Mathematical Models for Decision Making with Multiple Perspectives

Cover
Title Page
Copyright Page
Preface
Table of Contents
1. Single Criterion Decision Making
	1.1 Introduction
	1.2 Single Criterion Decision Making Methodologies
		1.2.1 Decision Making in an Uncertainty Context
		1.2.2 Decision Making in an Risk Context
	1.3 Final Remarks
	1.4 Proposed Exercises
2. Sequential Decisions and Introduction to Utility Theory
	2.1 Introduction
	2.2 Sequential Decision Making and Decision Trees
		2.2.1 Drawing the Decision Tree
		2.2.2 Assessing the Leaves
		2.2.3 Assessing the Nodes
		2.2.4 Some Comments about Sequential Decisions
	2.3 Utility Theory
		2.3.1 Probability Equivalence Method
		2.3.2 Certainty Equivalence Method
		2.3.3 Types of Utility Functions
		2.3.4 Final Remarks Concerning Utility Theory
	2.4 Proposed Exercises
3. Simple Multi-Attribute Rating Technique – SMART
	3.1 Introduction
	3.2 The Method
		3.2.1 Value Trees
		3.2.2 Alternatives’ Assessment
		3.2.3 Value Functions
		3.2.4 Dominance Analysis
		3.2.5 Assigning Weights to the Criteria – Swing Weight
		3.2.6 Calculate the Weighted Sum for All Alternatives
		3.2.7 Sensitivity Analysis
	3.3 Final Remarks
	3.4 Proposed Exercises
4. The ELECTRE Methods
	4.1 Introduction
	4.2 ELECTRE I
		4.2.1 Outranking Relation
		4.2.2 Concordance Matrix
		4.2.3 Discordance and Veto
		4.2.4 The Nucleus
	4.3 Electre III
		4.3.1 Preference and Indifference Relations
		4.3.2 Outranking Relation
		4.3.3 Concordance Matrix
		4.3.4 Discordance Matrices
		4.3.5 Credibility Matrix
		4.3.6 Alternatives Ranking
	4.4 Final Remarks
	4.5 Proposed Exercises
5. Analytic Hierarchy Process
	5.1 Introduction
	5.2 The Method
		5.2.1 Pairwise Comparisons, Judgement Matrix and Priority Vector
		5.2.2 Consistency of Judgement Matrices. Consistency Index. Random Consistency Index. Consistency Ratio
		5.2.3 Concerning the Alternatives
		5.2.4 Non-Consistency
		5.2.5 Integrating the Problem’s Hierarchic Levels
		5.2.6 More Complex Hierarchies
	5.3 Final Remarks
	5.4 Exercises
6. TOPSIS and Fuzzy TOPSIS
	6.1 Introduction
	6.2 The Method
	6.3 Some of the Method’s Limitations
		6.3.1 Normalization Step
		6.3.2 Weights
		6.3.3 Rank Reversal
	6.4 Fuzzy TOPSIS
		6.4.1 Fuzzy Sets and Fuzzy Numbers
		6.4.2 The Method
		6.4.3 Fuzzy TOPSIS for Group Decision Making
	6.5 Final Remarks
	6.6 Proposed Exercises
7. Multi-Objective Linear Programming
	7.1 Introduction
	7.2 Efficient Solutions and Objective Functions Space
	7.3 Weakly Efficient Solution
	7.4 Payoff Table, and Ideal and Nadir Solutions
	7.5 Final Remarks
	7.6 Exercises
		7.6.1 Solved Exercises
		7.6.2 Proposed Exercises
8. Lexicographic and ε-Constraint Methods
	8.1 Introduction
	8.2 The Lexicographic Method
		8.2.1 The Algorithm
		8.2.2 The Lexicographic Method as a Tool to Identify Multiple Optimal Solutions
		8.2.3 Final Remarks
	8.3 ε-Constraint Method
		8.3.1 Infeasibility
		8.3.2 Weak Efficiency
		8.3.3 How to Approximate the Pareto Front using ε-Constraint Method?
		8.3.4 Final Remarks
	8.4 Exercises
		8.4.1 Solved Exercises
		8.4.2 Proposed Exercises
9. Weighted Sum and Distance Minimization Methods
	9.1 Introduction
	9.2 Weighted Sum Model
		9.2.1 Definition of a Weighted Sum Objective Function
		9.2.2 Dealing with Functions in Different Scales
		9.2.3 Final Remarks
	9.3 Distance Minimization Model
		9.3.1 Distance Minimization to the Ideal Solution
		9.3.2 L∞-Distance Minimization to the Ideal Solution
		9.3.3 L2-Distance Minimization to the Iideal Solution
		9.3.4 Final Remarks
	9.4 Final Remarks
	9.5 Exercises
		9.5.1 Solved Exercises
		9.5.2 Proposed Eexercises
10. Interactive Methods
	10.1 Introduction
	10.2 The Step Method (STEM)
		10.2.1 Augmented Weighted Tchebychev Distance
		10.2.2 Iterative Process
		10.2.3 Final Rremarks
	10.3 Other Methods
		10.3.1 Zionts-Wallenius Method
		10.3.2 Pareto Race
		10.3.3 NAUTILUS
	10.4 Final Remarks
	10.5 Exercises
		10.5.1 Solved Exercises
		10.5.2 Proposed Exercises
	Appendix A
		Models in GAMS
11. Goal Programming
	11.1 Introduction
	11.2 Goals and the Utopian Set
		11.2.1 What if the Utopian Set Does Not Intersect the Feasible Region?
		11.2.2 What if the Utopian Set is an Empty Set?
	11.3 Goal Programming Models
		11.3.1 Preemptive GP Model
		11.3.2 The Archimedean GP Model
		11.3.3 A GP Model Combining Preemptive Priorities and Weighting
		11.3.4 The Tchebychev GP Model
	11.4 Final Remarks
	11.5 Proposed Exercises
	Appendix B: Definitions
		A.1 Multi-Criteria Methods
			A.1.1 An Example
		A.2 Multi-Objective Methods
Index