Additional Information
Book Details
Abstract
This book covers all aspects of linear programming from the two-dimensional LPs and their extension to higher dimensional LPs, through duality and sensitivity analysis and finally to the examination of commented software outputs.
The book is organised into three distinct parts: the first part studies the concepts of linear programming and presents its founding theorems complete with proofs and applications; the second part presents linear programming in the diversity of its variants (Integer Programming, Game Theory, Transportation Problem, Assignment Model), and highlights the modelling problems that are involved in network optimisation; the final part furthers the discussion on selected topics and presents an opening to nonlinear programming through quadratic programming.
Table of Contents
| Section Title | Page | Action | Price |
|---|---|---|---|
| Cover | Cover | ||
| Linear Programming, Sensitivity Analysis and Related Topics | i | ||
| To my family, for their love and support | v | ||
| Contents | vii | ||
| Preface | xiii | ||
| Acknowledgements | xv | ||
| Introduction | 1 | ||
| Modelling using Linear Programming | 1 | ||
| Solving linear programmes | 3 | ||
| Linear Programming: the approach par excellence for understanding modelling | 7 | ||
| The approach of the book | 11 | ||
| Part I Linear Programming and Sensitivity Analysis | 13 | ||
| The Geometric Approach | 15 | ||
| The founding concepts of Linear Programming | 16 | ||
| The Maximization Form | 21 | ||
| The Minimization Form | 32 | ||
| Chapter 2 Exercises and applications | 34 | ||
| The Simplex Method | 39 | ||
| The Maximization Form | 39 | ||
| The Minimization Form | 58 | ||
| The Revised Simplex Method | 62 | ||
| Chapter 3 Exercises and applications | 73 | ||
| Understanding Special Cases and Mixed Function Problems | 77 | ||
| Identifying special cases: graphical and simplex approaches | 77 | ||
| The mixed function problem | 87 | ||
| Chapter 4 Exercises and applications | 90 | ||
| Duality | 95 | ||
| Theorems of duality and relationships | 95 | ||
| The Dual Simplex Method | 107 | ||
| Particular cases | 109 | ||
| Chapter 5 Exercises and applications | 118 | ||
| Sensitivity Analysis | 123 | ||
| A visual approach to Sensitivity Analysis | 124 | ||
| The Maximization Form | 124 | ||
| The Minimization Form | 135 | ||
| Sensitivity Analysis under the Simplex Method, using Matrix Algebra | 137 | ||
| The Maximization Form | 137 | ||
| Introduction of a new variable or of a new constraint | 149 | ||
| Note on the Minimization Form [The Portfolio 3D modified] | 151 | ||
| Embedded modifications | 152 | ||
| Revisiting mixed function problem | 156 | ||
| Discussion on optimality ranges: simplex and graphical approaches | 156 | ||
| Chapter 6 Exercises and applications | 160 | ||
| Understanding Computer Outputs and LP Applications | 171 | ||
| Highlighting outputs | 171 | ||
| Using software packages to solve LP problems | 172 | ||
| Study of outputs with respect to Chapters 3 and 6: the Simplex Method and Sensitivity Analysis | 177 | ||
| Commented outputs with respect to Chapters 4 and 5: special cases and duality | 183 | ||
| The Various Fields of Application | 190 | ||
| Production and make-or-buy | 191 | ||
| Purchase plans | 196 | ||
| Finance | 198 | ||
| Advertising | 203 | ||
| Staff scheduling | 205 | ||
| Blending and nutrition | 209 | ||
| Efficiency problems | 216 | ||
| Chapter 7 Applications | 219 | ||
| Part II Variants and Related Topics | 227 | ||
| The Variants of Linear Programmes | 229 | ||
| Integer Programming | 230 | ||
| Game Theory | 243 | ||
| The Transportation Problem | 256 | ||
| The Assignment Model | 274 | ||
| Chapter 8 Exercises and applications | 288 | ||
| Related Topics: Graphs and Networks | 301 | ||
| The main building concepts of Graph Theory | 301 | ||
| Flow networks | 308 | ||
| The shortest path | 325 | ||
| The Minimal Spanning Tree | 338 | ||
| Chapter 9 Exercises and applications | 347 | ||
| Part III Mathematical Corner and Note on Nonlinear Programming | 355 | ||
| Mathematical Corner | 357 | ||
| Coping with infeasibility | 357 | ||
| Flow networks | 366 | ||
| The Shortest Route Algorithm: discussion on Sensitivity Analysis | 370 | ||
| The Minimal Spanning Tree | 374 | ||
| Chapter 10 Exercises and applications | 383 | ||
| Note on Nonlinear Programming | 385 | ||
| Quadratic Programming: definition | 386 | ||
| Illustrations and graphical displays: solution method using Lagrange multipliers | 387 | ||
| Formulating the quadratic programme | 392 | ||
| Comment on shadow prices and ‘RHS ranges’ | 396 | ||
| Chapter 11 Exercises | 400 | ||
| Basic Review Chapter | 401 | ||
| Basic Matrix Algebra | 401 | ||
| Derivatives and local extrema | 408 | ||
| Answers to Selected Problems and Applications | 417 | ||
| Study Applications | 435 | ||
| Index | 436 |