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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
The Inverse of a Matrix
Linear Independence and Basis
Introduction to Linear Programming: The Linear Programming Problem
Geometry of Linear Programming Problems
The Extreme Point Theorem
The Simplex Method: The Simplex Method for Problems in Standard Form
Degeneracy and Cycling
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
Integer Programming: Examples
Cutting Plane Methods
Branch and Bound Methods
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
Appendices: Karmarkar's Algorithm
Answers to Odd-Numbered Exercises
Table of Contents provided by Publisher. All Rights Reserved.