**Operations Research & Computers at IBM from the 1960s to 1990s**

As the preeminent computer manufacturer of the twentieth century, IBM has been a major player in advancing operations research and management science. In the 1960s and 1970s, IBM-manufactured systems led the way for OR practitioners in academia, industry, and the government, and IBM researchers developed influential techniques which saw applicability beyond their main line of business. This effort stemmed largely from the Thomas J. Watson Research Center and the Mathematical Sciences Department, Yorktown Heights, NY, though other divisions within the company developed and employed OR/MS methods as well.

The Thomas J. Watson Center (IBM Research) was established in 1961, sixteen years after the foundations of IBM Research were laid at Columbia University. Even in its earliest years, the Mathematical Sciences group in Yorktown Heights was home to many individuals who made significant contributions to operations research. Mid-century directors of the group included Herman Goldstine (1960-1965), Ralph Gomory (1965-1970), Hirsch Cohen (*Acting*, 1967-1968), Shmuel Winograd (1970-74 & 1980-1994), and Alan Hoffman (*Acting*, 1971-1972). These individuals and their peers brought with them diversified experiences that created a mosaic of personalities and unique thinkers, many of whom came to IBM by way of Princeton University. Goldstine, the group’s first director, joined IBM after working on the ENIAC computer at the Institute for Advanced Study (IAS). Gomory, his successor, joined the company after serving as an officer within the Office of Naval Research and a brief teaching career at Princeton. Although his tenure as director, and subsequently IBM corporate Director of Research, partially slowed down his prolific research, Gomory oversaw explorations in the geometry, algebra, computations, and economics of integer programming. He continued collaborating with Ellis L. Johnson even after he became IBM VP of Science & Technology. During World War II, Hoffman served in the European and Pacific theaters and followed that with positions at IAS, the National Bureau of Standards, and the Office of Naval Research. By the time he joined IBM in 1961, Hoffman had learned linear programming from OR pioneer George Dantzig and was acquainted with many other luminaries of the period. He authored over two hundred papers during his forty-one years in Yorktown Heights.

Operations research at IBM covered a wide variety of topics, ranging from those directly affecting their own computer manufacturing to diverse problems with widespread applicability. Linear programming (LP) research was significant amidst this collection. The importance of integer programs, i.e., optimization with some variables restricted in integer values, was previously noted by George Dantzig, Ray Fulkerson, and Selmer Johnson in 1954, and by Harry Markowitz and Alan Manne in 1957. Ralph Gomory, however, was considered the father of integer programming, because he was the first to provide a well-defined method for solving integer programs – the so-called “cutting plane method.” With Hoffman he wrote an influential paper on the convergence of an integer programming process, analyzing the finiteness of a particular procedure (Gomory & Hoffman 1963). Gomory was also well known for his introduction of the cutting stock problem in 1961 with Paul C. Gilmore (Gilmore & Gomory 1961). This was motivated by an application in the paper industry. Since then, the cutting stock model has been widely applied in not only in the paper industry, but also in steel and wood fabrication. This work was awarded the INFORMS Lanchester Prize in 1963. In 1983, a paper by Harlan Crowder and Ellis L. Johnson at IBM Yorktown Heights and Manfred Padberg at New York University showed that integer programming could be used to solve problems of practical size if one combined branch-and-bound with cutting plane methods of various types, not just those first described by Gomory (Crowder et al. 1983). This work was awarded the INFORMS Lanchester Prize in 1983.

Under Gomory’s direction, IBM brought in RAND’s Philip Wolfe to lead a team specializing in continuous optimization. Wolfe wrote a series of papers on convergence theory in the late 1960s and subgradients in the 1970s. Among those Wolfe collaborated with was Crowder (Crowder & Wolfe 1972), who wrote a report on computational improvements for subgradient optimizations (Crowder 1974). In the realm of game theory, Princeton-educated economist Martin Shubik worked on experimental teaching and operational gaming during his stint with the company. It should also be noted that a significant portion of the work done by the Mathematical Sciences group was highly confidential because many projects were Cold War-era contracts with the US Government.

