Linear Programming Methods and Applications

ISBN-10: 048643284X

ISBN-13: 9780486432847

Edition: 5th 2003 (Revised)

Authors: Saul I. Gass

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Clear and comprehensive, this volume introduces theoretical, computational, and applied concepts and is useful both as text and as a reference book. Considerations of theoretical and computational methods include the general linear programming problem, the simplex computational procedure, the revised simplex method, the duality problems of linear programming degeneracy procedures, parametric linear programming and sensitivity analysis, and additional computational techniques. The treatment of applications covers the transportation problem and general linear programming applications, and a final part examines nonlinear programming. Numerical examples and exercises with selected answers appear in every chapter. 1995 ed.
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Book details

List price: $29.95
Edition: 5th
Copyright year: 2003
Publisher: Dover Publications, Incorporated
Publication date: 11/18/2010
Binding: Paperback
Pages: 544
Size: 6.00" wide x 9.00" long x 1.00" tall
Weight: 1.496
Language: English

General Discussion
Linear-Programming Problems
Examples of Linear-Programming Problems
Mathematical Background
Vectors and Vector Spaces
Convex Sets
Linear Inequalities
Solution of a Set of Linear Equations
Methods: Theoretical and Computational
The General Linear-Programming Problem
The Linear-Programming Problem
Properties of a Solution to the Linear-Programming Problem
Generating Extreme-Point Solutions
The Simplex Computational Procedure
Development of a Minimum Feasible Solution
Computational Procedure
The Artificial-Basis Technique
A First Feasible Solution Using Slack Variables
Geometric Interpretation of the Simplex Procedure
The Revised Simplex Method
The General Form of the Inverse
The Product Form of the Inverse
Computational Considerations
The Duality Problems of Linear Programming
The Unsymmetric Primal-Dual Problems
The Symmetric Primal-Dual Problems
Economic Interpretation of the Primal-Dual Problems
Degeneracy and Anticycling Procedures
Perturbation Techniques
The Lowest-Index Anticycling Rules
Example of Cycling
Parametric Linear Programming and Sensitivity Analysis
The Parametric Objective Function
The Parametric Dual Problem
Sensitivity Analysis
Multiobjective Linear Programming
Additional Computational Techniques
Determining a First Feasible Solution
The Dual Simplex Method
Integer Programming
The Decomposition of Large-Scale Systems
Bounded-Variable Problems
The Simplex Algorithm and Computational Efficiency
The Transportation Problem
The General Transportation Problem
Computational Procedure for Solving the Transportation Problem
Variations of the Transportation Problem
General Linear-Programming Applications
Production-Scheduling and Inventory-Control Problems
Interindustry Problems
Diet Problems
Network-Flow Problems
Sample of Applications
Linear Programming and the Theory of Games
Nonlinear Programming
Nonlinear Programming
The General Problem of Mathematical Programming
Mathematical Background
The Convex-Programming Problem
Quadratic Programming
Separable Programming
Bibliography of Linear-Programming Applications
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