Linear Programming and Extensions
1st Edition
Published on 10. August 2016
656 pages
978-1-4008-8417-9 (ISBN)
Description
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.
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.
More details
Other editions
Additional editions
George B. Dantzig
Linear Programming and Extensions
Book
08/1998
Princeton University Press
€115.80
Article not available at the moment
George B. Dantzig
Linear Programming and Extensions
Book
09/1963
Princeton University Press
€113.89
Article exhausted; check different version
Person
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.
Content
Preface
Ch. 1 The Linear Programming Concept
Ch. 2 Origins and Influences
Ch. 3 Formulating a Linear Programming Model
Ch. 4 Linear Equation and Inequality Systems
Ch. 5 The Simplex Method
Ch. 6 Proof of the Simplex Algorithm and the Duality Theorem
Ch. 7 The Geometry of Linear Programs
Ch. 8 Pivoting, Vector Spaces, Matrices, and Inverses
Ch. 9 The Simplex Method Using Multipliers
Ch. 10 Finiteness of the Simplex Method Under Perturbation
Ch. 11 Variants of the Simplex Algorithm
Ch. 12 The Price Concept in Linear Programming
Ch. 13 Games and Linear Programs
Ch. 14 The Classical Transportation Problem
Ch. 15 Optimal Assignment and Other Distribution Problems
Ch. 16 The Transshipment Problem
Ch. 17 Networks and the Transshipment Problem
Ch. 18 Variables with Upper Bounds
Ch. 19 Maximal Flows in Networks
Ch. 20 The Primal-Dual Method for Transportation Problems
Ch. 21 The Weighted Distribution Problem
Ch. 22 Programs with Variable Coefficients
Ch. 23 A Decomposition Principle for Linear Programs
Ch. 24 Convex Programming
Ch. 25 Uncertainty
Ch. 26 Discrete Variable Extremum Problems
Ch. 27 Stigler's Nutrition Model: An Example of Formulation and Solution
Ch. 28 The Allocation of Aircraft to Routes Under Uncertain Demand
Bibliography
Index
Ch. 1 The Linear Programming Concept
Ch. 2 Origins and Influences
Ch. 3 Formulating a Linear Programming Model
Ch. 4 Linear Equation and Inequality Systems
Ch. 5 The Simplex Method
Ch. 6 Proof of the Simplex Algorithm and the Duality Theorem
Ch. 7 The Geometry of Linear Programs
Ch. 8 Pivoting, Vector Spaces, Matrices, and Inverses
Ch. 9 The Simplex Method Using Multipliers
Ch. 10 Finiteness of the Simplex Method Under Perturbation
Ch. 11 Variants of the Simplex Algorithm
Ch. 12 The Price Concept in Linear Programming
Ch. 13 Games and Linear Programs
Ch. 14 The Classical Transportation Problem
Ch. 15 Optimal Assignment and Other Distribution Problems
Ch. 16 The Transshipment Problem
Ch. 17 Networks and the Transshipment Problem
Ch. 18 Variables with Upper Bounds
Ch. 19 Maximal Flows in Networks
Ch. 20 The Primal-Dual Method for Transportation Problems
Ch. 21 The Weighted Distribution Problem
Ch. 22 Programs with Variable Coefficients
Ch. 23 A Decomposition Principle for Linear Programs
Ch. 24 Convex Programming
Ch. 25 Uncertainty
Ch. 26 Discrete Variable Extremum Problems
Ch. 27 Stigler's Nutrition Model: An Example of Formulation and Solution
Ch. 28 The Allocation of Aircraft to Routes Under Uncertain Demand
Bibliography
Index
