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150 Decision trees and influence diagrams Utility 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 Figure 6.4 – The engineer’s utility function 0.9275 Develop electric-powered design Develop gas-powered design Do not develop the product 0 −12 −8 −4 0 4 8 12 16 $0 m 0.85 0.9275 0.9104 Monetary payoffs ($m) Success 0.75 Failure 0.25 Success Failure 0.4 $10 m 0.97 0.8 $15 m 1.0 0.6 0.776 Modify design Abandon project Modify design 0.737 0.776 Abandon project Success Failure −$ 3 m 0.8 Success Failure −$7 m 0.65 $6 m 0.94 0.3 −$7 m 0.65 0.7 $10 m 0.97 0.8 −$12 m 0 0.2 Figure 6.5 – Applying the rollback method to a decision tree involving utilities Decision trees involving continuous probability distributions In the decision problem we considered above there were only two possible outcomes for each course of action, namely success and failure.
Decision trees involving continuous probability distributions 151 However, in some problems the number of possible outcomes may be very large or even infinite. Consider, for example, the possible percentage market share a company might achieve after an advertising campaign or the possible levels of cost which may result from the development of a new product. Variables like these could be represented by continuous probability distributions, but how can we incorporate such distributions into our decision tree format? One obvious solution is to use a discrete probability distribution as an approximation. For example, we might approximate a market share distribution with just three outcomes: high, medium and low. A number of methods for making this sort of approximation have been suggested, and we will discuss the Extended Pearson-Tukey (EP-T) approximation here. This was proposed by Keefer and Bodily, 4 who found it to be a very good approximation to a wide range of continuous distributions. The method is based on earlier work by Pearson and Tukey 5 and requires three estimates to be made by the decision maker: (i) The value in the distribution which has a 95% chance of being exceeded. This value is allocated a probability of 0.185. (ii) The value in the distribution which has a 50% chance of being exceeded. This value is allocated a probability of 0.63. (iii) The value in the distribution which has only a 5% chance of being exceeded. This value is also allocated a probability of 0.185. To illustrate the method, let us suppose that a marketing manager has to decide whether to launch a new product and wishes to represent on a decision tree the possible sales levels which will be achieved in the first year if the product is launched. To apply the EP-T approximation to the sales probability distribution we would need to obtain the three estimates from the decision maker. Suppose that she estimates that there is a 95% chance that first-year sales will exceed 10 000 units, a 50% chance that they will exceed 15 000 units and a 5% chance they will exceed 25 000 units. The resulting decision tree is shown in Figure 6.6(a), while Figure 6.6(b) illustrates how the discrete distribution has been used to approximate the continuous distribution. Of course, in many decision trees the probability distributions will be dependent. For example, in our product launch example one might expect second-year sales to be related to the sales which were achieved in the first year. In this case, questions like the following would need to be asked to obtain the distribution for second-year sales: ‘Given that first-year sales were around 25 000 units, what level of sales in the second year would have a 50% chance of being exceeded?’
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Decision Analysis for Management Ju
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Decision Analysis for Management Ju
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To Mary and Josephine, Jamie, Jerom
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viii Contents Chapter 16 The analyt
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x Foreword real problems, and it is
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xii Preface accountancy, where rece
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1 Introduction Complex decisions Im
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The role of decision analysis 3 you
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Applications of decision analysis 5
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Overview of the book 11 and profit.
