线性规划/Linear programming

2003-12  

Oversea Publishing House  

Gass, Saul I.  

532  

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 transDortation 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 book，this volume provides invaluable help to research analysts，applied mathematicians，economists，statisticians，and others wishing to make effective use of modern programming techniques．

PrefacePart 1 INTRODUCTION chapter 1 General Discussion 1. Linear-Programming Problems 2. Examples of Linear-Programming Problems chapter 2 Mathematical Background 1. Matrices 2. Vectors and Vector Spaces 3. Convex Sets 4. Linear Inequalities 5. Solution of a Set of Linear EquationsPart 2 METHODS: THEORETICAL AND COMPUTATIONAL chapter 3 The General Linear-Programming Problem 1. The Linear-Programming Problem 2. Properties of a Solution to the Linear-Programming Problem 3. Generating Extreme-Point Solutions chapter 4 The Simplex Computational Procedure 1. Development of a Minimum Feasible Solution 2. Computational Procedure 94 3. The Artificial-Basis Technique 106 4. A First Feasible Solution Using Slack Variables 5. Geometric Interpretation of the Simplex Procedure chapter 5 The Revised Simplex Method 1. The General Form of the Inverse 2. The Product Form of the Inverse 3. Computational Considerations chapter 6 The Duality Problems of Linear Programming 1. The Unsymmetric Primal-Dual Problems 2. The Symmetric Primal-Dual Problems 3. Economic Interpretation of the Primal-Dual Problems chapter 7 Degeneracy and Anticycling Procedures 1. Perturbation Techniques 2. The Lowest-Index Anticycling Rules 3. Example of Cycling chapter 8 Parametric Linear Programming and Sensitivity Analysis 1. The Parametric Objective Function 2. The Parametric Dual Problem 3. Sensitivity Analysis 4. Multiobjective Linear Programming chapter 9 Additional Computational Techniques 1. Determining a First Feasible Solution 2. The Dual Simplex Method 3. Integer Programming 4. The Decomposition of Large-Scale Systems 5. Bounded-Variable Problems 6. The Simplex Algorithm and Computational EfficiencyPart 3 APPLICATIONS chapter 10 The Transportation Problem 1. The General Transportation Problem 2. Computational Procedure for Solving the Transportation Problem 3. Variations of the Transportation Problem chapter 11 General Linear-Programming Applications 1. Production-Scheduling and Inventory-Control Problems 2. Interindustry Problems ……Part 4 NONLNEAR PROGRAMMING chapter 12 Nonlinear ProgrammingBibliography of Linear－Programming ApplicationsReferencesIndex

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