Linear Programming and Extensions
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Part 1
Prefatory Material, Chapters 1-8
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Part 2
Chapters 9-20
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Chapters 21-28, Bibliography, Index
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A basic text in linear programming, the solution of systems of linear equalities. The subjects covered include the concepts, origins and formulations of linear programs, and the simplex method of solution as applied to the price concept, matrix games, and transportation problems. Also included is the background, on convex sets and linear spaces, necessary to forward the discussion on such topics as duality, variants of the simplex method, and the extensions of linear programming to convex programs, to programming under uncertainty, and to certain network, topological, and combinatorial problems that may be couched in the form of linear inequalities with integer-valued variables.
Table of Contents
Chapter 1
The Linear Programming Concept
Chapter 2
Origins and Influences
Chapter 3
Formulating a Linear Programming Model
Chapter 4
Linear Equation and Inequality Systems
Chapter 5
The Simplex Method
Chapter 6
Proof of the Simplex Algorithm and the Duality Theorem
Chapter 7
The Geometry of Linear Programs
Chapter 8
Pivoting, Vector Spaces, Matrices, and Inverses
Chapter 9
The Simplex Method Using Multipliers
Chapter 10
Finiteness of the Simplex Method Under Perturbation
Chapter 11
Variants of the Simplex Algorithm
Chapter 12
The Price Concept in Linear Programming
Chapter 13
Games and Linear Programs
Chapter 14
The Classical Transportation Problem
Chapter 15
Optimal Assignment and Other Distribution Problems
Chapter 16
The Transshipment Problem
Chapter 17
Networks and the Transshipment Problem
Chapter 18
Variables with Upper Bounds
Chapter 19
Maximal Flows in Networks
Chapter 20
The Primal-Dual Method for Transportation Problems
Chapter 21
The Weighted Distribution Problem
Chapter 22
Programs with Variable Coefficients
Chapter 23
A Decomposition Principle for Linear Programs
Chapter 24
Convex Programming
Chapter 25
Uncertainty
Chapter 26
Discrete Variable Extremum Problems
Chapter 27
Stigler's Nutrition Model: An Example of Formulation and Solution
Chapter 28
The Allocation of Aircraft to Routes Under Uncertain Demand
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