Linear Programming and Extensions

by George Bernard Dantzig


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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


  • 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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