Author 
Dantzig, George B. (George Bernard), 19142005.

Series 
Princeton Landmarks in Mathematics and Physics

Subject 
Linear programming.


Mathematical optimization.

Description 
1 online resource 
Note 
Print version record. 
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 PrimalDual 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. DiscreteVariable 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 
Summary 
In realworld 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. 
Note 
In English. 
ISBN 
1400884179 (electronic bk.) 

9781400884179 (electronic bk.) 

0691059136 
ISBN/ISSN 
10.1515/9781400884179 
OCLC # 
953848356 