The Mathematical Sciences group was not the only one to employ OR/MS at IBM. The Business Analytics group and the Data Processing Division, which was established as the company’s primary marketing and sales organization in 1956, employed many management science techniques to help in the sale and rollout of IBM computers. Early use of operations research in manufacturing (such as scheduling and material allocation) was prevalent but not publicized. By the early 2000s, much of the OR/MS work at IBM fell under the heading of Business Analytics and Mathematical Sciences. This group grew to more than 300 researchers, led by Brenda Dietrich, an IBM Fellow, INFORMS Fellow, and past president of INFORMS (2007).

**IBM Computers for Operations Research**

The success of OR often depends on using computing systems capable of supporting the necessary calculations. In tandem with advances in OR, IBM researchers made major contributions to both computer hardware and software needed to implement OR methods. These advances contributed to the successful use of OR by IBM and its customers as the company’s focus moved beyond hardware to software and to services. For instance, the IBM 305 RAMAC (“Random Access Method of Accounting and Control”), the first computer to use a magnetic disk for long term storage, was introduced in 1956. IBM computers were the systems of choice for OR/MS practitioners in academia, industry, and the government. An early example of this was one of the earliest commercial computer implementations of the simplex method, on an IBM 701 at RAND circa 1954 (RAND n.d). (The first computer implementation was probably in 1952 on the SEAC research computer at the National Bureau of Standards.) The mid-century popularity of IBM systems is evident in how often research run on their machines was published in the 1950s-1970s. Over the course of its delivery lifespan (1965-1978), the IBM System/360 family of computers is mentioned in more than seventy articles published in *Operations Research* and over one hundred articles published in *Management Science*, the formal publications of the Operations Research Society of America and The Institute for Management Sciences, respectively. This marked a significant growth compared to select predecessors such as the IBM 704 (1955-1960), the world’s first core memory computer, which is mentioned only seventeen times in *Operations Research*. This growth was the product of multiple factors including increased broad computing demand and IBM’s ability to more easily mass manufacture their systems. In the 1950s, IBM deployed one hundred twenty-three 704s (IBM n.d.a). By comparison, over one thousand s/360s were ordered within the first four weeks of their initial announcement alone. By streamlining all their product lines under a strictly compatible family, IBM revolutionized the computer hardware industry (IBM n.d.b). The IBM s/360 was also the machine that introduced the 8-bit byte as the standard unit of information.

This is not to say IBM did not face any competition. The RCA Spectra 70 line of computers (introduced in 1965) was nearly compatible with the IBM s/360 series and was advertised to provide benefits of its exceptional cost and performance (Devany 2019). Bendix Aviation’s G-series of computers of the late 1950s and early 1960s were also well-suited for operations research of the period (Devany 2020). In 1960 and 1964, respectively, supercomputer pioneer Seymour Cray introduced the CDC 1604 and CDC 6600 at Control Data Corporation, cutting into both IBM’s low-end and high-end markets. Furthermore, the inventor of the System/360, Gene Amdahl, left IBM to form his own company. He built a series of computers that were cheaper, and in many cases faster, than those in the s/360 family. Nevertheless, IBM remained in the driver’s seat, so to speak, when it came to dominating and defining the market. The s/360s and subsequent s/370s were followed by the IBM 3090, a high-end system with an added vector processor for doing fast computations on significant arrays of numbers.

By providing the leading computers of the era, IBM researchers subsequently developed valuable accompanying programming environments and languages. In 1954, John Backus at IBM started work on the FORTRAN (FORmulaTRANslation) language. It became a standard tool in 1958 with the release of FORTRAN II for the IBM 701 computer. One of the notable features of FORTRAN II was that it introduced the SUBROUTINE statement and capability. In the 1950s through 1970s, most computational OR work was done in FORTRAN.

