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Linear programming : methods and applications / Saul I. Gass.

By: Material type: TextTextPublication details: New York : Dover Publications, 2003.Edition: 5th edDescription: xi, 532 p. ; 24 cm.ReprintISBN:
  • 048643284X (pbk.)
  • 9780486432847
Subject(s): DDC classification:
  • 519.72   22
Contents:
Prefacep. vii Introduction General Discussionp. 3 Linear-Programming Problemsp. 3 Examples of Linear-Programming Problemsp. 7 Mathematical Backgroundp. 17 Matricesp. 17 Vectors and Vector Spacesp. 28 Convex Setsp. 32 Linear Inequalitiesp. 37 Solution of a Set of Linear Equationsp. 43 Methods: Theoretical and Computational The General Linear-Programming Problemp. 67 The Linear-Programming Problemp. 67 Properties of a Solution to the Linear-Programming Problemp. 69 Generating Extreme-Point Solutionsp. 77 The Simplex Computational Procedurep. 86 Development of a Minimum Feasible Solutionp. 88 Computational Procedurep. 94 The Artificial-Basis Techniquep. 106 A First Feasible Solution Using Slack Variablesp. 113 Geometric Interpretation of the Simplex Procedurep. 114 The Revised Simplex Methodp. 123 The General Form of the Inversep. 123 The Product Form of the Inversep. 139 Computational Considerationsp. 142 The Duality Problems of Linear Programmingp. 157 The Unsymmetric Primal-Dual Problemsp. 157 The Symmetric Primal-Dual Problemsp. 166 Economic Interpretation of the Primal-Dual Problemsp. 173 Degeneracy and Anticycling Proceduresp. 181 Perturbation Techniquesp. 183 The Lowest-Index Anticycling Rulesp. 186 Example of Cyclingp. 190 Parametric Linear Programming and Sensitivity Analysisp. 195 The Parametric Objective Functionp. 196 The Parametric Dual Problemp. 207 Sensitivity Analysisp. 213 Multiobjective Linear Programmingp. 224 Additional Computational Techniquesp. 238 Determining a First Feasible Solutionp. 240 The Dual Simplex Methodp. 245 Integer Programmingp. 249 The Decomposition of Large-Scale Systemsp. 266 Bounded-Variable Problemsp. 282 The Simplex Algorithm and Computational Efficiencyp. 303 Applications The Transportation Problemp. 319 The General Transportation Problemp. 319 Computational Procedure for Solving the Transportation Problemp. 328 Variations of the Transportation Problemp. 343 General Linear-Programming Applicationsp. 351 Production-Scheduling and Inventory-Control Problemsp. 353 Interindustry Problemsp. 362 Diet Problemsp. 368 Network-Flow Problemsp. 372 Sample of Applicationsp. 390 Linear Programming and the Theory of Gamesp. 406 Nonlinear Programming Nonlinear Programmingp. 431 The General Problem of Mathematical Programmingp. 432 Mathematical Backgroundp. 435 The Convex-Programming Problemp. 442 Quadratic Programmingp. 451 Separable Programmingp. 458 Bibliography of Linear-Programming Applicationsp. 469 Referencesp. 491 Indexp. 525 Table of Contents provided by Ingram. All Rights Reserved.
Summary: 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, more. Examples and exercises with selected answers appear in every chapter. 1995 edition.
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Item type Current library Call number Copy number Status Date due Barcode
Books Books Main library General Stacks 519.72 / GA.L 2003 (Browse shelf(Opens below)) 1 Available 007358

Reprint. Originally published: New York : McGraw-Hill, 1985.

Includes bibliographical references (p. 469-523) and index.

Prefacep. vii Introduction General Discussionp. 3 Linear-Programming Problemsp. 3 Examples of Linear-Programming Problemsp. 7 Mathematical Backgroundp. 17 Matricesp. 17 Vectors and Vector Spacesp. 28 Convex Setsp. 32 Linear Inequalitiesp. 37 Solution of a Set of Linear Equationsp. 43 Methods: Theoretical and Computational The General Linear-Programming Problemp. 67 The Linear-Programming Problemp. 67 Properties of a Solution to the Linear-Programming Problemp. 69 Generating Extreme-Point Solutionsp. 77 The Simplex Computational Procedurep. 86 Development of a Minimum Feasible Solutionp. 88 Computational Procedurep. 94 The Artificial-Basis Techniquep. 106 A First Feasible Solution Using Slack Variablesp. 113 Geometric Interpretation of the Simplex Procedurep. 114 The Revised Simplex Methodp. 123 The General Form of the Inversep. 123 The Product Form of the Inversep. 139 Computational Considerationsp. 142 The Duality Problems of Linear Programmingp. 157 The Unsymmetric Primal-Dual Problemsp. 157 The Symmetric Primal-Dual Problemsp. 166 Economic Interpretation of the Primal-Dual Problemsp. 173 Degeneracy and Anticycling Proceduresp. 181 Perturbation Techniquesp. 183 The Lowest-Index Anticycling Rulesp. 186 Example of Cyclingp. 190 Parametric Linear Programming and Sensitivity Analysisp. 195 The Parametric Objective Functionp. 196 The Parametric Dual Problemp. 207 Sensitivity Analysisp. 213 Multiobjective Linear Programmingp. 224 Additional Computational Techniquesp. 238 Determining a First Feasible Solutionp. 240 The Dual Simplex Methodp. 245 Integer Programmingp. 249 The Decomposition of Large-Scale Systemsp. 266 Bounded-Variable Problemsp. 282 The Simplex Algorithm and Computational Efficiencyp. 303 Applications The Transportation Problemp. 319 The General Transportation Problemp. 319 Computational Procedure for Solving the Transportation Problemp. 328 Variations of the Transportation Problemp. 343 General Linear-Programming Applicationsp. 351 Production-Scheduling and Inventory-Control Problemsp. 353 Interindustry Problemsp. 362 Diet Problemsp. 368 Network-Flow Problemsp. 372 Sample of Applicationsp. 390 Linear Programming and the Theory of Gamesp. 406 Nonlinear Programming Nonlinear Programmingp. 431 The General Problem of Mathematical Programmingp. 432 Mathematical Backgroundp. 435 The Convex-Programming Problemp. 442 Quadratic Programmingp. 451 Separable Programmingp. 458 Bibliography of Linear-Programming Applicationsp. 469 Referencesp. 491 Indexp. 525 Table of Contents provided by Ingram. All Rights Reserved.

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, more. Examples and exercises with selected answers appear in every chapter. 1995 edition.

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