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