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Multiobjective linear programming : an introduction / Dinh The Luc.

By: Publication details: Cham : Springer, ©2016.Description: xii, 325 p. : illustrations ; 24 cmISBN:
  • 9783319210902
Subject(s): DDC classification:
  • 519.72 23 L931
Contents:
1. Introduction -- 2. Convex polyhedra -- 3. Linear programming -- 4. Pareto optimality -- 5. Duality -- 6. Sensitivity and stability -- 7. Multiobjective simplex method -- 8. Normal cone method -- 9. Outcome space method -- Bibliographical notes -- References -- Index.
Summary: This book introduces the reader to the field of multiobjective optimization through problems with simple structures, namely those in which the objective function and constraints are linear. Fundamental notions as well as state-of-the-art advances are presented in a comprehensive way and illustrated with the help of numerous examples. Three of the most popular methods for solving multiobjective linear problems are explained, and exercises are provided at the end of each chapter, helping students to grasp and apply key concepts and methods to more complex problems. The book was motivated by the fact that the majority of the practical problems we encounter in management science, engineering or operations research involve conflicting criteria and therefore it is more convenient to formulate them as multicriteria optimization models, the solution concepts and methods of which cannot be treated using traditional mathematical programming approaches.
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Includes bibliographical references and index.

1. Introduction --
2. Convex polyhedra --
3. Linear programming --
4. Pareto optimality --
5. Duality --
6. Sensitivity and stability --
7. Multiobjective simplex method --
8. Normal cone method --
9. Outcome space method --
Bibliographical notes --
References --
Index.

This book introduces the reader to the field of multiobjective optimization through problems with simple structures, namely those in which the objective function and constraints are linear. Fundamental notions as well as state-of-the-art advances are presented in a comprehensive way and illustrated with the help of numerous examples. Three of the most popular methods for solving multiobjective linear problems are explained, and exercises are provided at the end of each chapter, helping students to grasp and apply key concepts and methods to more complex problems. The book was motivated by the fact that the majority of the practical problems we encounter in management science, engineering or operations research involve conflicting criteria and therefore it is more convenient to formulate them as multicriteria optimization models, the solution concepts and methods of which cannot be treated using traditional mathematical programming approaches.

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