Linear and Multiobjective Programming with Fuzzy Stochastic Extensions

✍ Scribed by Masatoshi Sakawa, Hitoshi Yano, Ichiro Nishizaki (auth.)

Publisher: Springer US
Year: 2013
Tongue: English
Leaves: 347
Series: International Series in Operations Research & Management Science 203
Edition: 1
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

Although several books or monographs on multiobjective optimization under uncertainty have been published, there seems to be no book which starts with an introductory chapter of linear programming and is designed to incorporate both fuzziness and randomness into multiobjective programming in a unified way. In this book, five major topics, linear programming, multiobjective programming, fuzzy programming, stochastic programming, and fuzzy stochastic programming, are presented in a comprehensive manner. Especially, the last four topics together comprise the main characteristics of this book, and special stress is placed on interactive decision making aspects of multiobjective programming for human-centered systems in most realistic situations under fuzziness and/or randomness.

Organization of each chapter is briefly summarized as follows: Chapter 2 is a concise and condensed description of the theory of linear programming and its algorithms. Chapter 3 discusses fundamental notions and methods of multiobjective linear programming and concludes with interactive multiobjective linear programming. In Chapter 4, starting with clear explanations of fuzzy linear programming and fuzzy multiobjective linear programming, interactive fuzzy multiobjective linear programming is presented. Chapter 5 gives detailed explanations of fundamental notions and methods of stochastic programming including two-stage programming and chance constrained programming. Chapter 6 develops several interactive fuzzy programming approaches to multiobjective stochastic programming problems. Applications to purchase and transportation planning for food retailing are considered in Chapter 7.

The book is self-contained because of the three appendices and answers to problems. Appendix A contains a brief summary of the topics from linear algebra. Pertinent results from nonlinear programming are summarized in Appendix B. Appendix C is a clear explanation of the Excel Solver, one of the easiest ways to solve optimization problems, through the use of simple examples of linear and nonlinear programming.

✦ Table of Contents

Front Matter....Pages i-xiii
Introduction....Pages 1-6
Linear Programming....Pages 7-72
Multiobjective Linear Programming....Pages 73-103
Fuzzy Linear Programming....Pages 105-148
Stochastic Linear Programming....Pages 149-196
Interactive Fuzzy Multiobjective Stochastic Linear Programming....Pages 197-232
Purchase and Transportation Planning for Food Retailing....Pages 233-270
Back Matter....Pages 271-339

✦ Subjects

Operation Research/Decision Theory; Operations Research, Management Science; Probability Theory and Stochastic Processes

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