Elementary linear programming with applications
Author(s)
Bibliographic Information
Elementary linear programming with applications
（Computer science and applied mathematics : a series of monographs and textbooks）
Academic Press, c1980
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Includes index
Description and Table of Contents
Description
Elementary Linear Programming with Applications presents a survey of the basic ideas in linear programming and related areas. It also provides students with some of the tools used in solving difficult problems which will prove useful in their professional career. The text is comprised of six chapters. The Prologue gives a brief survey of operations research and discusses the different steps in solving an operations research problem. Chapter 0 gives a quick review of the necessary linear algebra. Chapter 1 deals with the basic necessary geometric ideas in Rn. Chapter 2 introduces linear programming with examples of the problems to be considered, and presents the simplex method as an algorithm for solving linear programming problems. Chapter 3 covers further topics in linear programming, including duality theory and sensitivity analysis. Chapter 4 presents an introduction to integer programming. Chapter 5 covers a few of the more important topics in network flows. Students of business, engineering, computer science, and mathematics will find the book very useful.
Table of Contents
- Preface Acknowledgments Prologue Introduction to Operations Research Further Readings Chapter 0 Review of Linear Algebra (Optional) 0.1 Matrices 0.2 Gauss-Jordan Reduction 0.3 The Inverse of a Matrix 0.4 Subspaces 0.5 Linear Independence and Basis Further Readings Chapter 1 Geometry in Rn 1.1 Hyperplanes 1.2 Convex Sets Further Reading Chapter 2 Introduction to Linear Programming 2.1 The Linear Programming Problem 2.2 Matrix Notation
- Geometric Solutions 2.3 The Simplex Method 2.4 Degeneracy and Cycling (Optional) 2.5 Artificial Variables Further Readings Chapter 3 Further Topics in Linear Programming 3.1 Duality 3.2 Computational Relations Between the Primal and Dual Problems 3.3 The Dual Simplex Method 3.4 The Revised Simplex Method 3.5 Sensitivity Analysis 3.6 Computer Aspects (Optional) Further Readings Chapter 4 Integer Programming 4.1 Examples 4.2 Cutting Plane Methods 4.3 Branch and Bound Methods 4.4 Computer Aspects (Optional) Further Readings Chapter 5 Special Types of Linear Programming Problems 5.7 The Transportation Problem Further Readings 5.2 The Assignment Problem Further Readings 5.3 Graphs and Networks. Basic Definitions Further Reading 5.4 The Maximal Flow Problem Further Readings 5.5 The Shortest Route Problem Further Readings 5.6 The Critical Path Method Further Readings 5.7 Computer Aspects (Optional) Solutions to Odd-Numbered Exercises Index
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