1940-1950 Dantzig 2005

J. J. O'Connor and E. F. Robertson George Dantzig Biographies of Mathematicians http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Dantzig_George.html 2005, 1952, 1940s

     "During my first year at Berkeley I arrived late one day to one of Neyman's classes. On the blackboard were two problems which I assumed had been assigned for homework. I copied them down. A few days later I apologized to Neyman for taking so long to do the homework-the problems seemed to be a little harder to do than usual. I asked him if he still wanted the work. He told me to throw it on his desk. I did so reluctantly because his desk was covered with such a heap of papers that I feared my homework would be lost there forever.

     "About six weeks later, one Sunday morning about eight o'clock, Anne and I were awakened by someone banging on our front door. It was Neyman. He rushed in with papers in hand, all excited: "I've just written an introduction to one of your papers. Read it so I can send it out right away for publication." For a minute I had no idea what he was talking about. To make a long story short, the problems on the blackboard which I had solved thinking they were homework were in fact two famous unsolved problems in statistics. That was the first inkling I had that there was anything special about them. "

"When the United States entered World War II in 1941 Dantzig put his graduate studies on hold for a second time, although by this time he had already completed the coursework and written his Ph.D. thesis. He went to Washington and joined the Air Force as a civilian. From 1941 to 1946 he was Head of the Combat Analysis Branch, U.S.A.F. Headquarters Statistical Control. In 1944 he was awarded the War Department Exceptional Civilian Service Medal. He wrote of his time there:-

"My office collected data about sorties flown, bombs dropped, aircraft lost... I also helped other divisions of the Air Staff prepare plans called "programs". ... everything was planned in greatest detail: all the nuts and bolts, the procurement of airplanes, the detailed manufacture of everything. There were hundreds of thousands of different kinds of material goods and perhaps fifty thousand specialties of people. My office collected data about the air combat such as the number of sorties flown, the tons of bombs dropped, attrition rates. I also became a skilled expert on doing planning by hand techniques. "

"In 1946, after a break of five years, Dantzig returned to Berkeley for one semester, receiving his doctorate in mathematics from the University of California. He was offered an academic post by Berkeley but turned down the offer:-

"Berkeley made me an offer, but I didn't like it because it was too small. Or, to be more exact, my wife did not like it. It was a grand salary of fourteen hundred dollars a year. She did not see how we could live on that with our child David."

"By June 1946 he was in Washington considering a number of different possible jobs. His colleagues at the Pentagon asked him to take on the job of mechanizing the planning process. This appeared to fit in exactly with his interests so that year he was appointed Mathematical Advisor at the Defense Department to undertake the task.

"In 1947 Dantzig made the contribution to mathematics for which he is most famous, the simplex method of optimization. It grew out of his work with the U.S. Air Force where he become an expert on planning methods solved with desk calculators. In fact this was known as "programming," a military term that, at that time, referred to plans or schedules for training, logistical supply or deployment of men. Dantzig mechanized the planning process by introducing "programming in a linear structure", where "programming" has the military meaning explained above. The term "linear programming" was proposed by T.J. Koopmans during a visit Dantzig made to the RAND corporation in 1948 to discuss his ideas. Having discovered his algorithm, Dantzig made an early application to the problem of eating adequately at minimum cost. He describes this in his book Linear programming and extensions (1963):-

     "One of the first applications of the simplex algorithm was to the determination of an adequate diet that was of least cost. In the fall of 1947, Jack Laderman of the Mathematical Tables Project of the National Bureau of Standards undertook, as a test of the newly proposed simplex method, the first large-scale computation in this field. It was a system with nine equations in seventy-seven unknowns. Using hand-operated desk calculators, approximately 120 man-days were required to obtain a solution ... The particular problem solved was one which had been studied earlier by George Stigler (who later became a Nobel Laureate) who proposed a solution based on the substitution of certain foods by others which gave more nutrition per dollar. He then examined a "handful" of the possible 510 ways to combine the selected foods. He did not claim the solution to be the cheapest but gave his reasons for believing that the cost per annum could not be reduced by more than a few dollars. Indeed, it turned out that Stigler's solution (expressed in 1945 dollars) was only 24 cents higher than the true minimum per year $39.69."

"In [11] Dantzig wrote . . .:-

     "Linear programming is viewed as a revolutionary development giving man the ability to state general objectives and to find, by means of the simplex method, optimal policy decisions for a broad class of practical decision problems of great complexity. In the real world, planning tends to be ad hoc because of the many special-interest groups with their multiple objectives."

      "But he also modestly wrote:-

"The tremendous power of the simplex method is a constant surprise to me."

"The importance of linear programming methods was described, in 1980, by Laszlo Lovasz who 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."

"Also in 1980 Eugene Lawler wrote:-

     "[Linear programming] is used to allocate resources, plan production, schedule workers, plan investment portfolios and formulate marketing (and military) strategies. The versatility and economic impact of linear programming in today's industrial world is truly awesome."

      "Balinski [4] writes:-

      "Mathematical programming has been blessed by the involvement of at least two exceptionally creative geniuses: George Dantzig and Leonid Kantorovich."

      "He then goes on to say that Kantorovich received the Nobel Prize for his contribution and expresses "outrage" that Dantzig did not."

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 Kelyn Roberts 2017