Linear Programming in Industry

1. Front Matter

   Pages I-VIII

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2. Introduction

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   Pages 1-4

3. Elements of the Mathematical Theory of Linear Programming

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   Pages 5-14

4. A Practical Example

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   Pages 15-25

5. Linear Models of Production and Economic Optimization

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   Pages 26-32

6. Industrial Applications

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   Pages 33-64

7. Computational Procedures for Solving Linear Programming Problems

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   Pages 65-89

8. Duality in Linear Programming

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   Pages 90-95

9. The Effects of Coefficient Variations on the Solution

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   Pages 96-99

10. The Applicability of Linear Programming in Industry

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    Pages 100-103

11. Back Matter

    Pages 104-120

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The present volume is intended to serve a twofold purpose. First, it provides a university text of Linear Programming for students of .economics or operations research interested in the theory of production and cost and its practical applications; secondly, it is the author's hope that engineers, business executives, managers, and others responsible for the organization and planning of industrial operations may find the book useful as an introduction to Linear Programming methods and techniques. Despite the different backgrounds of these categories of potential readerft, their respective fields overlap to a considerable extent; both are concernE:'d with economic optimization problems, and the use of Linear Programming to problems of production planning is simply applied theory of production. The non-economist reader may, but should not, pass over Chapter IV in which the linear production model is linked up with the economic theory of production. Without bE:'ing an advanced text, the book aims at covering enough ground to make the reader capable of detecting, formulating, and solving such linear planning problems as he may encounter within his particular field. No heavy demands are made on the reader's mathematical profi­ ciency; except for the proofs in the Appendix-which may be skipped if desired-the mathematical exposition is purely elementary, involving only simple linear relations. In the author's experience, the pedagogical advantages of this approach, as compared with the use of matrix algebra, amply justify the sacrifice of mathematical elegance and typographical simplicity, particularly in explaining the simplex method.

• algebra
• algorithms
• engineer
• machine
• model
• operations research
• optimization
• organization
• planning
• production
• programming
• research

• University of Copenhagen, Dänemark

  Sven Danø

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