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George Dantzig

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George Dantzig

George Bernard Dantzig
Gerald R. Ford awarded George B. Dantzig at the National Medal of Science Awards Ceremony, 1976
Born (1914-11-08)November 8, 1914
Portland, Oregon
Died May 13, 2005(2005-05-13) (aged 90)
Stanford, California
Citizenship American
Fields Mathematician
Operations research
Computer science

U.S. Air Force Office of Statistical Control
RAND Corporation

University of California, Berkeley
Stanford University
Alma mater Bachelor's degrees - University of Maryland
Master's degree - University of Michigan
Doctor of Philosophy - University of California, Berkeley
Doctoral advisor Jerzy Neyman
Doctoral students
Robert Fourer
Ellis L. Johnson
Thomas Magnanti
Roger J-B Wets
Yinyu Ye
Known for Linear programming
Simplex algorithm
Dantzig-Wolfe decomposition principle
Generalized linear programming
Generalized upper bounding
Max-flow min-cut theorem of networks
Quadratic programming
Complementary pivot algorithms
Linear complementary problem
Stochastic programming
Influences Wassily Leontief
John von Neumann
Marshal K. Wood
Influenced Kenneth J. Arrow
Robert Dorfman
Leonid Hurwicz
Tjalling C. Koopmans
Thomas L. Saaty
Paul Samuelson
Philip Wolfe
Notable awards John von Neumann Theory Prize (1974)
National Medal of Science in Mathematical, Statistical, and Computational Sciences (1975)
Harvey Prize (1985)
Harold Pender Award (1995)
George Bernard Dantzig (November 8, 1914 – May 13, 2005) was an American mathematical scientist who made important contributions to operations research, computer science, economics, and statistics.

Dantzig is known for his development of the simplex algorithm,[1] an algorithm for solving linear programming problems, and his work with linear programming. In statistics, Dantzig solved two open problems in statistical theory, which he had mistaken for homework after arriving late to a lecture of Jerzy Neyman.[2]

Dantzig was the Professor Emeritus of Transportation Sciences and Professor of Operations Research and of Computer Science at Stanford.


  • Biography 1
  • Work 2
    • Mathematical statistics 2.1
    • Linear programming 2.2
  • Publications 3
  • See also 4
  • Notes 5
  • Further reading 6
  • External links 7


Born in

  • Works by or about George Dantzig in libraries (WorldCat catalog)
  •  .
  • Obituaries of George Dantzig
  • Interview with George B. Dantzig: The Father of Linear Programming - The College Mathematical Journal, 1986
  • INFORMS George Dantzig Memorial Website
  • George Dantzig at the Mathematics Genealogy Project

External links

  • Cottle, Richard; Johnson, Ellis; Wets, Roger (March 2007). "George B. Dantzig (1914–2005)". Notices of the American Mathematical Society 54 (3): 344–62. 
  • "Professor George Dantzig: Linear Programming Founder Turns 80", SIAM News, November 1994
  •  .
  • Dantzig, George B. (1990). "The Diet Problem". Interfaces 20 (4): 43–7.  
  • Cottle, Richard W. (2005). "George B. Dantzig: a legendary life in mathematical programming". Mathematical Programming 105 (1): 1–8.  

Further reading

  1. ^ Gass, Saul I. (2011). "Profiles in Operations Research". International Series in Operations Research & Management Science 147. pp. 217–240.  
  2. ^ a b c d e Joe Holley (2005). "Obituaries of George Dantzig". In: Washington Post, May 19, 2005; B06
  3. ^ a b c Richard W. Cottle, B. Curtis Eaves and Michael A. Saunders (2006). "Memorial Resolution: George Bernard Dantzig". Stanford Report, June 7, 2006.
  4. ^ a b c d e f g h Albers, Donald J.;  
  5. ^ National Science Foundation - The President's National Medal of Science
  6. ^ Robert Freund (1994). "Professor George Dantzig: Linear Programming Founder Turns 80". In: SIAM News, November 1994.
  7. ^ a b "The Unsolvable Math Problem". Snopes. June 28, 2011. 
  8. ^ Dantzig, George (1940). "On the non-existence of tests of" Student's" hypothesis having power functions independent of σ". The Annals of Mathematical Statistics. Retrieved 14 October 2014. 
  9. ^ Allende, Sira M.; Bouza, Carlos N. (2005). "Professor George Bernard Dantzig, Life & Legend". Revista Investigación Operacional 26 (3): 205–11. 
  10. ^ Dantzig, George; Wald, Abraham (1951). "On the Fundamental Lemma of Neyman and Pearson". The Annals of Mathematical Statistics. Retrieved 14 October 2014. 
  11. ^ Todd, Michael J. (2011). , by Richard W. Cottle"The Basic George B. Dantzig"Review: . Bull. Amer. Math. Soc. (N.S.) 48 (1): 123–129.  


