Table Of ContentDECISION MODELING
IN
POLICY MANAGEMENT
DECISION MODELING
IN
POLICY MANAGEMENT
An Introduction to the Analytic Concepts
Giampiero E.G. Beroggi
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Springer Science+Business Media, LLC
Library of Congress Cataloging-in-Publication Data
Beroggi, Giampiero E. G., 1960-
Decision mode ling in policy management an introduction to the
analytic concepts / Giampiero E. G. Beroggi.
p. cm.
Includes bibliographical references and index.
ISBN 978-0-7923-8331-4 ISBN 978-1-4615-5599-5 (eBook)
DOI 10.1007/978-1-4615-5599-5
(pbk. : acid-free paper)
1. Decision making--Mathematical models. 2. Management science.
1. Title.
T57.95.B47 1998
658.4'03--dc21 98-42966
CIP
Copyright © 1999 by Springer Science+Business Media New York
Originally published by Kluwer Academic Publishers in 1999
Softcover reprint of the hardcover Ist edition 1999
AII rights reserved. No part of this publication may be reproduced, stored in a
retrieval system or transmitted in any form or by any means, mechanical, photo
copying, record ing, or otherwise, without the prior written permission of the
publisher, Springer Science+Business Media, LLC.
Printed an acid-free paper.
In memory of
Emilia Bosi-Pari
TABLEOFCONTENTS
Preface xv
Acknowledgments xvii
Introduction xix
CHAPTERI: THEPROBLEMSOLVINGPROCESS
1. The Context ofProblem Solving 1
1.1 What is aProblem? 1
1.2The Problem Solving Process in Policy Management 3
2. Problem Identification: The Elements ofDecision Making 6
2.1 Actors and Decision Makers 6
2.2 Attribute, Criterion, Objective, and Goal 8
2.3 Actions and Decision Variables 14
2.4 Uncertainties, States, and Scenarios 16
3. Problem Definition 17
3.1 Evaluation Measures 17
3.2 Measurement Scales 20
3.3 Preference Elicitation 22
3.4 Binary Preference Relations 24
4. Problem Solution 26
4.1 Preference Aggregation 26
4.2 Dominant and Efficient Alternatives 27
4.3 Preference Graphs 28
4.4 Search for Solutions 30
4.5 Sensitivity Analysis 31
5. Summary 32
6. Problems 33
CHAPTERII: THEANALYTIC MODELINGPROCESS
1. From Problem to Model 36
1.1 The Model as Abstraction ofReality 36
1.2 The Analytic Modeling Process 37
Decision Modeling in Policy Management Page vii
2. Structural Models 38
2.1 Definitions and Elements 38
2.2 Actions 41
2.3 Criteria 43
2.4 Scenarios 44
2.5 Decision Makers 45
3. Formal Models 46
3.1 General Aspects 46
3.2 Descriptivevs. NormativePreferenceElicitation 47
A) DescriptivePreference Elicitation 48
B) NormativePreferenceElicitation 49
3.3 Singleversus Multiaction Decision Problems 51
4. Resolution Models 53
4.1 General Resolution Approach 53
4.2 Resolution Complexity 55
5. Interactive Complete Strong Preference Ordering 56
5.1 Structural Model 56
5.2 Formal Model 57
5.3 Resolution Model 58
6. Summary 60
7. Problems 61
CHAPTERIII:DESCRIPTIVEASSESSMENT·CRITERIAANDWEIGHTS
1. RelativeIntensitiesandWeights 64
1.1 ConsistentAssessment 64
1.2 Relative Importanceand RatioScale 67
1.3 Resolution ofInconsistencies 69
2. Hierarchical Decomposition ofCriteria 74
2.1 Structural Model 74
2.2 Formal Model 75
3. Aggregation ofCriteria 76
3.1 Differentiation PowerofCriteria 76
3.2 Computational Aspects 79
3.3 An Example ofDimension Reduction and Interpretation 82
4. Summary and Further Readings 85
5. Problems 85
Page viii Decision Modeling in Policy Management
CHAPTERIV:DESCRIPTIVEASSESSMENT
ALTERNATIVES AND RANKING
1. Structural Model ofDescriptive Approaches 88
l.l BasicConcepts 88
1.2Preference Aggregation: Basic Principles 90
2. Formal and Resolution Models 92
2.1 Ordinal and Interval Scales 92
2.2 Aggregation ofPreference Values 94
A) Preference Aggregation with Type A Preference Function 95
B) Preference Aggregation with Type B Preference Function 96
2.3 Incomplete Preference Ranking ofAlternatives 98
