Linear Programming

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Macmillan, Sep 15, 1983 - Mathematics - 478 pages
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For upper-division/graduate courses in operations research/management science, mathematics, and computer science, this text covers basic theory, selected applications, network flow problems, and advanced techniques.
 

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Contents

Introduction
3
How the Simplex Method Works
13
Pitfalls and How to Avoid Them
27
How Fast Is the Simplex Method?
45
The Duality Theorem
54
Gaussian Elimination and Matrices
71
The Revised Simplex Method
97
Solutions by the Simplex Method
118
Approximating Data by Linear Functions
213
Matrix Games
228
Systems of Linear Inequalities
240
Finding All Vertices of a Polyhedron
271
The Network Simplex Method
291
Applications of the Network Simplex Method
320
UpperBounded Transshipment Problems
353
Maximum Flows Through Networks
367

Theorems on Duality and Infeasibility
137
Sensitivity Analysis
148
Selected Applications
169
Efficient Allocation of Scarce Resources
171
Scheduling Production and Inventory
188
The CuttingStock Problem
195
The PrimalDual Method
390
Updating a Triangular Factorization of the Basis
405
The DantzigWolfe Decomposition Principle
425
The Ellipsoid Method
443
Solutions to Selected Problems
465
Copyright

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About the author (1983)

David L. Applegate is a researcher at AT&T Labs. Robert E. Bixby is Research Professor of Management and Noah Harding Professor of Computational and Applied Mathematics at Rice University. Vasek Chvatal is Canada Research Chair in Combinatorial Optimization at Concordia University. William J. Cook is Chandler Family Chair in Industrial and Systems Engineering at the Georgia Institute of Technology.

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