George Dantzig: Quotes about problems

“In retrospect… 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.”

George Dantzig

Dantzig (1991) as cited in: " Professor George Dantzig: Linear Programming Founder Turns 80 http://www.stanford.edu/group/SOL/dantzig.html", in: SIAM News, November 1994.

World , Problem , Time

“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.”

George Dantzig

cited in: John J. O'Connor & Edmund F.; Robertson (2003) " George Dantzig http://www-history.mcs.st-and.ac.uk/Biographies/Dantzig_George.html". in: MacTutor History of Mathematics archive, University of St Andrews.
Linear programming and extensions (1963)

Food , Way , Mathematics , Problem

“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.”

George Dantzig

Dantzig (1986) in: D.J. Albers and C. Reid "An interview with George B. Dantzig : the father of linear programming". In: The College Mathematics Journal Vol 17, nr 4, 1986, p. 293-314.

Fear , Idea , Problem , Thinking

“All such problems can be formulated as mathematical programming problems. Naturally, we can propose many sophisticated algorithms and a theory but the final test of a theory is its capacity to solve the problems which originated it.”

George Dantzig

Source: Linear programming and extensions (1963), p. vii.

Mathematics , Nature , Problem

“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.”

George Dantzig

Dantzig (1983) "Reminiscences about the origins of linear programming". In: Mathematical programming : the state of the art. New York, 1983, p. 78-86.

World , Optimism , Problem , Decision