Linear Programming 1: Introduction

by George Bernard Dantzig, Mukund N. Thapa

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."

473 pages, Paperback

First published January 1, 1997

Reviews

[Greg · Rating 5 out of 5]

This is one of the best written math books I have ever encountered. Dantzig was the inventor of the simplex algorithm for doing linear programming. His book is so well written with clear explanations and just enough theory to learn how the methods for solving various families of problems. Were I teaching a course in linear programming, it would be the book I would use.