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 |
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