Linear Programming and Extensions / George Dantzig.

Format:

Book

Author/Creator:

Dantzig, George, author.

Series:

Princeton landmarks in mathematics and physics.

Princeton Landmarks in Mathematics and Physics

Language:

English

Subjects (All):

Linear programming.

Mathematical models.

Physical Description:

1 online resource (651 p.)

Place of Publication:

Princeton, NJ : Princeton University Press, [2016]

Language Note:

In English.

Summary:

In real-world problems related to finance, business, and management, mathematicians and economists frequently encounter optimization problems. In this classic book, George Dantzig looks at a wealth of examples and develops linear programming methods for their solutions. He begins by introducing the basic theory of linear inequalities and describes the powerful simplex method used to solve them. Treatments of the price concept, the transportation problem, and matrix methods are also given, and key mathematical concepts such as the properties of convex sets and linear vector spaces are covered. George Dantzig is properly acclaimed as the "father of linear programming." Linear programming is a mathematical technique used to optimize a situation. It can be used to minimize traffic congestion or to maximize the scheduling of airline flights. He formulated its basic theoretical model and discovered its underlying computational algorithm, the "simplex method," in a pathbreaking memorandum published by the United States Air Force in early 1948. Linear Programming and Extensions provides an extraordinary account of the subsequent development of his subject, including research in mathematical theory, computation, economic analysis, and applications to industrial problems. Dantzig first achieved success as a statistics graduate student at the University of California, Berkeley. One day he arrived for a class after it had begun, and assumed the two problems on the board were assigned for homework. When he handed in the solutions, he apologized to his professor, Jerzy Neyman, for their being late but explained that he had found the problems harder than usual. About six weeks later, Neyman excitedly told Dantzig, "I've just written an introduction to one of your papers. Read it so I can send it out right away for publication." Dantzig had no idea what he was talking about. He later learned that the "homework" problems had in fact been two famous unsolved problems in statistics.

Contents:

Frontmatter

Preface

Contents

1. The Linear Programming Concept

2. Origins and Influences

3. Formulating a Linear Programming Model

4. Linear Equation and Inequality Systems

5. The Simplex Method

6. Proof of the Simplex Algorithm and the Duality Theorem

7. The Geometry of Linear Programs

8. Pivoting, Vector Spaces, Matrices, and Inverses

9. The Simplex Method Using Multipliers

10. Finiteness of the Simplex Method under Perturbation

11. Variants of the Simplex Algorithm

12. The Price Concept in Linear Programming

13. Games And Linear Programs

14. The Classical Transportation Problem

15. Optimal Assignment and Other Distribution Problems

16. The Transshipment Problem

17. Networks and the Transshipment Problem

18. Variables with Upper Bounds

19. Maximal Flows in Networks

20. The Primal-Dual Method for Transportation Problems

21. The Weighted Distribution Problem

22. Programs with Variable Coefficients

23. A Decomposition Principle for Linear Programs

24. Convex Programming

25. Uncertainty

26. Discrete-Variable Extremum Problems

27. Stigler's Nutrition Model: An Example of Formulation and Solution

28. The Allocation of Aircraft to Routes under Uncertain Demand

Bibliography

Subject Index

Name Index

Selected Rand Books

Notes:

Description based upon print version of record.

Bibliography.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 08. Jul 2019)

ISBN:

1-4008-8417-9

OCLC:

953848356