G. B. Dantzig
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George Bernard Dantzig (; November 8, 1914 – May 13, 2005) was an American mathematical scientist who made contributions to
industrial engineering Industrial engineering (IE) is concerned with the design, improvement and installation of integrated systems of people, materials, information, equipment and energy. It draws upon specialized knowledge and skill in the mathematical, physical, an ...
,
operations research Operations research () (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the initialism OR, is a branch of applied mathematics that deals with the development and application of analytical methods to improve management and ...
,
computer science Computer science is the study of computation, information, and automation. Computer science spans Theoretical computer science, theoretical disciplines (such as algorithms, theory of computation, and information theory) to Applied science, ...
,
economics Economics () is a behavioral science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services. Economics focuses on the behaviour and interac ...
, and
statistics Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...
. Dantzig is known for his development of the
simplex algorithm In mathematical optimization, Dantzig's simplex algorithm (or simplex method) is a popular algorithm for linear programming. The name of the algorithm is derived from the concept of a simplex and was suggested by T. S. Motzkin. Simplices are ...
, an algorithm for solving
linear programming Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements and objective are represented by linear function#As a polynomia ...
problems, and for his other work with linear programming. In
statistics Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...
, Dantzig solved two
open problem In science and mathematics, an open problem or an open question is a known problem which can be accurately stated, and which is assumed to have an objective and verifiable solution, but which has not yet been solved (i.e., no solution for it is kno ...
s in
statistical theory The theory of statistics provides a basis for the whole range of techniques, in both study design and data analysis, that are used within applications of statistics. The theory covers approaches to statistical-decision problems and to statistica ...
, which he had mistaken for homework after arriving late to a lecture by Jerzy Spława-Neyman.Joe Holley (2005)
"Obituaries of George Dantzig"
In: ''Washington Post'', May 19, 2005; B06
At his death, Dantzig was professor emeritus of Transportation Sciences and Professor of Operations Research and of Computer Science at
Stanford University Leland Stanford Junior University, commonly referred to as Stanford University, is a Private university, private research university in Stanford, California, United States. It was founded in 1885 by railroad magnate Leland Stanford (the eighth ...
.


Early life

Born in
Portland, Oregon Portland ( ) is the List of cities in Oregon, most populous city in the U.S. state of Oregon, located in the Pacific Northwest region. Situated close to northwest Oregon at the confluence of the Willamette River, Willamette and Columbia River, ...
, George Bernard Dantzig was named after
George Bernard Shaw George Bernard Shaw (26 July 1856 – 2 November 1950), known at his insistence as Bernard Shaw, was an Irish playwright, critic, polemicist and political activist. His influence on Western theatre, culture and politics extended from the 188 ...
, the Irish writer.Richard W. Cottle, B. Curtis Eaves and Michael A. Saunders (2006)
"Memorial Resolution: George Bernard Dantzig"
. Stanford Report, June 7, 2006.
He was born to
Jewish Jews (, , ), or the Jewish people, are an ethnoreligious group and nation, originating from the Israelites of History of ancient Israel and Judah, ancient Israel and Judah. They also traditionally adhere to Judaism. Jewish ethnicity, rel ...
parents; his father,
Tobias Dantzig Tobias Dantzig (; February 19, 1884 – August 9, 1956) was a Russian-American mathematician, the father of George Dantzig, and the author of '' Number: The Language of Science (A critical survey written for the cultured non-mathematician)'' (1930) ...
, was a mathematician and linguist, and his mother, Anja Dantzig (née Ourisson), was a Russian-born linguist of
French French may refer to: * Something of, from, or related to France ** French language, which originated in France ** French people, a nation and ethnic group ** French cuisine, cooking traditions and practices Arts and media * The French (band), ...
-
Lithuanian Lithuanian may refer to: * Something of, from, or related to Lithuania, a country in the Baltic region in northern Europe ** Lithuanian language ** Lithuanians, a Baltic ethnic group, native to Lithuania and the immediate geographical region ** L ...
origin. Dantzig's parents met during their study at the
University of Paris The University of Paris (), known Metonymy, metonymically as the Sorbonne (), was the leading university in Paris, France, from 1150 to 1970, except for 1793–1806 during the French Revolution. Emerging around 1150 as a corporation associated wit ...
, where Tobias studied mathematics under
Henri Poincaré Jules Henri Poincaré (, ; ; 29 April 185417 July 1912) was a French mathematician, Theoretical physics, theoretical physicist, engineer, and philosophy of science, philosopher of science. He is often described as a polymath, and in mathemati ...
, after whom Dantzig's brother was named. The Dantzigs emigrated to the United States, where they settled in Portland, Oregon. Early in the 1920s the Dantzig family moved from
Baltimore Baltimore is the most populous city in the U.S. state of Maryland. With a population of 585,708 at the 2020 census and estimated at 568,271 in 2024, it is the 30th-most populous U.S. city. The Baltimore metropolitan area is the 20th-large ...
to
Washington, D.C. Washington, D.C., formally the District of Columbia and commonly known as Washington or D.C., is the capital city and federal district of the United States. The city is on the Potomac River, across from Virginia, and shares land borders with ...
His mother became a linguist at the
Library of Congress The Library of Congress (LOC) is a research library in Washington, D.C., serving as the library and research service for the United States Congress and the ''de facto'' national library of the United States. It also administers Copyright law o ...
, and his father became a math tutor at the
University of Maryland, College Park The University of Maryland, College Park (University of Maryland, UMD, or simply Maryland) is a public university, public Land-grant university, land-grant research university in College Park, Maryland, United States. Founded in 1856, UMD i ...
.


