George Dantzig and History of Linear Programming

George B. Dantzig and History of Linear Programming

Also, History of Optimal allocation of Resources  and Optimization

Key People

  • Tjalling C Koopmans
  • George B Dantzig
  • Leonid V Kantorovich
  • John Von Neumann
  • Wassily Leontief

 

Koopmans and Kantorovich got the 1975 Nobel prize for their work in optimal allocation of resources.

 

From Linear Programming  The Story about How It Began:

Some legends, a little about its historical significance, and comments about where its many mathematical programming extensions may be headed

 

Linear programming can be viewed as a part of a great revolutionary development which has given mankind the ability to state general goals and to lay out a path of detailed decisions to take in order to ‘best’ achieve its goals when faced with practical situations of great complexity. Our tools for doing this are ways to formulate real-world problems in detailed mathematical terms (models), techniques for solving the models (algorithms), and engines for executing the steps of algorithms (computers and software).

This ability began in 1947, shortly after World War II, and has been keeping pace ever since with the extraordinary growth of computing power. So rapid has been the advance in decision science that few remember the contributions of the great pioneers that started it all. Some of their names are von Neumann, Kantorovich, Leontief, and Koopmans. The first two were famous mathematicians. The last three received the Nobel Prize in economics for their work.

In the years from the time when it was first proposed in 1947 by the author (in connection with the planning activities of the military), linear programmming and its many extensions have come into wide use. In academic circles decision scientists (operations researchers and management scientists), as well as numerical analysts, mathematicians, and economists have written hundreds of books and an uncountable number of articles on the subject.

 

Key Sources of Research:

 

George B. Dantzig (1914–2005)

Richard Cottle, Ellis Johnson, and Roger Wets

 

http://gymportalen.dk/sites/lru.dk/files/lru/docs/Projekt_7-1DantzigAMS.pdf

 

Linear Programming and Its Extensions

G Dantzig

1963

http://www.rand.org/content/dam/rand/pubs/reports/2007/R366part1.pdf

 

Linear Programming: Theory and its extensions Part 2

G Dantzig and M Thapa

http://ruangbacafmipa.staff.ub.ac.id/files/2012/02/ebooksclub.org__Linear_Programming_2__Theory_and_Extensions.pdf

 

Linear Programming: Introduction  Part 1

G Dantzig and M Thapa

https://linux.ime.usp.br/~felipecp/linear_programming_vol1-dantzig_thapa.pdf

 

LINEAR PROGRAMMING

 

GEORGE B. DANTZIG

 

http://bioinfo.ict.ac.cn/~dbu/AlgorithmCourses/Lectures/Dantzig2002.pdf

 

George B. Dantzig 1914–2005

By J. Dupaˇcov ́a and D.P. Morton

 

http://www.me.utexas.edu/~orie/morton_journal/dupacova_morton_05.pdf

 

Linear Programming

The Story about How It Began:
Some legends, a little about its historical significance, and comments about where its many mathematical programming extensions may be headed

George B. Dantzig

 

http://www.ece.northwestern.edu/~morales/PSfiles/dantzig.pdf

 

Linear Programming under uncertainty

G Dantzig

1955

http://prof.if.ktu.lt/~jonas.mockus/dantzig.pdf

 

ORIGINS OF THE SIMPLEX METHOD

by

George B. Dantzig

TECHNICAL REPORT SOL 87-5

May 1987

 

http://www.dtic.mil/dtic/tr/fulltext/u2/a182708.pdf

 

A Brief History of Linear and Mixed-Integer Programming Computation

Robert E. Bixby

2010

 

https://www.math.uni-bielefeld.de/documenta/vol-ismp/25_bixby-robert.pdf

 

Biography of George Bernard Dantzig

 

http://stochastikon.no-ip.org:8080/encyclopedia/en/dantzigGeorge.pdf

 

Activity Analysis of Production and Allocation

Cowles Commision Research in Economics Monograph 13

T Koopmans

1951

http://cowles.yale.edu/sites/default/files/files/pub/mon/m13-all.pdf

 

THE FIRST LINEAR-PROGRAMMING SHOPPE

SAUL I. GASS

 

http://academic.udayton.edu/charlesebeling/MSC521/Downloads/LP%20Gass.pdf

 

Special Issue of Discrete Optimization

In memory of George Dantzig

2008

http://www.sciencedirect.com/science/journal/15725286/5/2

 

George B. Dantzig and systems optimization

Philip E. Gilla, Walter Murray, Michael A. Saunders, John A. Tomlin, Margaret H. Wright,

Discrete Optimization 5 (2008) 151–158

http://www.sciencedirect.com/science/article/pii/S1572528607000321

 

George Dantzig in the development of economic analysis

Kenneth J. Arrow

http://www.sciencedirect.com/science/article/pii/S1572528607000436

 

Solving Real-World Linear Programs: A Decade and More of Progress.

Robert E. Bixby,

(2002)

Operations Research 50(1):3-15. http://dx.doi.org/10.1287/opre.50.1.3.17780

 

 

”On the Shoulders of Giants”
A brief excursion into the history of mathematical programming 

R. Tichatschke

 

http://www.math.u-szeged.hu/~hajnal/courses/MSc_Optimalizalas/Tichaschke.pdf

 

Is the constancy of technical coefficients

a matter of tolerance ?

A methodological inquiry
about the justification of a controversial assumption 1936-1952

Amanar Akhabbar

 

https://www.iioa.org/conferences/15th/pdf/akhabbar.pdf

 

Mathematical Methods of Organizing and Planning Production

Author(s): L. V. Kantorovich

Source: Management Science, Vol. 6, No. 4 (Jul., 1960), pp. 366-422

 

http://www.feg.unesp.br/~mapereira/PL_arquivos/ManSci-v6_n4-366_422-1960.pdf

 

Wassily W. Leontief, Leonid V. Kantorovich, Tjalling C. Koopmans and J. Richard N. Stone
Pioneering Papers of the Nobel Memorial Laureates in Economics series

Edited by Howard R. Vane,  Chris Mulhearn,

Publication Date: 2009
ISBN: 978 1 84720 840 8

http://www.e-elgar.com/shop/wassily-w-leontief-leonid-v-kantorovich-tjalling-c-koopmans-and-j-richard-n-stone?___website=uk_warehouse

 

Advertisements

Author: Mayank Chaturvedi

You can contact me using this email mchatur at the rate of AOL.COM. My professional profile is on Linkedin.com.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s