Linear Programming and Extensions

George B. Dantzig

Book

Linear Programming and Extensions

George B. Dantzig

Language: English

Published/Copyright: 1963

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This book is in the series

Volume 25 | Princeton Landmarks in Mathematics and Physics

About this book

The influential book that established the mathematical discipline of linear programming

In the worlds of finance, business, and management, mathematicians and economists frequently encounter problems of optimization. In this classic book, George Dantzig shows how the methods of linear programming can provide solutions. Drawing on a wealth of examples, he introduces the basic theory of linear inequalities and describes the powerful simplex method used to solve them. He discusses the price concept, the transportation problem, and matrix methods, and covers key mathematical concepts such as the properties of convex sets and linear vector spaces. Dantzig demonstrates how linear programming can be applied to a host of optimization problems, from minimizing traffic congestion to maximizing the scheduling of airline flights.

An invaluable resource for students and practitioners alike, Linear Programming and Extensions is an extraordinary account of the development and uses of this versatile mathematical technique, blending foundational research in mathematical theory with computation, economic analysis, and applications to industrial problems.

Author / Editor information

George B. Dantzig (1914–2005) is widely acclaimed as the father of linear programming and was a leading figure in the development of mathematical optimization, making important contributions to fields such as industrial engineering, economics, and statistics. He was professor emeritus of operations research and computer science at Stanford University.

Reviews

"The author of this book was the main force in establishing a new mathematical discipline, and he has contributed to its further development at every stage and from every angle. [Linear Programming and Extensions] is a treasure trove for those who work in this field—teachers, students, and users alike. Its encyclopaedic coverage, due in part to collaboration with other experts, makes it an absolute must."—S. Vajda, Zentralblatt für Mathematik und ihre Grenzgebiete

Topics

Mathematics General Mathematics

Frontmatter Publicly Available Download PDF	i
Preface Requires Authentication Unlicensed Licensed	vii
Contents Publicly Available Download PDF	xi
1. The Linear Programming Concept Requires Authentication Unlicensed Licensed	1
2. Origins and Influences Requires Authentication Unlicensed Licensed	12
3. Formulating a Linear Programming Model Requires Authentication Unlicensed Licensed	32
4. Linear Equation and Inequality Systems Requires Authentication Unlicensed Licensed	69
5. The Simplex Method Requires Authentication Unlicensed Licensed	94
6. Proof of the Simplex Algorithm and the Duality Theorem Requires Authentication Unlicensed Licensed	120
7. The Geometry of Linear Programs Requires Authentication Unlicensed Licensed	147
8. Pivoting, Vector Spaces, Matrices, and Inverses Requires Authentication Unlicensed Licensed	173
9. The Simplex Method Using Multipliers Requires Authentication Unlicensed Licensed	210
10. Finiteness of the Simplex Method under Perturbation Requires Authentication Unlicensed Licensed	228
11. Variants of the Simplex Algorithm Requires Authentication Unlicensed Licensed	240
12. The Price Concept in Linear Programming Requires Authentication Unlicensed Licensed	254
13. Games And Linear Programs Requires Authentication Unlicensed Licensed	277
14. The Classical Transportation Problem Requires Authentication Unlicensed Licensed	299
15. Optimal Assignment and Other Distribution Problems Requires Authentication Unlicensed Licensed	316
16. The Transshipment Problem Requires Authentication Unlicensed Licensed	335
17. Networks and the Transshipment Problem Requires Authentication Unlicensed Licensed	352
18. Variables with Upper Bounds Requires Authentication Unlicensed Licensed	368
19. Maximal Flows in Networks Requires Authentication Unlicensed Licensed	385
20. The Primal-Dual Method for Transportation Problems Requires Authentication Unlicensed Licensed	404
21. The Weighted Distribution Problem Requires Authentication Unlicensed Licensed	413
22. Programs with Variable Coefficients Requires Authentication Unlicensed Licensed	433
23. A Decomposition Principle for Linear Programs Requires Authentication Unlicensed Licensed	448
24. Convex Programming Requires Authentication Unlicensed Licensed	471
25. Uncertainty Requires Authentication Unlicensed Licensed	499
26. Discrete-Variable Extremum Problems Requires Authentication Unlicensed Licensed	514
27. Stigler’s Nutrition Model: An Example of Formulation and Solution Requires Authentication Unlicensed Licensed	551
28. The Allocation of Aircraft to Routes under Uncertain Demand Requires Authentication Unlicensed Licensed	568
Bibliography Requires Authentication Unlicensed Licensed	592
Subject Index Requires Authentication Unlicensed Licensed	617
Name Index Requires Authentication Unlicensed Licensed	625
Selected Rand Books Requires Authentication Unlicensed Licensed	629

Publishing information

Pages and Images/Illustrations in book

eBook published on:

August 10, 2016

eBook ISBN:

9781400884179

Pages and Images/Illustrations in book

Main content:

656

Other:

99 figs. 64 tables

https://doi.org/10.1515/9781400884179

eBook ISBN: 9781400884179

Keywords for this book

Variable (mathematics); Linear programming; Equation; Simplex algorithm; Basic solution (linear programming); Theorem; Coefficient; Iteration; Quantity; Duality (optimization); Simultaneous equations; Dynamic programming; Mathematical optimization; Linear inequality; Parametric programming; Linear combination; Linear equation; Summation; Linear interpolation; Iterative method; Canonical form; Linear function; Approximation theory; Integer programming; Computation; Ford–Fulkerson algorithm; Linear approximation; Nonlinear programming; Linear map; Solution set; Loss function; Pivot element; Linearity; Slack variable; Algorithm; Monotonic function; Permutation matrix; Neyman–Pearson lemma; Polynomial; Quadratic programming; Variable (computer science); Dimensional analysis; Invertible matrix; Utilization; Upper and lower bounds; Input-Output Analysis; Programming tool; Linear differential equation; Theory of computation; Elementary matrix; Automatic programming; Dynamic problem (algorithms); Change of variables; Requirement; Uniqueness theorem; Gradient descent; Permutation; Sensitivity analysis; Maxima and minima; Counterexample; Accuracy and precision; Projection method (fluid dynamics); Computational complexity theory; Combination; Local optimum; Special case; Dual basis; Lagrange multiplier; Axiom; Optimality criterion

Audience(s) for this book

College/higher education;Professional and scholarly;

Linear Programming and Extensions

Overview

About this book

Author / Editor information

Reviews

Topics

Table of contents

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