See also

  • Dantzig, George B. (June 1940). "On the Non-Existence of Tests of 'Student's' Hypothesis Having Power Functions Independent of σ". The Annals of Mathematical Statistics 11 (2): 186–92.  
  • Wood, Marshall K.; Dantzig, George B. (1949). "Programming of Interdependent Activities: I General Discussion". Econometrica 17 (3/4): 193–9.  
  • Dantzig, George B. (1949). "Programming of Interdependent Activities: II Mathematical Model". Econometrica 17 (3): 200–211.  
  • Dantzig, George B. (1955). "Optimal Solution of a Dynamic Leontief Model with Substitution". Econometrica 23 (3): 295–302.  

Articles, a selection:

  • Dantzig, George B. (1960), "General convex objective forms", in  

Book chapters:

  • 1953. Notes on linear programming. RAND Corporation.
  • 1956. Linear inequalities and related systems. With others. Edited by H.W. Kuhn and A.W. Tucker. Princeton University Press.
  • 1963. Linear programming and extensions. Princeton University Press and the RAND Corporation. pdf from RAND
  • 1966. On the continuity of the minimum set of a continuous function. With Jon H. Folkman and Norman Shapiro.
  • 1968. Mathematics of the decision sciences. With Arthur F. Veinott, Jr. Summer Seminar on Applied Mathematics 5th : 1967 : Stanford University. American Mathematical Society.
  • 1969. Lectures in differential equations. A. K. Aziz, general editor. Contributors: George B. Dantzig and others.
  • 1970. Natural gas transmission system optimization. With others.
  • 1973. Compact city; a plan for a liveable urban environment. With Thomas L. Saaty.
  • 1974. Studies in optimization. Edited with B.C. Eaves. Mathematical Association of America.
  • 1985. Mathematical programming : essays in honor of George B. Dantzig. Edited by R.W. Cottle. Mathematical Programming Society.
  • 1997. Linear programming 1: Introduction. G.B.D. and Mukund N. Thapa. Springer-Verlag.
  • 2003. Linear programming 2: Theory and Extensions. G.B.D. and Mukund N. Thapa. Springer-Verlag.
  • 2003. The Basic George B. Dantzig. Edited by Richard W. Cottle. Stanford Business Books, Stanford University Press, Stanford, California.[11]

Books by George Dantzig:


In 1963, Dantzig’s Linear Programming and Extensions was published by Princeton University Press. Rich in insight and coverage of significant topics, the book quickly became “the bible” of linear programming.

Dantzig's original example of finding the best assignment of 70 people to 70 jobs exemplifies the usefulness of linear programming. The computing power required to test all the permutations to select the best assignment is vast; the number of possible configurations exceeds the number of particles in the universe. However, it takes only a moment to find the optimum solution by posing the problem as a linear program and applying the Simplex algorithm. The theory behind linear programming drastically reduces the number of possible optimal solutions that must be checked.

The founders of this subject are Leonid Kantorovich, a Russian mathematician who developed linear programming problems in 1939, Dantzig, who published the simplex method in 1947, and John von Neumann, who developed the theory of the duality in the same year.

Linear programming is a mathematical method for determining a way to achieve the best outcome (such as maximum profit or lowest cost) in a given mathematical model for some list of requirements represented as linear relationships. Linear programming arose as a mathematical model developed during World War II to plan expenditures and returns in order to reduce costs to the army and increase losses to the enemy. It was kept secret until 1947. Postwar, many industries found its use in their daily planning.

