简介
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.
目录
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
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