Education

Dantzig attended Powell Junior High School and Central High School. 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 In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that, compared to elementary Euclidean geometry, projective geometry has a different setting (''p ...
. George Dantzig received his B.S. from
University of Maryland The University of Maryland, College Park (University of Maryland, UMD, or simply Maryland) is a public land-grant research university in College Park, Maryland, United States. Founded in 1856, UMD is the flagship institution of the Univ ...
in 1936 in mathematics and physics. He earned his master's degree in mathematics from the
University of Michigan The University of Michigan (U-M, U of M, or Michigan) is a public university, public research university in Ann Arbor, Michigan, United States. Founded in 1817, it is the oldest institution of higher education in the state. The University of Mi ...
in 1937. After working as a junior statistician at the Bureau of Labor Statistics from 1937 to 1939, he enrolled in the doctoral program in mathematics at the
University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California), is a Public university, public Land-grant university, land-grant research university in Berkeley, California, United States. Founded in 1868 and named after t ...
, where he studied statistics under Jerzy Spława-Neyman. During his study in 1939, Dantzig solved two unproven statistical theorems due to a misunderstanding. Near the beginning of a class, Professor Spława-Neyman wrote two problems on the blackboard. Dantzig arrived late and assumed that they were a homework assignment. According to Dantzig, they "seemed to be a little harder than usual", but a few days later he handed in completed solutions for both problems, still believing that they were an assignment that was overdue. Six weeks later, an excited Spława-Neyman eagerly told him that the "homework" problems he had solved were two of the most famous unsolved problems in
statistics Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...
. He had prepared one of Dantzig's solutions for publication in a mathematical journal. This story began to spread and was used as a motivational lesson demonstrating the power of positive thinking. Over time, some facts were altered, but the basic story persisted in the form of an
urban legend Urban legend (sometimes modern legend, urban myth, or simply legend) is a genre of folklore concerning stories about an unusual (usually scary) or humorous event that many people believe to be true but largely are not. These legends can be e ...
and as an introductory scene in the movie ''
Good Will Hunting ''Good Will Hunting'' is a 1997 American drama film directed by Gus Van Sant and written by Ben Affleck and Matt Damon. It stars Robin Williams, Damon, Affleck, Stellan Skarsgård and Minnie Driver. The film tells the story of janitor Will Hunt ...
''. Dantzig recalled in a 1986 interview in the ''
College Mathematics Journal The ''College Mathematics Journal'' is an expository magazine aimed at teachers of college mathematics, particularly those teaching the first two years. It is published by Taylor & Francis on behalf of the Mathematical Association of America and i ...
'', "A year later, when I began to worry about a thesis topic, Spława-Neyman just shrugged and told me to wrap the two problems in a binder and he would accept them as my thesis." Years later, another researcher,
Abraham Wald Abraham Wald (; ; , ;  – ) was a Hungarian and American mathematician and statistician who contributed to decision theory, geometry and econometrics, and founded the field of sequential analysis. One of his well-known statistical works was ...
, was preparing to publish a paper where he had arrived at a conclusion for the second problem when he learned of Dantzig's earlier solution. When Dantzig suggested publishing jointly, Wald simply added Dantzig's name as co-author.


