- Paperback: 648 pages
- Publisher: Princeton University Press; New Ed edition (3 Aug 1998)
- Language English
- ISBN-10: 0691059136
- ISBN-13: 978-0691059136
- Product Dimensions: 23.4 x 15.5 x 3.3 cm
- Amazon Bestsellers Rank: 1,385,829 in Books (See Top 100 in Books)
- See Complete Table of Contents
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Review
Ter Haar, who studied with Kramers, has a unique approach to scientific biography: He makes us read the original papers [along with] discussion of the published work and an eludication of these papers... On quantum electrodynamics] and the other subjects on which he touches, [ter Haar] has written a stimulating book that brings Kramers's history-making work even more into focus... Physics Today
Product Description
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.
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In the summer of 1949 at the University of Chicago, a conference was held under the sponsorship of the Cowles Commission for Research in Economics; mathematicians, economists, and statisticians from academic institutions and various government agencies presented research using the linear programming tool. Read the first page
Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
In the summer of 1949 at the University of Chicago, a conference was held under the sponsorship of the Cowles Commission for Research in Economics; mathematicians, economists, and statisticians from academic institutions and various government agencies presented research using the linear programming tool. Read the first page
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Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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2 reviews
29 of 29 people found the following review helpful
good to have but not to learn from
26 Feb 2008
Format:Paperback
I disagree with the other reviewer. This is a textbook on linear programming and its extension written by George Dantzig the inventor of the simplex method. Even though the simplex method is still popular and useful there are other interesting algorithms that were dsicovered in the 1980s and 1990s that have theoretical and in some cases practical value.
In 1974 I was a graduate student in Operations Research ae Stanford and I took the three quarter mathematical programming course sequence. The first two quarters were taught by George Dantzig out of this book. George was a delightful person to talk to and probably a good thesis advisor and his stories about his graduate school days and the early years at RAND are delightful. However his lectures were disorganized and vague. I found it impossible to learn much from them and the book was not much help either as it too was vague, disjointed and not well organized. Better understanding of the basics of linear programming can be gotten from the fine general books on operations research such as the book by Hillier and Lieberman and the one by Wagner.
I do not know what is the best modern book on linear programming is. It should have good coverage of the simplex method and a lot of applications. Leontiff systems and other special structured programming problems that lead to modifications of the simplex method are covered in this book and should also be in the "ideal" linear progamming book. Integer programming and other special cases of problems with linear constraints should also be included along with alternative algorithms to the simplex method.
This book is more valuable for historic purposes, as it was Dantzig's first book and the first account of the simplex method by its inventor.
In 1974 I was a graduate student in Operations Research ae Stanford and I took the three quarter mathematical programming course sequence. The first two quarters were taught by George Dantzig out of this book. George was a delightful person to talk to and probably a good thesis advisor and his stories about his graduate school days and the early years at RAND are delightful. However his lectures were disorganized and vague. I found it impossible to learn much from them and the book was not much help either as it too was vague, disjointed and not well organized. Better understanding of the basics of linear programming can be gotten from the fine general books on operations research such as the book by Hillier and Lieberman and the one by Wagner.
I do not know what is the best modern book on linear programming is. It should have good coverage of the simplex method and a lot of applications. Leontiff systems and other special structured programming problems that lead to modifications of the simplex method are covered in this book and should also be in the "ideal" linear progamming book. Integer programming and other special cases of problems with linear constraints should also be included along with alternative algorithms to the simplex method.
This book is more valuable for historic purposes, as it was Dantzig's first book and the first account of the simplex method by its inventor.
1 of 2 people found the following review helpful
Review of Dantzig's book
8 May 2007
Format:Paperback
This softbound newly reprinted edition is clear and light; considering the original version I knew back in 1970's was a thick, heavy hardbound.
The book is a compilation of several authors on linear programming, it includes a table explaining the genesis of linear programming and the programming code for computer calculation.
It is a rich and indispensable book for optimization problems.
The book is a compilation of several authors on linear programming, it includes a table explaining the genesis of linear programming and the programming code for computer calculation.
It is a rich and indispensable book for optimization problems.
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