## Table of contents for Multiobjective decision making : theory and methodology / Vira Chankong, Yacov Y. Haines.

Bibliographic record and links to related information available from the Library of Congress catalog
Note: Electronic data is machine generated. May be incomplete or contain other coding.

```PART I THEORY                                                                   1
Chapter 1 Elements of Multiobjective Decision Problems                          3
1.1 Introduction                                                  3
1.2 The Multiobjective Decision Problem                           4
1.2.1 The Multiobjective Decision-Making Process              4
1.2.2 Judgment and the Value System                           6
1.2.3 The Decision-Making Unit and the Decision Maker         7
1.2.4 Objectives and Attributes                               8
1.2.5 The Decision Situation                                 13
1.2.6 The Decision Rule                                      15
1.3 Symbolic Representation of a Multiobjective
Decision Problem                                              17
1.4 Outline of the Book                                          21
References                                                       23
Chapter 2 Fundamentals: Selected Background Topics                             25
2.1 Scales of Measurement                                        25
2.1.1 Logical Foundation of the Theory of Scales             26
2.1.2 Nominal Scales                                         27
2.1.3 Ordinal Scales                                         28
2.1.4 Interval Scales                                        29
2.1.5 Ratio Scales                                           30
2.1.6 Multidimensional Scales                                30
2.2 Elementary Decision Analysis                                 30
2.2.1 Model of the Decision Problem                          31
2.2.2 Example: Developing a New Product                    32
2.2.3 Types of Decision Problems                           33
2.2.4 Choosing a Decision Rule                             34
2.2.5 Decision Trees                                       39
2.2.6 Using Additional Information                         44
2.3 Optimality Conditions in Mathematical Programming          47
2.3.1 Unconstrained Optimization                           49
2.3.2 Equality-Constrained Optimization                    50
2.3.3 Inequality-Constrained Optimization                  55
2.3.4 Necessary and Sufficient Conditions Without Derivatives  59
References                                                     60
Chapter 3 Utility Theory                                                    62
3.1 Introduction                                               62
3.2 The Preference Order                                       63
3.3 The Ordering Relation                                      64
3.4 Deterministic Utility Theory                               66
3.4.1 The Existence of Value Functions                     66
3.4.2 Additive Value Functions                             72
3.4.3 Other Decomposition Forms of Value Functions         81
3.5 Utility Theory Under Certainty:
Expected Utility Theory                                    88
3.5.1 The Problem Setting                                  89
3.5.2 Existence Theorems on Expected Utility:
Bemrnoulli's Principle                                 90
3.5.3 Additive Utility Functions                          101
3.5.4 Quasi-Additive and Multiplicative Utility Functions  103
3.5.5 Other Decomposition Forms                            106
3.6 Summary                                                   108
References                                                    109
Chapter 4 Vector Optimization Theory                                       113
4.1 Introduction                                              113
4.2 Notions of Noninferior Solution                           114
4.3 Three Common Approaches to Characterizing
Noninferior Solutions                                      117
4.3.1 Relationships Among the Three Forms of Scalarization  121
4.3.2 Characterizing Noninferior Solutions in Terms of the
Solutions of Constraint Problems                      128
4.3.3 Characterizing Noninferior Solutions in Terms of the
Solutions of Weighting Problems                       133
4.3.4 Characterizing Noninferior Solutions in Terms of the
Solutions of Lagrangian Problems                      136
4.4 The Kuhn-Tucker Necessary and Sufficient Conditions
for Noninferiority                                        137
4.5 Necessary and Sufficient Conditions
for Proper Noninferiority                                 140
4.6 Other Characterizations of Noninferior Solutions         144
4.6.1 The Weighted-Norm Approach                         144
4.6.2 The Proper Equality Constraint Approach            146
4.6.3 The Hybrid Approach: Weighting and Constraint      148
4.6.4 Characterization and Noninferiority Test           150
4.7 Local Noninferior Solutions                              152
4.8 Special Results for Linear Problems                      153
4.9 Trade-offs on the (Local) Noninferior Surface            159
4.9.1 Trade-offs and Kuhn-Tucker Multipliers             160
4.9.2 Trade-offs and Simplex Multipliers in Linear Problems  165
4.9.3 Example                                            167