Career

With the outbreak of
World War II World War II or the Second World War (1 September 1939 – 2 September 1945) was a World war, global conflict between two coalitions: the Allies of World War II, Allies and the Axis powers. World War II by country, Nearly all of the wo ...
, Dantzig took a leave of absence from the doctoral program at Berkeley to work as a civilian for the
United States Army Air Forces The United States Army Air Forces (USAAF or AAF) was the major land-based aerial warfare service component of the United States Army and ''de facto'' aerial warfare service branch of the United States during and immediately after World War II ...
. From 1941 to 1946, he became the head of the combat analysis branch of the Headquarters Statistical Control for the Army Air Forces. In 1946, he returned to Berkeley to complete the requirements of his program and received his
PhD A Doctor of Philosophy (PhD, DPhil; or ) is a terminal degree that usually denotes the highest level of academic achievement in a given discipline and is awarded following a course of graduate study and original research. The name of the deg ...
that year. Although he had a faculty offer from Berkeley, he returned to the Air Force as mathematical advisor to the
comptroller A comptroller (pronounced either the same as ''controller'' or as ) is a management-level position responsible for supervising the quality of accountancy, accounting and financial reporting of an organization. A financial comptroller is a senior- ...
. In 1952, Dantzig joined the mathematics division of the
RAND Corporation The RAND Corporation, doing business as RAND, is an American nonprofit global policy think tank, research institute, and public sector consulting firm. RAND engages in research and development (R&D) in several fields and industries. Since the ...
. 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 managed the Methodology Group at the
International Institute for Applied Systems Analysis The International Institute for Applied Systems Analysis (IIASA) is an independent International research institute located in Laxenburg, near Vienna in Austria, founded as an East-West scientific cooperation initiative during the Cold War. Th ...
(IIASA) in Laxenburg, Austria. Later, he became the C. A. Criley Professor of Transportation Sciences at
Stanford University Leland Stanford Junior University, commonly referred to as Stanford University, is a Private university, private research university in Stanford, California, United States. It was founded in 1885 by railroad magnate Leland Stanford (the eighth ...
. He was a member of the
National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, NGO, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the ...
, the
National Academy of Engineering The National Academy of Engineering (NAE) is an American Nonprofit organization, nonprofit, NGO, non-governmental organization. It is part of the National Academies of Sciences, Engineering, and Medicine (NASEM), along with the National Academ ...
, and the
American Academy of Arts and Sciences The American Academy of Arts and Sciences (The Academy) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and other ...
. Dantzig was the recipient of many honors, including the first
John von Neumann Theory Prize The John von Neumann Theory Prize of the Institute for Operations Research and the Management Sciences (INFORMS) is awarded annually to an individual (or sometimes a group) who has made fundamental and sustained contributions to theory in opera ...
in 1974, the
National Medal of Science The National Medal of Science is an honor bestowed by the President of the United States to individuals in science and engineering who have made important contributions to the advancement of knowledge in the fields of behavioral science, behavior ...
in 1975, and an
honorary doctorate An honorary degree is an academic degree for which a university (or other degree-awarding institution) has waived all of the usual requirements. It is also known by the Latin phrases ''honoris causa'' ("for the sake of the honour") or '' ad hon ...
from the
University of Maryland, College Park The University of Maryland, College Park (University of Maryland, UMD, or simply Maryland) is a public university, public Land-grant university, land-grant research university in College Park, Maryland, United States. Founded in 1856, UMD i ...
in 1976. The
Mathematical Programming Society The Mathematical Optimization Society (MOS), known as the Mathematical Programming Society (MPS) until 2010,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. He was elected to the 2002 class of
Fellow A fellow is a title and form of address for distinguished, learned, or skilled individuals in academia, medicine, research, and industry. The exact meaning of the term differs in each field. In learned society, learned or professional society, p ...
s of the
Institute for Operations Research and the Management Sciences The Institute for Operations Research and the Management Sciences (INFORMS) is an international society for practitioners in the fields of operations research Operations research () (U.S. Air Force Specialty Code: Operations Analysis), often s ...
.


