Linear Programming and Extensions

George B. Dantzig

ISBN 10: 0691059136 / ISBN 13: 9780691059136

Published by Princeton University Press, US, 1998

About this Item

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.

Seller Inventory # LU-9780691059136

Bibliographic Details

• Title: Linear Programming and Extensions
• Publisher: Princeton University Press, US
• Publication Date: 1998
• Language: English
• ISBN 10: 0691059136
• ISBN 13: 9780691059136
• Binding: Paperback
• Condition: New
• Weight: 879 grams

About this title

Synopsis

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.

About the Author

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.