Linear programming

This story began to spread, and was used as a motivational lesson demonstrating the power of positive thinking. Over time Dantzig's name was removed and facts were altered, but the basic story persisted in the form of an urban legend, and as an introductory scene in the movie Good Will Hunting.[7]

Years later another researcher, Abraham Wald, was preparing to publish a paper which arrived at a conclusion for the second problem, and included Dantzig as its co-author when he learned of the earlier solution.[4][10]

A year later, when I began to worry about a thesis topic, Neyman just shrugged and told me to wrap the two problems in a binder and he would accept them as my thesis.

Six weeks later, Dantzig received a visit from an excited professor Neyman, who was eager to tell him that the homework problems he had solved were two of the most famous unsolved problems in statistics.[2][4] He had prepared one of Dantzig's solutions for publication in a mathematical journal.[8] As Dantzig told it in a 1986 interview in the College Mathematics Journal:[9]

An event in Dantzig's life became the origin of a famous story in 1939 while he was a graduate student at UC Berkeley. Near the beginning of a class for which Dantzig was late, professor Jerzy Neyman wrote two examples of famously unsolved statistics problems on the blackboard. When Dantzig arrived, he assumed that the two problems were a homework assignment and wrote them down. According to Dantzig, the problems "seemed to be a little harder than usual", but a few days later he handed in completed solutions for the two problems, still believing that they were an assignment that was overdue.[4][7]

Mathematical statistics

Dantzig's seminal work allows the airline industry, for example, to schedule crews and make fleet assignments. Based on his work tools are developed "that shipping companies use to determine how many planes they need and where their delivery trucks should be deployed. The oil industry long has used linear programming in refinery planning, as it determines how much of its raw product should become different grades of gasoline and how much should be used for petroleum-based byproducts. It is used in manufacturing, revenue management, telecommunications, advertising, architecture, circuit design and countless other areas".[2]

Freund wrote further that "through his research in mathematical theory, computation, economic analysis, and applications to industrial problems, [Dantzig] has contributed more than any other researcher to the remarkable development of linear programming".[6]


Dantzig died on May 13, 2005, in his home in Stanford, California, of complications from diabetes and cardiovascular disease. He was 90 years old.[2]

He was a member of the George B. Dantzig Prize, bestowed every three years since 1982 on one or two people who have made a significant impact in the field of mathematical programming.

In 1952 Dantzig joined the mathematics division of the RAND Corporation. By 1960 he became a professor in the Department of Industrial Engineering at UC Berkeley, where he founded and directed the Operations Research Center. In 1966 he joined the Stanford faculty as Professor of Operations Research and of Computer Science. A year later, the Program in Operations Research became a full-fledged department. In 1973 he founded the Systems Optimization Laboratory (SOL) there. On a sabbatical leave that year, he headed the Methodology Group at the International Institute for Applied Systems Analysis (IIASA) in Laxenburg, Austria. Later he became the C. A. Criley Professor of Transportation Sciences at Stanford, and kept going, well beyond his mandatory retirement in 1985.[3]

With the outbreak of U.S. Air Force Office of Statistical Control. In 1946, he returned to Berkeley to complete the requirements of his program and received his Ph.D. that year.[3] Although he had a faculty offer from Berkeley, he returned to the Air Force as mathematical advisor to the comptroller.[4]

George Dantzig earned bachelor's degrees in mathematics and physics from the University of Maryland in 1936, and his master's degree in mathematics from the University of Michigan in 1938. After a two-year period at the Bureau of Labor Statistics, he enrolled in the doctoral program in mathematics at the University of California, Berkeley, where he studied statistics under Jerzy Neyman.

Early in the 1920s the Dantzig family moved from Abraham Seidenberg, who also became a professional mathematician.[4] By the time he reached high school he was already fascinated by geometry, and this interest was further nurtured by his father, challenging him with complicated problems, particularly in projective geometry.[2][4]

, where they settled in Portland, Oregon. United States The Dantzigs immigrated to the [4], after whom Dantzig's brother was named.Henri Poincaré, where Tobias studied mathematics under Paris in Sorbonne University linguist. Dantzig's parents met during their study at the French mathematician and linguist, and his mother, Anja Dantzig (née Ourisson), was a German Baltic, was a Tobias Dantzig His father, [4][3]

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