Research

Freund wrote further that "through his research in mathematical theory, computation, economic analysis, and applications to industrial problems, Dantzig contributed more than any other researcher to the remarkable development of linear programming".Robert Freund (1994)
"Professor George Dantzig: Linear Programming Founder Turns 80"
. In: ''SIAM News'', November 1994.
Dantzig's 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".


Linear programming

Linear programming Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements and objective are represented by linear function#As a polynomia ...
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 A mathematical model is an abstract and concrete, abstract description of a concrete system using mathematics, mathematical concepts and language of mathematics, language. The process of developing a mathematical model is termed ''mathematical m ...
for some list of requirements represented as linear relationships. Linear programming arose as a mathematical model developed during
World War II World War II or the Second World War (1 September 1939 – 2 September 1945) was a World war, global conflict between two coalitions: the Allies of World War II, Allies and the Axis powers. World War II by country, Nearly all of the wo ...
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. The founders of this subject are
Leonid Kantorovich Leonid Vitalyevich Kantorovich (, ; 19 January 19127 April 1986) was a Soviet mathematician and economist, known for his theory and development of techniques for the optimal allocation of resources. He is regarded as the founder of linear programm ...
, a Russian mathematician who developed linear programming problems in 1939, Dantzig, who published the
simplex method In mathematical optimization, Dantzig's simplex algorithm (or simplex method) is a popular algorithm for linear programming. The name of the algorithm is derived from the concept of a simplex and was suggested by T. S. Motzkin. Simplices are n ...
in 1947, and
John von Neumann John von Neumann ( ; ; December 28, 1903 – February 8, 1957) was a Hungarian and American mathematician, physicist, computer scientist and engineer. Von Neumann had perhaps the widest coverage of any mathematician of his time, in ...
, who developed the theory of the duality in the same year. Dantzig was asked to work out a method the Air Force could use to improve their planning process. This led to his original example of finding the best assignment of 70 people to 70 jobs, showing the usefulness of
linear programming Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements and objective are represented by linear function#As a polynomia ...
. 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. In 1963, Dantzig's ''Linear Programming and Extensions'' was published by
Princeton University Press Princeton University Press is an independent publisher with close connections to Princeton University. Its mission is to disseminate scholarship within academia and society at large. The press was founded by Whitney Darrow, with the financial ...
. The book quickly became a standard text in linear programming.


Personal life

Dantzig married Anne S. Shmuner in 1936. He died on May 13, 2005, in his home in
Stanford, California Stanford is a census-designated place (CDP) in the northwest corner of Santa Clara County, California, United States. It is the home of Stanford University, after which it was named. The CDP's population was 21,150 at the United States Census, ...
, of complications from
diabetes Diabetes mellitus, commonly known as diabetes, is a group of common endocrine diseases characterized by sustained high blood sugar levels. Diabetes is due to either the pancreas not producing enough of the hormone insulin, or the cells of th ...
and
cardiovascular disease Cardiovascular disease (CVD) is any disease involving the heart or blood vessels. CVDs constitute a class of diseases that includes: coronary artery diseases (e.g. angina, heart attack), heart failure, hypertensive heart disease, rheumati ...
. He was 90 years old. His children were named David, Paul, and Jessica.


