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Behnam Malakooti, Ph.D., P.E.
 

Multiple Objective Linear Programming: Interactive and Hierarchical Methods

Behnam Malakooti

Brief Table Of Contents Detailed Table Of Contents

  • Part I. Multiple Objective Linear Programming with Additive Multiple Criteria Utility Functions

    • Chapter 1 Identifying Efficient and Convex Efficient Alternatives with Partial Information
      • Identifying Nondominated Alternatives with Partial Information for Multiple Objective Discrete and Linear Programming Problems (34)
      • 1. Introduction
      • 2. Convex and Utility Nondominancy; Reduction of Set of Discrete Alternatives
        • 2.1. Construction of Partial Information for Additive MAUFs
        • 2.2. Utility Nondominancy and Convex Nondominancy
      • 3. Trade-Off and Utility Nondominancy; Establishing the Most Preferred Alternative through Interactive Paired Comparison Methods
        • 3.1. Trade-Off Nondominancy and Utility Nondominancy
        • 3.2. Minimal Partial Information for Optimality
        • 3.3. An Interactive Paired Comparison Method
        • 3.4. Examples Demonstrating Concepts from Sections II and III
      • 4. Extensions to Multiple Objective Linear Programming Problems
        • 4.1. Converting Discrete MCDM Problems to MOLP Problems
        • 4.2. MOLP Problems and Efficiency (Nondominancy) Properties
        • 4.3. Utility Nondominancy for MOLP Problems
        • 4.4. Convergence Properties for Interactive Paired Comparison Methods for MOLP Problems
        • 4.5. Enumeration of All Utility Nondominated Alternatives for MOLP Problems
      • 5. Extensions to Quasi-Nondominancy and Reference Nondominancy
        • 5.1. Quasi-Nondominancy
        • 5.2. Reference Nondominancy
      • 6. Conclusion
      • 7. Appendix 1 (An Example of Utility Nondominancy for Alternatives and Trade-Offs)
      • 8. Utility Nondominated Alternatives
      • 9. Minimum Information for Optimality
      • 10. Appendix 2 (An Example for MOLP Problems)
      • 11. Appendix 3 (An Algorithm for Identifying Utility Nondominated Alternatives or Trade-Offs
        • 11.1. Identifying All Utility Nondominted Alternatives
        • 11.2. Identifying All Utility Nondominted and Nondominated Trade-Offs
        • 11.3. The Algorithm
      • 12. References
    • Chapter 2 Interactive Paired Comparison Simplex Method for MOLP and use of Strengths of Preferences
      • Computational Procedures with Interactive Paired Comparison Methods for MOLP Problems (45)
      • 1. Abstract
      • 2. Keywords and Phrases
      • 3. Introduction
      • 4. Utility Efficiency
      • 5. Implementing the Strengths of Preferences
      • 6. Inconsistency and Resolution
      • 7. The Paired Comparison Simplex Method
      • 8. Computational Results
      • 9. Conclusions and Extensions
      • 10. References
    • Chapter 3 Application of Interactive Paired Comparison Simplex Method for MOLP in the Glass Industry
      • Implementation of a Multiple Criteria Decision Making Model to Solve the Glass Industry Energy Problem (44)
      • 1. Abstract
      • 2. Introduction
      • 3. Industry Background
      • 4. Energy Conservation Options
      • 5. Melting Step Options
      • 6. Modeling the Glass Industry Energy System
      • 7. Total Energy Consumption versus Total Cost (Bicriteria)
      • 8. Interactive Paired Comparison Simplex Method
      • 9. Implementation of the Interactive Paired Comparison Method into the Model: A Summary of Results
      • 10. Conclusions
      • 11. References
    • Chapter 4 Partial and Fuzzy Information on Single Objective Functions for MOLP Problems
      • An Approach for Solving Multiple Objective Linear Programming Problems with Partial Information on the Overall Utility and Single Objective Functions (25)
      • 1. Abstract
      • 2. Introduction
      • 3. Multiple Objective Linear Programming Problems and the Zionts and Wallenius Method
        • 3.1. MOLP Problems
        • 3.2. The Zionts and Wallenius Method
      • 4. Tradeoff and Utility Efficiency and Convergence for Multiple Objective Linear Programming Problems
        • 4.1. Tradeoff Efficiency Problems and Improvement
        • 4.2. Convergence Properties
        • 4.3. An Improved Paired Comparison Approach
      • 5. Implementation of Undecided (Fuzzy) Preferences
      • 6. Some Experiments with Strength of Preference
      • 7. Partial Information on Single Objective Functions
      • 8. An Interactive Approach for Multiple Objective Linear Programming Problems with Parametric Criteria Coefficients
      • 9. Conclusions
      • 10. References
      • 11. Appendix A: An Example of Strength of Preference for Tighter Bounds on Weights
      • 12. Appendix B: An Example for Parametric MOLP Problems
    • Chapter 5 A Critique of Some Well-Known Interactive Multiple Objective Linear Programming Methods (see Appendix B and C only)
      • An Exact Interactive Paired Comparison Method for Exploring the Efficient Facets of MOLP Problems with Underlying Quasi-Concave Utility Functions (39)
      • 1. Appendix B. A Critique of Some Well-Known Interactive Methods
        • 1.1. The Zionts and Wallenius Method
        • 1.2. The Geoffrion, Dyer, and Feinberg Method [7]
        • 1.3. The Horhonen and Laakso Method [12] (Visual Interactive Method)
        • 1.4. The Weighting Method of Steuer [22] (Internal Criterion Weight Method)
        • 1.5. The Zeleny Method (The Method of Displaced Ideals)
      • 2. The Benayoun et al Method (The STEM Method)
      • 3. Goal Programming
      • 4. Appendix C. A Critique of the Zionts and Wallenius Trade-Off Efficiency Test and Interactive Methods