4.10 Summary                                                  172
References                                                    172
PART II METHODOLOGY                                                        177
Chapter 5 Assessment Methodologies                                         179
5.1 Introduction                                              179
5.2 The Direct Assessment Approach: The Multiattribute
Utility Function                                          180
5.2.1 Verifying the Existence of the Multiattribute
Utility Function                                      180
5.2.2 Selecting Suitable Forms of the Multiattribute
Utility Function                                      181
5.2.3 Constructing Component Preference Functions         182
5.2.4 Assessing One-Dimensional Value Functions            182
5.2.5 Assessing One-Dimensional Utility Functions         189
5.2.6 Closing Remarks on Component Preference Functions   196
5.2.7 Estimating Scaling Constants                        196
5.2.8 Consistency Checks and Final Analysis               199
5.3 The Lexicographic Method                                  200
5.4 The ELECTRE Method                                        205
5.4.1 Properties of the Outranking Relation               207
5.4.2 Construction of the Outranking Relation             209
5.4.3 How to Use the Outranking Relation                  210
5.4.4 Summary of the Algorithm                            212
5.5 The Indifference Curves (Surfaces) Method                 214
5.6 Summary                                                   217
References                                                    218
Chapter 6 Methods for Generating Noninferior Solutions                     221
6.1 Introduction                                              221
6.2 Methods Based on a Weighting Characterization             224
6.2.1 The Analytical Approach                             225
6.2.2 Ad Hoc Numerical Approach                           234
6.2.3 Simplex-Based Methods for Linear Problems           236
6.2.4 Other Methods Applicable to Linear Problems         265
6.3 Methods Based on e-Constraint Characterizations        274
6.3.1 Analytical Approach                               276
6.3.2 Numerical Methods                                 283
6.4. Related Problems                                      286
6.5 Summary                                                286
References                                                 287
Chapter 7 Noninteractive and Interactive Multiobjective
Programming Methods                                        291
7.1 Introduction                                           291
7.2 Methods Based on Global Preference                     292
7.2.1 Ad Hoc Preference Function Programming Approach   293
7.2.2 Geoffrion's Bicriterion Method                    294
7.2.3 The Modified PROTRADE Method                      300
7.3 Methods Based on Weights, Priorities, Goals, and Ideals  302
7.3.1 Linear Goal Programming                           303
7.3.2 Extensions of Goal Programming                    316
7.3.3 Compromise Programming and the Method of the
Displaced Ideal                                    321
7.3.4 The STEP Method                                   325
7.3.5 The SEMOPS Method                                 329
7.4 Methods Based on Trade-offs                            331
7.4.1 What Is a Trade-off?                              331
7.4.2 The Zionts-Wallenius Method                       336
7.4.3 Geoffrion's Method and Its Variants               341
7.5 Summary                                                345
References                                                 346
Chapter 8 The Surrogate Worth Trade-off Method
and Its Extensions                                         351
8.1 Introduction                                           351
8.2 The SWT Method                                         351
8.3 The SWT Method with Multiple Decision Makers'          359
8.4 The Multiobjective Statistical Method                  363
8.5 Risk and Sensitivity as Multiple Objective Functions   365
8.5.1 The Uncertainty/Sensitivity Index Method          366
8.6 The Hierarchical Multiobjective Approach               367
8.6.1 Problem Formulation                               367
8.6.2 The Derivation of Hierarchical Schemes            370
8.7 The Interactive Surrogate Worth Trade-off Method       371
8.7.1 Introduction                                      371
8.7.2 Overview of the ISWT Method                       372
8.7.3 Detailed Components of the ISWT Method            373
8.8 Summary                                                379
References                                                 379
Chapter 9 Comparative Evaluation and Comments                        383
9.1 Introduction                                          383
9.2 Evaluation by Classification Scheme:
An ex ante Evaluation                                 383
9.2.1 Criterion A: Problem Structure or Decision Situation  385
9.2.2 Criterion B: Decision Rule or Preference Model  386
9.2.3 Criterion C: Input                              387
9.2.4 Criterion D: Output                             388
9.3 Some ex post Evaluations                              388
References                                                389

```

Library of Congress subject headings for this publication: Decision making Mathematical models