Elementary Linear Programming With Applications

by Kolman; Beck

• ISBN13: 9780124179103
• ISBN10: 012417910X
• Edition: 2nd
• Format: Hardcover
• Copyright: 1995-06-22
• Publisher: Elsevier Science

Summary

Linear programming finds the least expensive way to meet given needs with available resources. Its results are used in every area of engineering and commerce: agriculture, oil refining, banking, and air transport. Authors Kolman and Beck present the basic notions of linear programming and illustrate how they are used to solve important common problems. The software on the included disk leads students step-by-step through the calculations. the Second Edition is completely revised and provides additional review material on linear algebra as well as complete coverage of elementary linear programming. Other topics covered include: the Duality Theorem; transportation problems; the assignment problem; and the maximal flow problem. New figures and exercises are provided and the authors have updated all computer applications. the disk that comes with the book contains the student-oriented linear programming code SMPX, written by Professor Evar Nering of Arizona State University. The authors also recommend inexpensive linear programming software for personal computers.

Table of Contents

Prologue: Introduction to Operations Research

Review of Linear Algebra: Matrices

Gauss-Jordan Reduction

The Inverse of a Matrix

Subspaces

Linear Independence and Basis

Introduction to Linear Programming: The Linear Programming Problem

Matrix Notation

Geometry of Linear Programming Problems

The Extreme Point Theorem

Basic Solutions

The Simplex Method: The Simplex Method for Problems in Standard Form

Degeneracy and Cycling

Artificial Variables

Further Topics in Linear Programming: Duality

The Duality Theorem

Computational Relations between the Primal and Dual Problems

The Dual Simplex Method

The Revised Simplex Method

Sensitivity Analysis

Computer Aspects

Integer Programming: Examples

Cutting Plane Methods

Branch and Bound Methods

Computer Aspects

Special Types of Linear Programming Problems: The Transportation Problem

The Assignment Problem

Graphs and Networks (Basic Definitions). The Maximal Flow Problem

The Shortest Route Problem

The Critical Path Method

Computer Aspects

Appendices: Karmarkar's Algorithm

Microcomputer Software

SMPX

Answers to Odd-Numbered Exercises

Index

Table of Contents provided by Publisher. All Rights Reserved.