1. 1 1 Slide © 2008 Thomson South-Western. All Rights Reserved © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Slides by JOHN LOUCKS St. Edward’s University INTRODUCTION TO MANAGEMENT SCIENCE, 13e Anderson Sweeney Williams Martin © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

2. 2 2 Slide © 2008 Thomson South-Western. All Rights Reserved © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Chapter 13 Decision Analysis n Problem Formulation n Decision Making without Probabilities n Decision Making with Probabilities n Risk Analysis and Sensitivity Analysis n Decision Analysis with Sample Information n Computing Branch Probabilities

3. 3 3 Slide © 2008 Thomson South-Western. All Rights Reserved © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Decision Making process n Define the problem Requirements, goals Requirements, goals n Alternatives Identify alternatives Identify alternatives Develop evaluation criteria Develop evaluation criteria n Tools Select decision-making tools and formulate a model Select decision-making tools and formulate a model Apply tools and select a preferred alternative Apply tools and select a preferred alternative n Check the answer Check the answer, sensitivity analysis Check the answer, sensitivity analysis Consider qualitative analysis Consider qualitative analysis n Decision

4. 4 4 Slide © 2008 Thomson South-Western. All Rights Reserved © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Problem Formulation n Decision alternatives (d i ) branches from rectangle decision node branches from rectangle decision node n States of nature (s j ) branches from circle state of nature node branches from circle state of nature node n Consequences with payoff n Payoff table (V ij ) (p.599) n Decision Tree (p.599)

5. 5 5 Slide © 2008 Thomson South-Western. All Rights Reserved © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Decision Making without Probabillities n Optimistic Approach Maximax criterion Maximax criterion n Conservative Approach Maximin criterion n Minimax Regret Approach

6. 6 6 Slide © 2008 Thomson South-Western. All Rights Reserved © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Decision Making without Probabillities n n Payoff Table n Regret Tabel Aternative Strong Demand Weak Demand MaximaxMaximin Small Complex8787*** Medium Complex145 5 Large Complex20-920***-9 Aternative Strong Demand Weak Demand Minimax Regret Small Complex120 Medium Complex626*** Large Complex016

7. 7 7 Slide © 2008 Thomson South-Western. All Rights Reserved © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Decision Making with Probabillities n Maximize expected payoff Strong demand (0.8), Weak demand (0.2) Strong demand (0.8), Weak demand (0.2) Expected payoff for alternative j Expected payoff for alternative j n Evaluation EV(Small) = 0.8x8 + 0.2x7 = 7.8 EV(Small) = 0.8x8 + 0.2x7 = 7.8 EV(Medium) = 0.8x14 + 0.2x5 = 12.2 EV(Medium) = 0.8x14 + 0.2x5 = 12.2 EV(Large) = 0.8x20 + 0.2x(-9) = 14.2*** EV(Large) = 0.8x20 + 0.2x(-9) = 14.2*** n Decision Tree (p.602)

8. 8 8 Slide © 2008 Thomson South-Western. All Rights Reserved © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Decision Making with Probabillities n Expected value of Perfect Information Expected value with perfect information Expected value with perfect information if we know what will be the value of the state of nature, best payoff (Strong demand) = 20 best payoff (Strong demand) = 20 best payoff (Weak demand) = 7 best payoff (Weak demand) = 7 Considering the probability of the state of nature, Considering the probability of the state of nature, EVwPI = 0.8x20 + 0.2x7 = 17.4 EVwPI = 0.8x20 + 0.2x7 = 17.4 Expected value of Perfect Information (EVPI) Expected value of Perfect Information (EVPI) Difference between EVwPI and EVwoPI EVPI = EVwPI – EVwoPI = 17.4 – 14.2 = 3.2 EVPI = EVwPI – EVwoPI = 17.4 – 14.2 = 3.2 We may pay up to $3.2M to get the perfect information We may pay up to $3.2M to get the perfect information*** n Decision Tree (p.602)