2.4 Ratio Scale 100
A) Relative PreferenceAssessment 100
B) AbsolutePreference Assessment 101
2.5 Formalizing Structural and Content Goals 103
3.SensitivityAnalysis 104
3.1 Structural Instability 105
3.2 Functional Instability 107
3.3 Numerical Instability 109
4. Summary and Further Readings 110
5. Problems III
CHAPTERV: VALUES ANDNORMATIVECHOICE
1. The Structural Model 112
1.1 Conceptual Aspects 112
1.2 The Structure 114
2. The Formal Model ofValue Theory 115
2.1 Motivation and Axioms ofValue Theory 115
2.2 Preferential Independence 118
A)TwoCriteria 119
B) Three Criteria 120
C) More than three Criteria 121
2.3 Additive Value Functions 121
2.4 Linear Value Functions and Perfect Complements 123
2.5 Value Functions OverTime Streams 125
2.6 Interpretation of2-Dimensional Value Functions 126
2.7 Interpretation ofComponent Value Functions 128
Decision Modeling in PolicyManagement Pageix
3. The Resolution Model 129
3.1 The General Approach 129
3.2 Assessment ofMutual Preferential Independence 130
3.3 Elicitation of2-Dimensional Value Functions 131
3.4 Elicitation ofComponent Value Function 132
3.5 Assessment ofScalingConstants 134
3.6 Solution Search 136
A) Convex Setand Efficient Frontier 136
B) Evaluation ofExplicit versus Search for ImplicitAlternatives 138
C) Real-Valued Solutions 139
3.7 SensitivityAnalysis 140
4. Summary and FurtherReadings 141
5. Problems 142
CHAPTERVI: CHOICESUNDERUNCERTAINTY
1. Decision Making UnderComplete Uncertainty 144
1.1 Structural Model 144
1.2 Formal Model 145
A) Wald'sMaxMinRule 146
B) Savage'sMinMax RegretRule 147
C) Hurwicz'sOptimism-PessimismIndex 148
D) Laplace's Principle ofInsufficientReasoning 148
1.3 Resolution Model 149
2. Decision Making Under Risk 149
2.1 Structural Model 149
2.2 Formal Model: Concept ofProbability Theory 151
A) Types ofProbability 151
B) Probabilistic Independence 153
C) Arc Reversal (2-dimensional) 154
D) Arc Reversal (3-dimensional) 156
2.3 Decision Rules 161
A) Individual Risk 161
B)CollectiveRisk 161
C) Group Risk 164
2.4 Aggregation ofLinguistic Variables 166
2.5 Resolution Model 169
3. Summary and Further Readings 171
4. Problems 172
CHAPTERVII: UNCERTAINTYANDNORMATIVECHOICE
1. The Structural Model for Decision Making Under Uncertainty 174
1.1 Conceptual Aspects 174
1.2 The Structural Model 177
Pagex Decision Modeling in PolicyManagement
2. The Formal Model of Utility Theory 177
2.1 Motivation of Utility Theory 177
2.2 The Axioms of Utility Theory 179
2.3 Assessing Component Utility Functions 181
2.4 Interpretation ofthe Utility Function and Risk Attitudes 185
2.5 Utility Independence 186
2.6 Multidimensional Utility Functions 188
A) Multilinear Utility Functions 188
B) Multiplicative Utility Functions 189
C) Additive Utility Functions 190
3. The Resolution Model 191
3.1 The General Approach 191
3.2 Assessment ofMutual Utility Independence 193
3.3 Assessment ofScaling Constants and Selection ofModel 194
3.4 Assessment ofComponent Utility Functions and
EvaluationofAlternatives 195
3.5 Comments about Utility Theory 197
4. Summary and Further Readings 198
5. Problems 200
CHAPTERVIII: SEQUENTIALDECISIONMAKING
1. The Structure ofSequential Decisions 202
1.1 Concept of Probabilistic Influence Diagrams 202
1.2 The Meaning ofInfluences in Probabilistic Influence Diagrams 204
2. The Formal Model 209
2.1 Defining Probabilistic Relations 209
2.2 Decision Trees 210
2.3 Probabilistic Influence Diagrams 211
3. The Resolution Model 213
3.1 Resolution Steps 213
A) Barren Node Removal 215
B)Arc Reversal 215
C) Chance Node Removal 217
D) Decision Node Removal 220
3.2 Node Elimination Algorithm 221
4. Sensitivity Analysis 224
4.1 Probabilistic Sensitivity 224
4.2 Value of Information 225
5. Summary and Further Readings 226
6. Problems 227
Decision Modeling in Policy Management Pagexi
