Linear Programming 1

1. Front Matter

   Pages i-xxxviii

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2. The Linear Programming Problem

   Pages 1-33

3. Solving Simple Linear Programs

   Pages 35-61

4. The Simplex Method

   Pages 63-111

5. Interior-Point Methods

   Pages 113-127

6. Duality

   Pages 129-143

7. Equivalent Formulations

   Pages 145-170

8. Price Mechanism and Sensitivity Analysis

   Pages 171-203

9. Transportation and Assignment Problem

   Pages 205-252

10. Network Flow Theory

    Pages 253-313

11. Back Matter

    Pages 315-435

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By George B. Dantzig LINEAR PROGRAMMING The Story About How It Began: Some legends, a little about its historical sign- cance, and comments about where its many mathematical programming extensions may be headed. Industrial production, the ?ow of resources in the economy, the exertion of military e?ort in a war, the management of ?nances—all require the coordination of interrelated activities. What these complex undertakings share in common is the task of constructing a statement of actions to be performed, their timing and quantity(calledaprogramorschedule), that, ifimplemented, wouldmovethesystem from a given initial status as much as possible towards some de?ned goal. While di?erences may exist in the goals to be achieved, the particular processes, and the magnitudes of e?ort involved, when modeled in mathematical terms these seemingly disparate systems often have a remarkably similar mathematical str- ture. The computational task is then to devise for these systems an algorithm for choosing the best schedule of actions from among the possible alternatives. The observation, in particular, that a number of economic, industrial, ?nancial, and military systems can be modeled (or reasonably approximated) by mathem- ical systems of linear inequalities and equations has given rise to the development of the linear programming ?eld.

• calculus
• duality
• linear optimization
• programming
• sensitivity analysis
• matrix theory

• Department of Operations Research, Stanford University, Stanford, USA

  George B. Dantzig, Mukund N. Thapa

• Stanford Business Software, Inc., Mountain View

  Mukund N. Thapa

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