9. 9 9 Slide © 2008 Thomson South-Western. All Rights Reserved © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Risk Analysis and Sensitivity Analysis n Risk analysis n Sensitivity analysis Sensitivity of probability (two state-of-nature case) Sensitivity of probability (two state-of-nature case) Let P(Strong demand) = p, then P(Weak demand) = 1 – p Aternative Strong Demand Weak Demand Expected Value Small Complex877.8 Medium Complex14512.2 Large Complex20-914.2***

10. 10 Slide © 2008 Thomson South-Western. All Rights Reserved © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Risk Analysis and Sensitivity Analysis n Sensitivity analysis Sensitivity of probability (two state-of-nature case) Sensitivity of probability (two state-of-nature case) Let P(Strong demand) = p, then P(Weak demand) = 1 – p. EV(small complex) = EV(medium complex) = EV(large complex) = See p.610 Figure3.6 p+7 = 9p + 5  p = 0.25 p+7 = 9p + 5  p = 0.25 9p + 5 = 29p – 9  p = 0.7 9p + 5 = 29p – 9  p = 0.7 n

11. 11 Slide © 2008 Thomson South-Western. All Rights Reserved © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Risk Analysis and Sensitivity Analysis n Sensitivity analysis Sensitivity of payoff for large complex and Strong demand (currently 20) Sensitivity of payoff for large complex and Strong demand (currently 20) Let S be the payoff for large complex and Strong demand EV(large complex) =  S >= 17.5  S >= 17.5 Sensitivity of payoff for large complex and Weak demand Sensitivity of payoff for large complex and Weak demand Let W be the payoff for large complex and Weak demand EV(small complex) =  W >= –19  W >= –19 n

12. 12 Slide © 2008 Thomson South-Western. All Rights Reserved © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Decision making with Sample Information n Consider prior market research P (Favorable report in market research|Strong demand) = 0.9 P (Unfavorable report in market reseach|Strong demand) = 0.1 P (Favorable report in market reseach|Weak demand) = 0.25 P(Unfavorable report in market reseach|Weak demand) = 0.75 n n

13. 13 Slide © 2008 Thomson South-Western. All Rights Reserved © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Decision making with Sample Information n Prior probabilities and Posterior probabilities Prior probabilities : P(Strong) = 0.8, P(Weak) = 0.2 Conditional probabilities P(Favor|Strong) = 0.9, P(Unfavor|Strong) = 0.1 P(Favor|Weak) = 0.25, P(Unfavor|Weak) = 0.75 n State of Nature Prior Probabilities Conditional Probabilities P(F|S i )P(U|S i ) Strong demand0.80.90.1 Weak demand0.20.250.75

14. 14 Slide © 2008 Thomson South-Western. All Rights Reserved © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Decision making with Sample Information n Prior probabilities and Posterior probabilities Posterior probabilities Posterior probabilities Bayes’ Theorem Bayes’ Theorem State of Nature Prior Probabilities Conditional Probabilities P(F|S i )P(U|S i ) Strong demand0.80.90.1 Weak demand0.20.250.75

15. 15 Slide © 2008 Thomson South-Western. All Rights Reserved © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Decision making with Sample Information n Prior probabilities and Posterior probabilities Posterior probabilities Posterior probabilities n Decision Tree (p.616) EV(node 6) = 0.94*8 + 0.06*7 = 7.94 EV(node 7) = 0.94*14 + 0.06*5 = 13.46... EV(node 11) = 0.35*20 + 0.65*(-9) = 1.15... EV(node 14) = 0.8*20 + 0.2*(-9) = 14.2 n Decision Tree (p.617) Research ResultP(Research Result) Posterior Probabilities P(Strong demand|Result)P(Weak demand|Result) Market Favorable0.770.940.06 Market Unfavorable0.230.350.65

16. 16 Slide © 2008 Thomson South-Western. All Rights Reserved © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Decision making with Sample Information n Decision Tree (p.617) Decision (node 3) : Large complex Decision (node 4) : Medium complex Decision (node 5) : Large complex EV (node 2) = 0.77 * 18.26 + 0.23 * 8.15 = 15.93 Decision (node 1) : Market Research n Expected Value of Sample Information EVSI = 15.93 – 14.2 = 1.73 n Efficiency of Sample Information

17. 17 Slide © 2008 Thomson South-Western. All Rights Reserved © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. End of Chapter 13