Linear Programming and Extensions

✍ Scribed by George Dantzig

• Publisher: Princeton University Press
• Year: 1963
• Tongue: English
• Leaves: 650
• Series: Princeton Landmarks in Mathematics and Physics
• Category: Library

✦ Synopsis

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.

✦ Table of 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 Primal-Dual 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. Discrete-Variable 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.pdf