In 1939, George Dantzig rushed off to his graduate statistics class at UC Berkeley – he was very late and very anxious not to miss out on any lectures as a first-year student. As he sat down among the other graduate students in class, his eye was caught by a set of math problems written up on the blackboard. Assuming them to be the day’s assigned homework, he copied them down and turned them in to his professor, later remarking in 1990:
“A few days later I apologized to Neyman [his professor] for taking so long to do the homework – the problems seemed to be a little harder to do than usual.”
Early Sunday morning about six weeks later, Dantzig and his wife were awakened by someone banging on their front door. They were surprised to find an out-of-breath Neyman with an excited look on his face, clutching a couple of rumpled papers. “I’ve just written an introduction to one of your papers. Read it so I can send it out right away for publication.” As it turned out, the problems Dantzig had mistaken for homework were really two famous unsolved statistics problems that were now, at the suggestion of Neyman, taken up as his doctoral dissertation. This extraordinary event was the beginning of Dantzig’s successful career as a mathematical scientist and his revolutionary work on linear programming that would completely transform the fields of economics, engineering, and computer science – greatly impacting how the U.S military has dealt with logistics since World War II. It may have also inspired the critically acclaimed 1997 film, Good Will Hunting, where a South Boston delinquent easily solves mathematical proofs that had long puzzled an esteemed professor at MIT.
Dantzig grew up primarily in the Baltimore-Washington metropolitan area and earned his B.S in mathematics and physics from the University of Maryland. His father also had ties to the university as a math tutor and raised his son on a steady regimen of “thousands of geometry problems while [Dantzig] was still in high school…at the time when [his] brain was still growing [which] did more than anything else to develop [his] analytic power.” After receiving his Ph.D. in mathematics from Berkeley, Dantzig joined the Air Force and was head of the “Combat Analysis Branch” at the Pentagon’s U.S.A.F Headquarters of Statistical Control. His experience in the military helped him with his most important contribution in 1946 – optimization through the algorithm of linear programming. Linear programming is a way to evaluate the cost and resources used in any given activity in order to mechanize and therefore quicken the planning of that activity. Interdependent activities are chosen in the best way – the optimal way – through linear programming so that a system can operate at its optimum capacity. In the words of Eugene Lawler, a computer scientist at Berkeley, “[linear programming] is used to allocate resources, plan production, schedule workers, plan investment portfolios, and formulate marketing (and military) strategies.” It’s a method that has thousands of applications in diverse fields and has determined how large projects and operations are now run.
Dantzig then tried to apply his idea to what was called “The Diet Problem,” which was an optimization problem concerned with choosing a number of food items that give sufficient nutritional benefits at a minimum cost. With the help of other researchers like George Stigler, the optimal solution was calculated to be $39.69 per year (using 1939 prices). This work greatly helped the U.S Army’s nutritional planning for its GIs in the field, as well as show the world exactly what linear programming could achieve. In 1952, Dantzig helped further develop “operations research” at the RAND (Research and Development) Corporation, which involved using computers to solve optimization problems. He finally died in 2005 while working as an operations research and computer science professor at Stanford University.
The significance of linear programming cannot be understated. In 1980, the Hungarian mathematician László Lovász wrote, “if one would take statistics about which mathematical problem is using up most of the computer time in the world, then…the answer would probably be linear programming.” Dantzig earned numerous accolades for his incredibly important work, winning the National Medal of Science (1975), the John von Neumann Theory Prize of the Operations of Research Society of America and the Institute of Management Sciences (1974), and membership in the National Academy of Sciences and the National Academy of Engineering. His legacy is felt in most fields that require manufacturing and cost and resource planning – practically all fields. And to think that it all began on a day Dantzig was late to class.
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