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References 13 8. Walls, M. R., Mora
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16 How people make decisions involv
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28 Decisions involving multiple obj
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72 Introduction to probability Beca
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74 Introduction to probability prac
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76 Introduction to probability we w
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78 Introduction to probability whet
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80 Introduction to probability give
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82 Introduction to probability prob
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84 Introduction to probability deci
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86 Introduction to probability that
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88 Introduction to probability inte
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90 Introduction to probability subj
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92 Introduction to probability (5)
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94 Introduction to probability (a)
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96 Decision making under uncertaint
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98 Decision making under uncertaint
Page 116 and 117: 100 Decision making under uncertain
Page 159 and 160: 6 Decision trees and influence diag
Page 161 and 162: Constructing a decision tree 145 be
Page 163 and 164: Determining the optimal policy 147
Page 165: Decision trees and utility 149 succ
Page 169 and 170: Practical applications of decision
Page 171 and 172: Assessment of decision structure 15
Page 173 and 174: Assessment of decision structure 15
Page 175 and 176: Eliciting decision tree representat
Page 177 and 178: Eliciting decision tree representat
Page 179 and 180: Summary 163 where the resulting dec
Page 181 and 182: Exercises 165 other elements of the
Page 183 and 184: Exercises 167 (b) Assuming that Wes
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Page 187 and 188: Exercises 171 failing to meet the p
Page 189 and 190: Exercises 173 why it was rational f
Page 191 and 192: Exercises 175 (11) In the Eagle Mou
Page 193 and 194: References 177 ABC Chemicals are pl
Page 195 and 196: 7 Applying simulation to decision p
Page 197 and 198: Monte Carlo simulation 181 Of cours
Page 199 and 200: Monte Carlo simulation 183 Table 7.
Page 201 and 202: Applying simulation to a decision p
Page 213 and 214: Applying simulation to investment d
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Applying simulation to investment d
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Applying simulation to investment d
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Summary 205 Hull 10 ), some of them
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Exercises 207 (c) Use your simulati
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Exercises 209 For each factor the f
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Exercises 211 (b) Suppose that your
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References 213 6 million Therefore
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216 Revising judgments in the light
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9 Biases in probability assessment
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Introduction 249 of people watching
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The availability heuristic 251 make
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The representativeness heuristic 25
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The anchoring and adjustment heuris
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The anchoring and adjustment heuris
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Other judgmental biases 263 Other j
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Is human probability judgment reall
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Exercises 271 Did you receive timel
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References 273 have been taken from
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References 275 18. Hamilton, D. L.
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10 Methods for eliciting probabilit
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Preparing for probability assessmen
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Consistency and coherence checks 28
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Assessment of the validity of proba
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Assessment of the validity of proba
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Assessing probabilities for very ra
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Exercises 293 Odds in favor of even
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References 295 13. Wright, G. and W
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298 Risk and uncertainty management
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310 Decisions involving groups of i
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330 Resource allocation and negotia
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14 Decision framing and cognitive i
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How people frame decisions 357 Figu
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Imposing imaginary constraints and
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Inertia in strategic decision makin
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Studies in the psychological labora
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Overcoming inertia? 369 it is diffi
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Discussion questions 373 frame anal
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References 375 References 1. Luchin
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15 Scenario planning: an alternativ
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Introduction 379 documented in Chap
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Scenario construction: the extreme-
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Using scenarios in decision making
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Using scenarios in decision making
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Scenario construction: the driving
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Case study of a scenario interventi
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Table 15.1 - The components of the
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Illustrative case study 403 (b) Att
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Illustrative case study 405 Stage 4
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Illustrative case study 407 importa
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Conclusion 409 combinations. Often
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References 411 2. Van der Heijden,
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414 The analytic hierarchy process
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17 Alternative decision-support sys
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Expert systems 429 generally agreed
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Expert systems 431 that knowledge e
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Expert systems 433 (1) That the sub
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Expert systems 435 information syst
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Expert systems 437 to focus on ‘t
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Expert systems 439 On the basis of
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Is there any intention/expectation
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Expert systems 443 described above
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Expert systems 445 body of knowledg
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Statistical models of judgment 447
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Comparisons 453 ‘broken leg’ cu
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Some final words of advice 455 Ques
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Some final words of advice 457 of t
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References 459 Table 17.1 - Summary
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References 461 20. Eisenhart, J. (1
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Chapter 3 Suggested answers to sele
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Suggested answers to selected quest
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472 Index Brown, C.E. 446 Brown, S.
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474 Index HIVIEW 58 Hodgkinson, G.P
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476 Index scenario intervention cas
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