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Linear Programming 1

Introduction

  • Textbook
  • © 1997

Overview

Authors:
  1. George B. Dantzig

    1. Department of Operations Research, Stanford University, Stanford, USA

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    You can also search for this author in PubMed   Google Scholar

  2. Mukund N. Thapa

    1. Department of Operations Research, Stanford University, Stanford, USA
      Stanford Business Software, Inc., Mountain View

    View author publications

    You can also search for this author in PubMed   Google Scholar

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xxxviii
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  2. The Linear Programming Problem

    Pages 1-33

  3. Solving Simple Linear Programs

    Pages 35-61

  4. The Simplex Method

    Pages 63-111

  5. Interior-Point Methods

    Pages 113-127

  6. Duality

    Pages 129-143

  7. Equivalent Formulations

    Pages 145-170

  8. Price Mechanism and Sensitivity Analysis

    Pages 171-203

  9. Transportation and Assignment Problem

    Pages 205-252

  10. Network Flow Theory

    Pages 253-313

  11. Back Matter

    Pages 315-435
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Keywords

About this book

By George B. Dantzig LINEAR PROGRAMMING The Story About How It Began: Some legends, a little about its historical sign- cance, and comments about where its many mathematical programming extensions may be headed. Industrial production, the ?ow of resources in the economy, the exertion of military e?ort in a war, the management of ?nances—all require the coordination of interrelated activities. What these complex undertakings share in common is the task of constructing a statement of actions to be performed, their timing and quantity(calledaprogramorschedule), that, ifimplemented, wouldmovethesystem from a given initial status as much as possible towards some de?ned goal. While di?erences may exist in the goals to be achieved, the particular processes, and the magnitudes of e?ort involved, when modeled in mathematical terms these seemingly disparate systems often have a remarkably similar mathematical str- ture. The computational task is then to devise for these systems an algorithm for choosing the best schedule of actions from among the possible alternatives. The observation, in particular, that a number of economic, industrial, ?nancial, and military systems can be modeled (or reasonably approximated) by mathem- ical systems of linear inequalities and equations has given rise to the development of the linear programming ?eld.

Authors and Affiliations

  • Department of Operations Research, Stanford University, Stanford, USA

    George B. Dantzig, Mukund N. Thapa

  • Stanford Business Software, Inc., Mountain View

    Mukund N. Thapa

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