OR/MS Today - October 1999

October 1999

Hail the Giants

By Thomas Magnanti
magnanti@mit.edu

Every calling is great when greatly pursued.
— Oliver Wendell Holmes

It is fruitful at times to examine our roots, recalling previous accomplishments and seeking insight that might help in guiding our future. The past few months have provided me with this opportunity as I participated in a workshop in honor of Ralph Gomory's 70th birthday, and as I anticipate two sessions at the Philadelphia INFORMS meeting in honor of George Dantzig's 85th birthday. It is wonderful to honor these two giants of our profession and their extraordinary accomplishments, and to learn from their exceptional careers.

I have known George Dantzig for over 30 years. I was privileged to learn from him directly as my teacher and thesis Ph.D. advisor. I have "known" Ralph Gomory almost as long, but through his seminal research contributions rather than as a personal acquaintance. I believe that we might have met personally for the first time only about 10 years ago in his role as president of the Sloan Foundation. Nevertheless, both George Dantzig and Ralph Gomory have had a profound influence on my professional career, as they have on so many others.

George and Ralph have experienced different, although not dissimilar, career paths. George began his professional career at the U.S. Bureau of Labor Statistics (as a junior statistician), the U.S Air Force and the Rand Corporation. Later, in 1960 at the age of 46, he became an academic, first at the University of California at Berkeley and then at Stanford. Ralph started as an assistant professor at Princeton University and then joined IBM where he became an IBM Fellow and director of research. He eventually rose to the position of senior vice president of science and technology. He retired from IBM in 1989 to become president of the Sloan Foundation.

To say that George and Ralph are distinguished would be a vast understatement. They both have received abundant honors including: the United States National Medal of Science, numerous honorary degrees, membership in both the National Academy of Engineering and the National Academy of Science, and varied research awards including the INFORMS (then ORSA/TIMS) John von Neumann Theory Award. Ralph has won the Lanchester Prize and George has important prizes named in his honor.

Their combined research accomplishments are stunning, George as the father of mathematical programming and Ralph as the father of integer programming (though in integer programming, as in most fields of mathematical programming, George Dantzig made early seminal contributions). Their contributions include no less than the simplex method (including degeneracy analysis), sensitivity analysis, Dantzig-Wolfe decomposition, stochastic programming, the generalized upper bounding method, early results in complementary pivot theory, cutting plane methods, group theoretic integer programming and column generation. They are associated with innovations in modeling and with a wide range of applications including vehicle routing, cutting stocks, economic lot-sizing, network synthesis, ship routing and energy modeling.

Several aspects of George's and Ralph's careers are especially noteworthy. They share a deep appreciation for the bond between theory and practice. Indeed, many of their most fundamental theoretical contributions were prompted by their desire to solve real problems. The simplex method arose from modeling and solving real problems in logistics. Studies of the cutting stock and knapsack problems shaped the development of cutting planes and group theoretic methods.

The coupling of theory and practice, in the best tradition of the great 18th century mathematicians such as Leonhard Euler and Joseph-Louis Lagrange, was undoubtedly influenced by George's and Ralph's mutual experience working in industrial settings as well as at universities. Both have a keen interest in computations as well as theory. And, they seem to view the world a bit differently than most of us. George has always seemed to see "pivoting" in his head. At the recent workshop in his honor, Ralph spoke about an empirical investigation of the group theoretic method that he pioneered some 30 year ago. And finally, they both have an abiding passion for research. George has been retreating to his study to conduct research essentially every day for decades and Ralph, as president of one of the most famous foundations in the world, finds time at night and on weekends to conduct research on economics and on integer programming. Simply amazing, and truly inspiring.

As two of the most gifted applied mathematicians of this century, George Dantzig and Ralph Gomory have had defining influences on the mathematical sciences as a field of scientific inquiry. It certainly is too much to expect the rest of us to come even close to matching their accomplishments. We can, however, rejoice in the fact that our profession has been fortunate enough to attract them (or perhaps, more accurately, they have attracted us). And, we can learn from them as role models — by building upon the interplay between practice and theory, drawing on experiences both within and outside the university, and adopting somewhat different perspectives than the norm in our studies. We have a lot to admire about and learn from these most remarkable men.

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