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# George Dantzig

George Bernard Dantzig (Nov 8 1914May 13 2005) was an American mathematician, and the Professor Emeritus of Transportation Sciences and Professor of Operations Research and of Computer Science at Stanford.

George Dantzig is known as the father of linear programming and as the inventor of the "simplex method," an algorithm for solving linear programming problems.

## Biography

Born on November 8, 1914 in Portland, Oregon, George Dantzig was given the middle name “Bernard” as an expression of his parents’ hope that he would become a writer. His father, Tobias Dantzig, was a Russian mathematician who had studied with Henri Poincaré in Paris. Tobias married a fellow Sorbonne University student, Anja Ourisson, and the couple immigrated to the United States. In the early 1920s, the Dantzig family moved to Baltimore and then to Washington, where Anja Dantzig became a linguist at the Library of Congress and her husband taught mathematics at the University of Maryland, College Park. George attended Powell Junior High School and Central High School, where he was fascinated by geometry. His father nurtured his interest by challenging him with complex geometry problems.

George Dantzig earned bachelor's degrees in mathematics and physics from the University of Maryland in 1936, 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 studying statistics under mathematician Jerzy Neyman. With the outbreak of World War II, George took a leave of absence from the doctoral program at Berkeley to join the 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.

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.

He was a member of the National Academy of Sciences, the National Academy of Engineering, and the American Academy of Arts and Sciences. And he was the recipient of many honors, including the first John von Neumann Theory Prize in 1974, the National Medal of Science in 1975, an honorary doctorate from the University of Maryland, College Park in 1976. The Mathematical Programming Society honored Dantzig by creating 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.

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

## Work

Dantzig is generally regarded as one of the three founders of linear programming, along with John von Neumann and Leonid Kantorovich. Through his research in mathematical theory, computation, economic analysis, and applications to industrial problems, he has contributed more than any other researcher to the remarkable development of linear programming.

Dantzig's seminal work allows the airline industry, for example, to schedule crews and make fleet assignments. It's the tool 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's used in manufacturing, revenue management, telecommunications, advertising, architecture, circuit design and countless other areas.

"In retrospect," Dantzig wrote in the 1991 history book, "it is interesting to note that the original problem that started my research is still outstanding -- namely the problem of planning or scheduling dynamically over time, particularly planning dynamically under uncertainty. If such a problem could be successfully solved it could eventually through better planning contribute to the well-being and stability of the world."

### Mathematical statistics

An event in Dantzig's life became the origin of a famous urban legend 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 two, still believing that they were an assignment that was overdue.

Six weeks later, Dantzig received a visit from an excited professor Neyman, eager to tell him that the homework problems he had solved were two of the most famous unsolved problems in statistics. He had prepared one of Dantzig's solutions for publication in a mathematical journal. 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.

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.

### Linear programming

In 1946, as mathematical adviser to the U.S. Air Force Comptroller, he was challenged by his Pentagon colleagues to see what he could do to mechanize the planning process, "to more rapidly compute a time-staged deployment, training and logistical supply program." In those pre-electronic computer days, mechanization meant using analog devices or punch-card machines. "Program" at that time was a military term that referred not to the instruction used by a computer to solve problems, which were then called "codes," but rather to plans or proposed schedules for training, logistical supply, or deployment of combat units. The somewhat confusing name "linear programming," Dantzig explained in the book, is based on this military definition of "program."

Tasked with the mechanization of planning procedures to support the time-staged deployment training and supply activities, in 1947 George Dantzig formulated the linear programming problem as a mathematical model for the planning problem and devised the simplex method for its solution. These achievements led to his titles as the "father of linear programming" and the "inventor of the simplex method." At the RAND Corporation in the 1950s Dantzig further enhanced the computational strength of linear programming and found further extensions of its applicability. At RAND he wrote a long series of research memoranda entitled “Notes on Linear Programming”, which ultimately became material for his classic text/reference Linear Programming and Extensions.

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.

## 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.
• 1959. Linear programming and extensions. Princeton University Press.
• 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.
• 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.
• 1985. Mathematical programming : essays in honor of George B. Dantzig. Edited by R.W. Cottle.
• 1997. Linear programming. With Mukund N. Thapa.
• 2003. Basic George B. Dantzig. Edited by Richard W. Cottle.

Articles, a selection:

• 1940. "On the non-existence of tests of "Student's" hypothesis having power functions independent of $sigma$". In: Annals of Mathematical Statistics, Volume 11, number 2, pp 186-192.