An Introduction to Linear Programming and Game Theory

by Thie, Paul R.; Keough, Gerard E.

• ISBN13: 9780470232866
• ISBN10: 0470232862
• Edition: 3rd
• Format: Hardcover
• Copyright: 2008-08-11
• Publisher: Wiley-Interscience

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
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