  • Part II. Multiple Objective Linear Programming: Hierarchical Multi-Objective Optimization and Applications

    • Chapter 6 Hierarchical Multi-Objective for Computer Integrated Manufacturing
      • An Interactive Hierarchical Multi-Objective Approach for Computer Integrated Manufacturing (35)
      • 1. Introduction
      • 2. An Overview of Decision Making and Components of Computer-Integrated Manufacturing
        • 2.1. Classification of Decision Levels
        • 2.2. CIM at the Plant Level
      • 3. A Multi-Objective Decision Support System for Computer-Integrated Manufacturing
        • 3.1. Computer-Integrated Manufacturing Database (CIB DB)
        • 3.2. Structure of Multi-Objective Decision Support System
      • 4. A Hierarchical, Multi-Objective Approach for Analysis and Design of Computer-Integrated Manufacturing
        • 4.1. The Framework of Multi-Objective Structured Analysis and Design Technique (SADT)
        • 4.2. Mathematical Notation and Definitions for Multi-Objectives
        • 4.3. An Interactive, Hierarchical, Multi-Objective Approach
        • 4.4. A Notational Example
        • 4.5. A Numerical Example
      • 5. A Multi-Objective Approach for Selection of Software for Computer-Integrated Manufacturing
        • 5.1. Criteria for Evaluation
        • 5.2. Assessment of Criteria
        • 5.3. Selection of the Software
        • 5.4. An Example
      • 6. Conclusions
      • 7. References
    • Chapter 7 Hierarchical Multiple Objective for Production Planning
      • A Gradient-Based Approach for Solving Hierarchical Multiple Criteria Production Planning Problems (38)
      • 1. Introduction
      • 2. A Hierarchical Multi-Criteria Production Planning Framework
      • 3. Interactive Gradient-Based Method
      • 4. An Application to Facility Layout
      • 5. Conclusions
      • 6. References
      • 7. Appendix
    • Chapter 8 Multiple Objective Sampling in Quality Control
      • Selection of Acceptance Sampling Plans with Multi-Attribute Defects in Computer-Aided Quality Control (41)
      • 1. Introduction
      • 2. A Multi-Criteria Model for Acceptance Sampling
      • 3. An Interactive Paired Comparison Method for Planning Quality Control Systems
      • 4. A Computer Package with Experiments
      • 5. Lamp-making: a Case Study
      • 6. Conclusions
      • 7. Appendix
      • 8. References