Book 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.

Customer Reviews (2)

good to have but not to learn from
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 mcuh help either.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.

Review of Dantzig's book
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.

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Book Description
This book provides a comprehensive introduction to linear programming which encompasses all the major topics students will encounter in courses on the subject. The authors aim to teach both the underlying mathematical foundations and how these ideas are implemented in practice. The book illustrates all the concepts with both worked examples and plenty of exercises. In addition, Windows software is provided with the book so that students can try out numerical methods using the examples and exercises and hone their skills in interpreting the results. As a result, this will make an ideal textbook for all those coming to the subject for the first time.
Authors'note: A problem recently found with the software is due to a bug in Formula One, the third party commercial software package that was used for the development of the interface. It occurs when the date currency, etc. format is set to a non-United States version. Please try setting your computer date/currency option to the United States. The new version of Formula One, when ready, will be posted on WWW. ... Read more

Book Description

Book Description
Word count: 2112. ... Read more

Book Description
Linear programming represents one of the major applications of mathematics to business, industry, and economics. It provides a methodology for optimizing an output given that is a linear function of a number of inputs. George Dantzig is widely regarded as the founder of the subject with his invention of the simplex algorithm in the 1940's. This second volume is intended to add to the theory of the items discussed in the first volume. It also includes additional advanced topics such as variants of the simplex method, interior point methods (early and current methods), GUB, decomposition, integer programming, and game theory.Graduate students in the fields of operations research, industrial engineering, and applied mathematics will find this volume of particular interest. ... Read more

Customer Reviews (1)

interesting book
There is an example of piecewise linear convex problem which Iwas looking for. ... Read more