Presidential award

On October 18, 1976, President
Gerald Ford Gerald Rudolph Ford Jr. (born Leslie Lynch King Jr.; July 14, 1913December 26, 2006) was the 38th president of the United States, serving from 1974 to 1977. A member of the Republican Party (United States), Republican Party, Ford assumed the p ...
presented Dantzig with the
National Medal of Science The National Medal of Science is an honor bestowed by the President of the United States to individuals in science and engineering who have made important contributions to the advancement of knowledge in the fields of behavioral science, behavior ...
. The award was given "For inventing linear programming and discovering methods that led to wide-scale scientific and technical applications to important problems in logistics, scheduling, and network optimization, and to the use of computers in making efficient use of the mathematical theory."


Publications

Books by George Dantzig: * 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 The compact city or city of short distances is an urban planning and urban design concept, which promotes relatively high residential density with mixed land uses. It is based on an efficient public transport system and has an urban layout which ...
; 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. Book chapters: * Articles, a selection: * * * *


See also

*
Dantzig–Wolfe decomposition Dantzig–Wolfe decomposition is an algorithm for solving linear programming problems with special structure. It was originally developed by George Dantzig and Philip Wolfe and initially published in 1960. Many texts on linear programming have s ...
*
Knapsack problem The knapsack problem is the following problem in combinatorial optimization: :''Given a set of items, each with a weight and a value, determine which items to include in the collection so that the total weight is less than or equal to a given lim ...
*
Maximum flow problem In Optimization (mathematics), optimization theory, maximum flow problems involve finding a feasible flow through a flow network that obtains the maximum possible flow rate. The maximum flow problem can be seen as a special case of more complex ...
*
Optimization (mathematics) Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives. It is generally divided into two subfiel ...
*
Travelling salesman problem In the Computational complexity theory, theory of computational complexity, the travelling salesman problem (TSP) asks the following question: "Given a list of cities and the distances between each pair of cities, what is the shortest possible ...
*
Shadow price A shadow price is the monetary value assigned to an abstract or intangible commodity which is not traded in the marketplace. This often takes the form of an externality. Shadow prices are also known as the recalculation of known market prices in ...
*
List of Jewish American mathematicians This is a list of notable Jewish American mathematicians. For other Jewish Americans, see Lists of Jewish Americans. * Abraham Adrian Albert (1905-1972), abstract algebra * Kenneth Appel (1932-2013), four-color problem * Lipman Bers (1914-19 ...


Notes


Further reading

*
"Professor George Dantzig: Linear Programming Founder Turns 80"
, ''
SIAM Thailand, officially the Kingdom of Thailand and historically known as Siam (the official name until 1939), is a country in Southeast Asia on the Mainland Southeast Asia, Indochinese Peninsula. With a population of almost 66 million, it spa ...
News'', November 1994 * * *


External links

*
Tributes to George Dantzig and Leonid KhachiyanInterview with George B. Dantzig: The Father of Linear Programming – The College Mathematical Journal, 1986

INFORMS George Dantzig Memorial Website
*
Biography of George Dantzig
from the Institute for Operations Research and the Management Sciences (INFORMS) * An Interview with Nobel Laureate Harry M. Markowit

{{DEFAULTSORT:Dantzig, George 1914 births 2005 deaths 20th-century American mathematicians 21st-century American mathematicians American computer scientists American operations researchers American people of Baltic German descent American people of French-Jewish descent American statisticians American systems scientists Deaths from diabetes in California Fellows of the Econometric Society General equilibrium theorists Jewish American scientists John von Neumann Theory Prize winners Mathematical economists Mathematicians from Oregon Fellows of the Institute for Operations Research and the Management Sciences Members of the United States National Academy of Sciences National Medal of Science laureates Numerical analysts People from Stanford, California RAND Corporation people Stanford University School of Engineering faculty United States Air Force civilians University of California, Berkeley alumni UC Berkeley College of Engineering faculty University of Maryland, College Park alumni University of Michigan College of Literature, Science, and the Arts alumni United States Army Air Forces personnel of World War II United States Army civilians 20th-century American Jews 21st-century American Jews Scientists from Portland, Oregon