Reminiscences of George B. Dantzig
Monumental Contributions
to LP Met the Test
By Arthur F. Veinott Jr., Stanford University
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| Arthur Veinott Jr. (left) and George Dantzig, shown at a dinner party at Veinott's home in 2002. |
George involved me in his world from day one. At his invitation, we worked together as co-directors of the 1967 AMS 5th Summer Seminar on the Mathematics of the Decision Sciences and as co-editors of the resulting books, one of which was an AMS best seller for a while. He was a warm friend and beloved colleague for 39 years, and an extraordinarily creative scholar. He was tireless and successful in seeking research funding, and was generous in using it to involve students, faculty and visitors (including academic refugees) needing support.
George used to say that a paper should have only a single idea to get the attention of a reader. Our two joint papers probably met that test; each had one theorem and was two pages long. And at least the first — on integral extreme points — apparently got some attention since it is used in most texts on integer programming.
George believed that the best O.R. research developed mathematical models that are general enough to be broadly applicable and special enough to be computationally tractable. His monumental contributions to linear programming and its applications certainly met that test.
Perhaps the single area in which George influenced my own work the most was Leontief Substitution Systems. In 1955 he developed some of the basic properties of such systems. He thought of them as the most beautiful linear programs because they had so many lovely properties and had important applications as well.
In 1977 a very strong Ph.D. student was defending his thesis involving systems that are equivalent to Totally Leontief Substitution Systems. I asked the student if he knew how to check whether or not a system had this property. He said he did not. Soon George amazed us all by exhibiting a linear program that would solve the problem. Afterward he asked me to write up the result, which I did. Then he asked me to co-author the paper, which I resisted, but he insisted, and this became our second paper together.
In 1958 Ralph Gomory excited the optimization community by finding a finitely convergent cutting-plane method for solving integer programs. George then proposed a much simpler way of generating cuts. Alas, they did not always suffice to solve an integer program, but nevertheless came to be known as "Dantzig Cuts." George liked to joke that naming his cut the "Dantzig Cut" was the unkindest cut of all.
George was loyal to and appreciative of his family, students, colleagues and others. In 1989 he was working at his desk at Stanford during the Loma Prieta earthquake, which ripped the book case off the wall behind him and pinned him to his desk. A student and I removed the book case, and the first thing he said with alarm was, "I need to find out if (my wife) Anne is OK!"
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