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Linear Programming

Methods and Applications: Fifth Edition

By: SAUL I. GASS

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Paperback | 18 November 2010 | Edition Number 5

At a Glance

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544 Pages

Edition Type
Revised

Dimensions(cm)
23.5 x 15.5 x 2.5

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""One of the best introductory books on linear programming ... excellent."" - Journal of the American Statistical Association.""A good elementary text. ""- Mathematical Reviews.Clear and comprehensive in its coverage of the entire spectrum of linear programming techniques, this volume introduces theoretical, computational, and applied concepts. 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. Useful both as a text and as a reference, this volume provides valuable help to research analysts, applied mathematicians, economists, statisticians, and others wishing to make effective use of modern programming techniques.

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"One of the best introductory books on linear programming ... excellent."

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You Can Find This Book In

Non-Fiction Mathematics Optimisation Linear Programming

Preface	p. vii
Introduction
General Discussion	p. 3
Linear-Programming Problems	p. 3
Examples of Linear-Programming Problems	p. 7
Mathematical Background	p. 17
Matrices	p. 17
Vectors and Vector Spaces	p. 28
Convex Sets	p. 32
Linear Inequalities	p. 37
Solution of a Set of Linear Equations	p. 43
Methods: Theoretical and Computational
The General Linear-Programming Problem	p. 67
The Linear-Programming Problem	p. 67
Properties of a Solution to the Linear-Programming Problem	p. 69
Generating Extreme-Point Solutions	p. 77
The Simplex Computational Procedure	p. 86
Development of a Minimum Feasible Solution	p. 88
Computational Procedure	p. 94
The Artificial-Basis Technique	p. 106
A First Feasible Solution Using Slack Variables	p. 113
Geometric Interpretation of the Simplex Procedure	p. 114
The Revised Simplex Method	p. 123
The General Form of the Inverse	p. 123
The Product Form of the Inverse	p. 139
Computational Considerations	p. 142
The Duality Problems of Linear Programming	p. 157
The Unsymmetric Primal-Dual Problems	p. 157
The Symmetric Primal-Dual Problems	p. 166
Economic Interpretation of the Primal-Dual Problems	p. 173
Degeneracy and Anticycling Procedures	p. 181
Perturbation Techniques	p. 183
The Lowest-Index Anticycling Rules	p. 186
Example of Cycling	p. 190
Parametric Linear Programming and Sensitivity Analysis	p. 195
The Parametric Objective Function	p. 196
The Parametric Dual Problem	p. 207
Sensitivity Analysis	p. 213
Multiobjective Linear Programming	p. 224
Additional Computational Techniques	p. 238
Determining a First Feasible Solution	p. 240
The Dual Simplex Method	p. 245
Integer Programming	p. 249
The Decomposition of Large-Scale Systems	p. 266
Bounded-Variable Problems	p. 282
The Simplex Algorithm and Computational Efficiency	p. 303
Applications
The Transportation Problem	p. 319
The General Transportation Problem	p. 319
Computational Procedure for Solving the Transportation Problem	p. 328
Variations of the Transportation Problem	p. 343
General Linear-Programming Applications	p. 351
Production-Scheduling and Inventory-Control Problems	p. 353
Interindustry Problems	p. 362
Diet Problems	p. 368
Network-Flow Problems	p. 372
Sample of Applications	p. 390
Linear Programming and the Theory of Games	p. 406
Nonlinear Programming
Nonlinear Programming	p. 431
The General Problem of Mathematical Programming	p. 432
Mathematical Background	p. 435
The Convex-Programming Problem	p. 442
Quadratic Programming	p. 451
Separable Programming	p. 458
Bibliography of Linear-Programming Applications	p. 469
References	p. 491
Index	p. 525
Table of Contents provided by Ingram. All Rights Reserved.

Linear Programming

Methods and Applications: Fifth Edition

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

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