Ralph E. Gomory

Born: May 7, 1929

Brief Biography

Ralph Gomory is a pioneer in integer optimization who has served as Chairman of IBM Research’s Mathematical Sciences Department, Director of Research for IBM, President of the Alfred P. Sloan Foundation, and research professor at NYU’s Leonard N. Stern School of Business.  Earlier, he spent a pivotal summer at RAND and was an Andrew Dickson White Professor at Cornell. He has been elected to the National Academy of Sciences, the national Academy of Engineering and the American Philosophical Society, and to the Councils of all three societies.  In addition to his major contributions to Operations Research, he has written on the nature of industrial research and on global trade.

Gomory originally studied physics at Williams College but was drawn to mathematics there, and wrote a Princeton Ph.D. thesis on nonlinear differential equations.  After completing his Ph.D. he joined the U.S. Navy as an officer and was assigned to the Physics Branch of Office of Naval Research in DC.  There he discovered the Operations Research Group (ORG) and learned linear programming from Alan Goldman. 

He remained with ORG as a consultant after joining the Princeton faculty, traveling to Washington to consult on Navy problems.  One of these dealt with LP solutions that proposed such oddities as fractional aircraft carriers.  He discovered that constraints could be added to the problem that cut away fractional solutions, incorporated this cutting-plane approach into an algorithm, and proved that it converged to an integer optimum in a finite number of steps. His appointment as IBM’s Director of Research reduced his own research output, but he continued to explore the geometry, algebra, computation and economics of integer programming, with new contributions more than 45 years after his original cutting-plane paper.

Through his exposure to ORG, Gomory learned of OR as “mathematics applied to everyday problems: problems of a company, scheduling problems, etc.” and thought “oh, that’s what I want to do!”  Later, at IBM, he collaborated with co-authors including Michel Balinski, Paul Gilmore, T.C. Hu, Alan Hoffman and others on papers that tackled many core OR problems, such as the knapsack, traveling salesman, cutting stock, network flow, machine sequencing, lot size and inventory problems.  With Gilmore, he visited a number of IBM customer sites to understand their problems.  At paper mills, they hit upon the problem of minimizing waste in cutting a large standard-sized roll of paper into a mix of smaller rolls ordered by customers. Their solution to this practical problem won the Lanchester Prize in 1963.  This work, together with his contributions to the theoretical underpinnings of OR, earned Gomory the 1984 John von Neumann Theory Prize awarded by INFORMS. 

He became an IBM Fellow, the highest honor a scientist, engineer or programmer can achieve at the company, and moved into management, first of the Mathematical Sciences department and then all of IBM Research.  During his 20 year tenure as research head the Research Division made such technology advances as the single-transistor memory cell, high-density storage devices, silicon processing methods, the relational database and the RISC computer architecture. His researchers also won two successive Nobel Prizes in Physics.

During his eighteen years as Sloan Foundation President, the Foundation pioneered work on the threat of bioterrorism, online learning, under-represented minorities in science and technology, the Sloan Sky Survey, the Census of Marine Life, and the development of the Professional Science Masters degree.

Other Biographies

Profiles in Operations Research: Ralph E. Gomory
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Wikipedia Entry for Ralph Gomory

IBM Archives. IBM Builders (1988): Ralph Gomory. Accessed November 10, 2014. (link)

Johnson E.L .(2005)  IFORS' Operational Research Hall of Fame: Ralph E. Gomory International Transactions in Operations Research 12 (5): 539-543 (link)

NYU Stern Business School. Faculty Profile: Ralph Gomory. Accessed November 10, 2014. (link)

RalphGomory.com. Bio: Ralph E. Gomory. Accessed November 15, 2014. (link)

Education

Williams College, BA 1950

Cambridge University

Princeton University, PhD 1954 (Mathematical Genealogy)

Affiliations

Academic Affiliations
Non-Academic Affiliations

Key Interests in OR/MS

Methodologies
Application Areas

Oral Histories

Ralph Gomory (2017) Interview by Irv Lustig, May 10, 2017.  New York, NY.

NOTE:  The video chapter transcripts below are searchable, with search results displayed as marks on the time bar above the search box.  Click a mark to jump to the search word or phrase in the video and transcript, or click on any word in the transcript to jump to that point in the video.

Jump to Chapters

Chapter 1: Introduction: Early Life
Chapter 2: High School and College
Chapter 3: After College to Graduate School
Chapter 4: Introduction to Operations Research
Chapter 5: Discovering Integer Programming
Chapter 6: Moving to IBM Research and Column Generation
Chapter 7: Leading IBM Research
Chapter 8: IBM Research Accomplishments Under Gomory's Leadership
Chapter 9: The Sloan Foundation
Chapter 10: Research Professor at New York University
Chapter 11: Operations Research Today

R. E. Gomory (2010) Interview by William Thomas, July 19. Alfred P. Sloan Foundation: New York. (transcript)

Memoirs and Autobiographies

Memoirs

Gomory, R.E.  Early Integer Programming. Oper Res 50(1):78–81

Awards and Honors

Lanchester Prize 1963

John von Neumann Theory Prize 1984

IEEE Ernst Weber Engineering Leadership Recognition 1988

National Medal of Science 1988

Heinz Award for Technology, the Economy and Employment 1998

The Institute for Operations Research and the Management Sciences Fellow 2002

Harold Lardner Prize 2006

Selected Publications

Gomory E. E. (1958) Essentials of an algorithm method for integer solutions to linear programs. Bulletin of the American Mathematical Society, 64(5): 275-278.

Gomory R. (1960) An algorithm for the mixed integer problem (No. RAND-P-1885). Rand Corporation: Santa Monica, CA.

Gomory, R. E. (1960) Solving linear programming problems in integers. Combinatorial Analysis: Proceedings of the Tenth Symposium in Applied Mathematics: 211-215.

Gomory R. E. & Hu T. C. (1961) Multi-terminal network flows. Journal of the Society for Industrial & Applied Mathematics, 9(4): 551-570.

Gomory R. E. (1963) An all-integer integer programming algorithm. Muth J. F. & Thompson G. R., eds. in Industrial Scheduling, 193-206. Prentice Hall: Englewood Cliffs.

Gomory R. E., Hoffman A. J., & Watson T. J. (1963) On the convergence of an integer‐programming process. Naval Research Logistics Quarterly, 10(1): 121-123.

Gomory R. E. (1965) On the relation between integer and noninteger solutions to linear programs. Proceedings of the National Academy of Sciences of the United States of America, 53(2): 260.