Linear Optimization Problems with Inexact Data

  • M. Fiedler
  • J. Nedoma
  • J. Ramík
  • J. Rohn
  • K. Zimmermann

Table of contents

  1. Front Matter
    Pages I-XV
  2. M. Fiedler
    Pages 1-33
  3. J. Rohn
    Pages 79-100
  4. J. Nedoma, J. Ramík
    Pages 101-116
  5. J. Ramík
    Pages 117-164
  6. Back Matter
    Pages 195-214

About this book

Introduction

Linear programming attracted the interest of mathematicians during and after World War II when the first computers were constructed and methods for solving large linear programming problems were sought in connection with specific practical problems—for example, providing logistical support for the U.S. Armed Forces or modeling national economies. Early attempts to apply linear programming methods to solve practical problems failed to satisfy expectations. There were various reasons for the failure. One of them, which is the central topic of this book, was the inexactness of the data used to create the models. This phenomenon, inherent in most pratical problems, has been dealt with in several ways. At first, linear programming models used "average” values of inherently vague coefficients, but the optimal solutions of these models were not always optimal for the original problem itself. Later researchers developed the stochastic linear programming approach, but this too has its limitations. Recently, interest has been given to linear programming problems with data given as intervals, convex sets and/or fuzzy sets. The individual results of these studies have been promising, but the literature has not presented a unified theory. Linear Optimization Problems with Inexact Data attempts to present a comprehensive treatment of linear optimization with inexact data, summarizing existing results and presenting new ones within a unifying framework.

Audience

This book is intended for postgraduate or graduate students in the areas of operations research, optimization theory, linear algebra, interval analysis, reliable computing, and fuzzy sets. The book will also be useful for researchers in these respective areas.

Keywords

Operations Research Optimization Theory Systems of interval linear equations Systems of interval linear inequalities Weak and strong feasability Weak and strong solvability linear algebra linear optimization modeling optimization sets

Authors and affiliations

  • M. Fiedler
    • 1
  • J. Nedoma
    • 1
  • J. Ramík
    • 2
  • J. Rohn
    • 1
  • K. Zimmermann
    • 1
  1. 1.Academy of SciencesPragueCzech Republic
  2. 2.Silesian UniversityKarvináCzech Republic

Bibliographic information

  • DOI https://doi.org/10.1007/0-387-32698-7
  • Copyright Information Springer Science+Business Media, Inc. 2006
  • Publisher Name Springer, Boston, MA
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-32697-9
  • Online ISBN 978-0-387-32698-6
  • About this book