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146 Decision trees and influence diagrams Develop electric-powered design Develop gas-powered design Do not develop the product $0 Success 0.75 Failure 0.25 Success 0.6 Failure Figure 6.1 – An initial decision tree for the food-processor problem Develop electric-powered design Develop gas-powered design Do not develop the product $0 Success 0.75 Failure 0.25 Success 0.6 Failure 0.4 $10 m $15 m 0.4 Modify design Abandon project Modify design Abandon project Figure 6.2 – A new decision tree for the food-processor problem $10 m −$3 m $15 m −$7 m Success Failure −$3 m Success Failure −$7 m $6 m 0.3 −$7 m 0.7 $10 m 0.8 −$12 m 0.2
Determining the optimal policy 147 Determining the optimal policy It can be seen that our decision tree consists of a set of policies. A policy is a plan of action stating which option is to be chosen at each decision node that might be reached under that policy. For example, one policy would be: choose the electrical design; if it fails, modify the design. Another policy would be: choose the electrical design; if it fails, abandon the project. We will now show how the decision tree can be used to identify the optimal policy. For simplicity, we will assume that the engineer considers that monetary return is the only attribute which is relevant to the decision, and we will also assume that, because the company is involved in a large number of projects, it is neutral to the risk involved in this development and therefore the expected monetary value (EMV) criterion is appropriate. Considerations of the timing of the cash flows and the relative preference for receiving cash flows at different points in time will also be excluded from our analysis (this issue is dealt with in Chapter 7). The technique for determining the optimal policy in a decision tree is known as the rollback method. To apply this method, we analyze the tree from right to left by considering the later decisions first. The process is illustrated in Figure 6.3. Thus if the company chose the electrical design and it failed (i.e. if the decision node labeled with an A was reached), what would be the best course of action? Modifying the design would lead to an expected return of (0.3 × $6 m) + (0.7 ×−$7 m), which equals −$3.1 m. Since this is worse than the −$3 m payoff that would be achieved if the design was abandoned, abandoning the design would be the best course of action. Two bars are therefore placed over the inferior branch and the ‘winning’ payoff is moved back to the decision node where it is now treated as a payoff for the ‘failure’ branch. This means that the expected payoff of the electrical design is (0.75 × $10 m) + (0.25 ×−$3 m), which equals $6.75 m. The same analysis is applied to the section of the tree that represents the gas-powered design. It can be seen that if this design fails the best option is to modify it. Hence the expected payoff of the gas design is $11.24 m. This exceeds the expected payoff of the electrical design and the $0 payoff of not proceeding with the development. Two bars are therefore placed over the branches representing these options and the $11.24 m is moved back to the initial decision node. The optimum policy is therefore to develop the gas-powered design and, if it fails, to modify the design.
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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)
Page 112 and 113: 96 Decision making under uncertaint
Page 114 and 115: 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: Constructing a decision tree 145 be
Page 165 and 166: Decision trees and utility 149 succ
Page 167 and 168: Decision trees involving continuous
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
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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.
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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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