)

60 12-60 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Expected opportunity loss decision: Maintain status quo Expand $500,000(.7) + 0(.3) = $350,000 Status quo 0(.7) + 650,000(.3) = $195,000 Sell $980,000(.7) + 180,000(.3) = $740,000 Step 3 (part c): Compute EVPI. EV given perfect information = 1,300,000(.7) + 500,000(.3) = $1,060,000 EV without perfect information = $1,300,000(.7) - 150,000(.3) = $865,000 EVPI = $1,060,000 - 865,000 = $195,000 Decision Analysis Example Problem Solution (6 of 9)

61 12-61 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Step 4 (part d): Develop a decision tree. Decision Analysis Example Problem Solution (7 of 9)

62 12-62 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Step 5 (part e): Determine posterior probabilities. P(g  P) = P(P  g)P(g)/[P(P  g)P(g) + P(P  p)P(p)] = (.70)(.70)/[(.70)(.70) + (.20)(.30)] =.891 P(p  P) =.109 P(g  N) = P(N  g)P(g)/[P(N  g)P(g) + P(N  p)P(p)] = (.30)(.70)/[(.30)(.70) + (.80)(.30)] =.467 P(p  N) =.533 Decision Analysis Example Problem Solution (8 of 9)

63 12-63 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Step 6 (part f): Decision tree analysis. Decision Analysis Example Problem Solution (9 of 9)

64 12-64 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Printed in the United States of America.


Download ppt "12-1 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Decision Analysis Chapter 12."

Similar presentations


Ads by Google