An Introduction to Linear Programming and Game Theory
by Thie, Paul R.; Keough, Gerard E.Edition: 3rd
Format: Hardcover
Pub. Date: 2008-08-11
Publisher(s): Wiley-Interscience
Other versions by this Author
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Summary
* This third edition features various additions as well as improvements that have been developed over the last decade, and the most significant addition to the text involves technology. * It features an introduction, discussion, and utilization of Solver, a spreadsheet software package that solves mathematical programming problems. * PRT Simplex, a computer application for learning the simplex method, has been developed by co-author Gerard Keough and was designed to be used with this book.
Author Biography
PAUL R. THIE, PhD, is Professor Emeritus in the Department of Mathematics at Boston College. Dr. Thie has authored numerous journal articles in the areas of mathematical programming and several complex variables.
GERARD E. KEOUGH, PhD, is Associate Professor and former chair of the Department of Mathematics at Boston College. He has written extensively on operator theory, functional analysis, and the use of technology in mathematics. Dr. Keough is the coauthor of Getting Started with Maple®, Second Edition and Getting Started with Mathematica®, Second Edition,both published by Wiley.
Table of Contents
| Preface | p. xi |
| Mathematical Models | p. 1 |
| Applying Mathematics | p. 1 |
| The Diet Problem | p. 2 |
| The Prisoner's Dilemma | p. 5 |
| The Roles of Linear Programming and Game Theory | p. 8 |
| The Linear Programming Model | p. 9 |
| History | p. 9 |
| The Blending Model | p. 10 |
| The Production Model | p. 21 |
| The Transportation Model | p. 34 |
| The Dynamic Planning Model | p. 38 |
| Summary | p. 47 |
| The Simplex Method | p. 57 |
| The General Problem | p. 57 |
| Linear Equations and Basic Feasible Solutions | p. 63 |
| Introduction to the Simplex Method | p. 72 |
| Theory of the Simplex Method | p. 77 |
| The Simplex Tableau and Examples | p. 85 |
| Artificial Variables | p. 93 |
| Redundant Systems | p. 101 |
| A Convergence Proof | p. 106 |
| Linear Programming and Convexity | p. 110 |
| Spreadsheet Solution of a Linear Programming Problem | p. 115 |
| Duality | p. 121 |
| Introduction to Duality | p. 121 |
| Definition of the Dual Problem | p. 123 |
| Examples and Interpretations | p. 132 |
| The Duality Theorem | p. 138 |
| The Complementary Slackness Theorem | p. 154 |
| Sensitivity Analysis | p. 161 |
| Examples in Sensitivity Analysis | p. 161 |
| Matrix Representation of the Simplex Algorithm | p. 175 |
| Changes in the Objective Function | p. 183 |
| Addition of a New Variable | p. 189 |
| Changes in the Constant-Term Column Vector | p. 192 |
| The Dual Simplex Algorithm | p. 196 |
| Addition of a Constraint | p. 204 |
| Integer Programming | p. 211 |
| Introduction to Integer Programming | p. 211 |
| Models with Integer Programming Formulations | p. 214 |
| Gomory's Cutting Plane Algorithm | p. 228 |
| A Branch and Bound Algorithm | p. 237 |
| Spreadsheet Solution of an Integer Programming Problem | p. 244 |
| The Transportation Problem | p. 251 |
| A Distribution Problem | p. 251 |
| The Transportation Problem | p. 264 |
| Applications | p. 282 |
| Other Topics in Linear Programming | p. 299 |
| An Example Involving Uncertainty | p. 299 |
| An Example with Multiple Goals | p. 306 |
| An Example Using Decomposition | p. 314 |
| An Example in Data Envelopment Analysis | p. 325 |
| Two-Person, Zero-Sum Games | p. 337 |
| Introduction to Game Theory | p. 337 |
| Some Principles of Decision Making in Game Theory | p. 345 |
| Saddle Points | p. 350 |
| Mixed Strategies | p. 353 |
| The Fundamental Theorem | p. 360 |
| Computational Techniques | p. 370 |
| Games People Play | p. 382 |
| Other Topics in Game Theory | p. 391 |
| Utility Theory | p. 391 |
| Two-Person, Non-Zero-Sum Games | p. 393 |
| Noncooperative Two-Person Games | p. 397 |
| Cooperative Two-Person Games | p. 404 |
| The Axioms of Nash | p. 408 |
| An Example | p. 414 |
| Vectors and Matrices | p. 417 |
| An Example of Cycling | p. 421 |
| Efficiency of the Simplex Method | p. 423 |
| LP Assistant | p. 427 |
| Microsoft Excel and Solver | p. 431 |
| Bibliography | p. 439 |
| Solutions to Selected Problems | p. 443 |
| Index | p. 457 |
| Table of Contents provided by Ingram. All Rights Reserved. |
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