George Dantzig: The Architect of Linear Programming and Its Enduring Legacy
George Bernard Dantzig, a name synonymous with innovation in operations research and management science, left an indelible mark on the world through his pioneering work in linear programming. His contributions revolutionized decision-making processes across diverse industries and continue to shape the landscape of optimization and resource allocation.
Early Life and Education: A Foundation in Mathematics
Born on November 8, 1914, in Portland, Oregon, George Dantzig's intellectual journey began in a family deeply rooted in mathematics. His father, Tobias Dantzig, was a mathematician and linguist, while his mother, Anja Dantzig (née Ourisson), was a Russian-born linguist of French-Lithuanian origin. This nurturing environment fostered his early interest in mathematics.
The Dantzig family moved to Washington, D.C., in the early 1920s, where George attended Powell Junior High School and Central High School. He later attended the University of Maryland, College Park, where he received his A.B. in mathematics and physics in 1936. He continued his academic pursuits at the University of Michigan, earning his M.A. in mathematics in 1938.
Serendipitous Discovery: Solving the Unsolvable
In 1939, Dantzig embarked on his doctoral studies at the University of California, Berkeley, under the guidance of Jerzy Neyman. It was during this time that the "urban legend" of George Dantzig originated, a story that highlights his extraordinary problem-solving abilities.
Arriving late to a statistics class one day, Dantzig noticed two problems written on the blackboard. Mistaking them for a homework assignment, he diligently copied them down and set about solving them. According to Dantzig, they "seemed to be a little harder than usual," but he submitted completed solutions for both problems a few days later, still believing they were overdue homework.
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Six weeks later, an excited Neyman informed Dantzig that the "homework" problems he had solved were, in fact, two of the most famous unsolved problems in statistics. Neyman eagerly prepared one of Dantzig's solutions for publication in a mathematical journal. Years later, another researcher, Abraham Wald, 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.
This remarkable feat not only showcased Dantzig's exceptional mathematical prowess but also served as a motivational lesson, demonstrating the power of positive thinking and the potential for groundbreaking discoveries when approaching challenges with an open mind. Neyman had George submit his answers to the “homework” problems as his Ph.D. dissertation.
World War II and the Genesis of Linear Programming
With the outbreak of World War II, Dantzig took a leave of absence from his doctoral program at Berkeley to serve as a civilian for the United States Army Air Forces. He became chief of the combat analysis branch of the Army Air Forces. He later said his mission was to help create order in aircraft-supply flow lines. Dantzig's Pentagon colleagues challenged him to figure out how the Air Force could mechanize its planning process to speed up computation of the deployment of forces and equipment, training, and logistical support.
This experience proved to be pivotal in shaping his future research direction. He was able to state mathematically, for the first time, a wide class of practical and important problems that fell into the newly defined structure of linear programming. In 1944, he received the War Department’s Exceptional Civilian Service Medal for his efforts.
The Birth of Linear Programming and the Simplex Method
In 1947, while still working for the Air Force, Dantzig formulated the concept of linear programming, 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. This groundbreaking approach revolutionized resource allocation and decision-making in various sectors. By the end of that summer, he had developed the simplex method of solving such problems.
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About the same time, he invented the “simplex method,” an algorithm for solving linear programming problems. 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.
He decided to stay at the Pentagon, however, and become the mathematical advisor to the comptroller of the newly established Department of the Air Force. Although he considered the Pentagon a holding place until he found a decent-paying academic position, that job choice started him down a life-changing research path that led to the development of linear programming.
Academic Pursuits and Continued Innovation
After the war, he returned to Berkeley and finished his PhD work, continuing his studies with mathematician Jerzy Neyman. In June 1941, prior to defending his dissertation, George accepted a job in Washington with the Army Air Force Combat Analysis Branch of Statistical Control. Thus he did not receive his Ph.D.
In 1952, Dantzig joined the mathematics division of the RAND Corporation, where he played a major role in developing the new discipline of operations research using linear programming. In 1960, George began an illustrious academic career as professor of engineering science and chairman of the Operations Research Center, University of California, Berkeley. He remained with Project SCOOP until June 1952 when he joined the RAND Corporation as a research mathematician. Six years later he moved on to Stanford as professor of operations research and computer science. He retired in 1997. 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 (IIASA) in Laxenburg, Austria. Later, he became the C. A. Criley Endowed Chair in Transportation in 1973.
During his academic career, he authored or coauthored seven books and more than 150 papers. His publications include "Linear Programming and Extensions" (1963) and "Compact City" (1973). In 1963, Dantzig's Linear Programming and Extensions was published by Princeton University Press.
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Impact and Applications of Linear Programming
The virtually simultaneous development of linear programming and computers led to an explosion of applications, especially in the industrial sector. By the early 1950s, private enterprise -- initially petroleum companies -- had started using Dantzig’s methods.
Linear programming quickly found applications in various industries, including:
- Oil Companies: Blending gasoline for the right flash point, viscosity, and octane at the lowest cost. Scheduling tanker fleets, designing port facilities, and creating financial models.
- Shipping Companies: Determining truck and plane scheduling.
- Manufacturing: Optimizing production processes and resource allocation.
- Diet Planning: Creating balanced and cost-effective meal plans.
- Airline Industry: Scheduling crews and making fleet assignments.
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.
Recognition and Honors
Dantzig's groundbreaking contributions to mathematics and operations research earned him numerous accolades and honors throughout his career, including:
- Fellow of the Econometric Society
- Fellow of the Institute of Mathematical Statistics
- Fellow of the Association for the Advancement of Science
- Fellow of the Institute of Operations Research and the Management Sciences
- President of the Institute for Management Sciences
- Founder of the Mathematical Programming Society
- Silver Medal of the British Operational Research Society
- Harvey Prize in Science and Technology from Technion University
- The first John von Neumann Theory Prize in 1974
- National Medal of Science in 1975
- Honorary doctorate from the University of Maryland, College Park in 1976
- The Mathematical Programming Society created the George B. Dantzig Prize in his honor
On October 18, 1976, President Gerald Ford presented Dantzig with the National Medal of Science.
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