An Introduction to Linear Programming and the Simplex Algorithm

Covers LP formulation and the underlying assumptions, graphical solution on 2-var LP's, generalization to the n-var case, Basic Feasible Solutions and the Simplex Algorithm.

**Tag(s):**
Linear Algebra

**Publication date**: 31 Dec 1997

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**ISBN-13**:
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**Paperback**:
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**Views**: 19,803

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**Post time**: 05 Sep 2007 08:08:08

An Introduction to Linear Programming and the Simplex Algorithm

Covers LP formulation and the underlying assumptions, graphical solution on 2-var LP's, generalization to the n-var case, Basic Feasible Solutions and the Simplex Algorithm.

Excerpts from the Introduction:

This text is intended to function as an introduction to Linear Programming (LP) and the Simplex algorithm. The specific topics covered and the structure of the material is as follows:

* The LP formulation and the underlying assumptions

* Graphical solution of 2-var LP's

* Generalization to the n-var case: the "geometry" of the LP feasible region and the Fundamental Theorem of Linear Programming.

* An algebraic characterization of the solution search space: Basic Feasible Solutions

* The Simplex Algorithm

Most of the text material is presented inductively, by generalizing some introductory highlighting examples. In fact, the basic structure of the material and many of the examples used in the text have been inspired by W. L. Winston's Introduction to Mathematical Programming, ed. Duxbury, which has been used as the class text in an introductory LP course at the School of Industrial & Systems Engineering, at Georgia Tech.

An additional and innovative feature of this text is the integration of some software modules which allow the reader to run her own examples interactively. Specifically, this software is distributed at the end of key sections, and it is intended to demonstrate/visualize basic concepts and the functionality of the algorithms discussed in the text.

This text is intended to function as an introduction to Linear Programming (LP) and the Simplex algorithm. The specific topics covered and the structure of the material is as follows:

* The LP formulation and the underlying assumptions

* Graphical solution of 2-var LP's

* Generalization to the n-var case: the "geometry" of the LP feasible region and the Fundamental Theorem of Linear Programming.

* An algebraic characterization of the solution search space: Basic Feasible Solutions

* The Simplex Algorithm

Most of the text material is presented inductively, by generalizing some introductory highlighting examples. In fact, the basic structure of the material and many of the examples used in the text have been inspired by W. L. Winston's Introduction to Mathematical Programming, ed. Duxbury, which has been used as the class text in an introductory LP course at the School of Industrial & Systems Engineering, at Georgia Tech.

An additional and innovative feature of this text is the integration of some software modules which allow the reader to run her own examples interactively. Specifically, this software is distributed at the end of key sections, and it is intended to demonstrate/visualize basic concepts and the functionality of the algorithms discussed in the text.

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