Linear Programming

Front Cover
Macmillan, Sep 15, 1983 - Mathematics - 478 pages
"This comprehensive treatment of the fundamental ideas and principles of linear programming covers basic theory, selected applications, network flow problems, and advanced techniques. Using specific examples to illuminate practical and theoretical aspects of the subject, the author clearly reveals the structures of fully detailed proofs. The presentation is geared toward modern efficient implementations of the simplex method and appropriate data structures for network flow problems. Completely self-contained, it develops even elementary facts on linear equations and matrices from the beginning."--Back cover.
 

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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
Connections with Geometry
250
Finding All Vertices of a Polyhedron
271
Network Flow Problems
289
The Network Simplex Method
291
Applications of the Network Simplex Method
320
UpperBounded Transshipment Problems
353
Maximum Flows Through Networks
367
The PrimalDual Method
390

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
Approximating Data by Linear Functions
213
Matrix Games
228
Systems of Linear Inequalities
240
Advanced Techniques
403
Updating a Triangular Factorization of the Basis
405
Generalized Upper Bounding
415
The DantzigWolfe Decomposition Principle
425
The Ellipsoid Method
443
Bibliography
455
Solutions to Selected Problems
465
Index
468
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