In 1962, IBM’s Kenneth Iverson published a book on a powerful and compact mathematical notation, known at one time as Iverson notation. Its particular strength was handling arrays of arbitrary dimension. Later, this notation and language became more popular when implemented, with the help of Adin Falkoff and Larry Breed, as a time-sharing system cleverly named APL (“A Programming Language”). APL gained a cult-like following of enthusiasts for many years.

Another example is General Purpose Simulation System (GPSS), a discrete-time simulation programming language developed by IBM’s Geoffrey Gordon. He initially called the language “Gordon’s Programmable Simulation System”. GPSS was originally developed for the 7044 and 7090 mainframes but was subsequently released for later systems, including those in the IBM s/360 family (“GPSS/360”). Studies run in GPSS were used in many fields, such as a GPSS simulation of scheduling policies for surgical patients, developing an optimal policy that “satisfies the ‘real world’ constraints of an active hospital (Kwak et al. 1976).” Though it was introduced in the fall of 1961, there were still three kinds of GPSS systems being shipped and sold fifty years later (Stahl et al. 2011).

The PL/I language was introduced by IBM in 1964 in an attempt to provide a programming language that was not only useful for scientific computing but also for business and other applications. It had much better text handling capabilities than FORTRAN. Because of the generality and complexity of PL/I, it was difficult to write good compilers for it, and thus it took longer to compile a program in PL/I and programs written in PL/I tended to run slower than programs written in FORTRAN. PL/I never achieved the widespread use of FORTRAN.

Operations researchers at IBM played a key role in the development and deployment of major supercomputing systems at the turn of the millennium. William Pulleyblank joined IBM in the late 1960s but committed to academia following the completion of his PhD under future John von Neumann Theory Prize recipient, Jack Edmonds. He led a successful career as a professor at the Universities of Calgary and Waterloo, specializing in combinatorial optimization. Pulleyblank returned to IBM in the 1990s and, as the Director of Mathematical Sciences, managed the development of “Deep Blue”, the first supercomputer to defeat a reigning master in a chess tournament (see Kapica 2007, June 28). He also managed development of the system’s successor, “Blue Gene,” the first supercomputer to achieve 1 PetaFLOPS performance on the widely accepted Linpack performance benchmark, which entails solving a dense system of linear equations, a measure highly relevant to optimization. Pulleyblank remained at IBM through 2010 as Vice President for Business Analytics and Optimization and was elected a Fellow of INFORMS in 2007.

Not only did IBM develop simulation-based tools for analyzing industrial systems, it also developed sophisticated queueing theory-based tools for such applications. In the late 1970s IBM used results from the theory of networks of queues and so-called product-form solutions to produce the Research Queueing (RESQ) software system, (Sauer et al. 1982). It was a major success within IBM for modeling systems such as the AS/400 and S/390 computers, and local and wide area computer networks. Over time, new computational algorithms and statistical methods were added to RESQ, along with a graphical user interface, animation, and other features. Its widespread use in IBM continued into the 1990s. It was also made available to universities and research institutions.

**Optimization at IBM**

In the period of 1963 to 1965, IBM introduced one of the earliest commercial LP optimizers to run on the IBM 7040 and 7090 series of computers. When the IBM 360 series of computers was introduced around 1965, these LP codes were rewritten and introduced as MPS/360. These were some of the most widely used LP optimizers during the second half of the 20^{th} century. Later, these codes were extended as MPSX. The IBM-France/Paris group, including Jean-Michel Gauthier, Gerard Hentges, Michel Benichou and Gerard Ribière, played an important role in the evolution of MPSX. During the period of 1972 to 1985, MPSX was probably the leading LP optimizer in the market.

At each pivot step of the simplex method for solving LPs, an entering column replaces a departing column in a square matrix. The revised simplex method computes the inverse of this square matrix at each step. A key feature of an efficient implementation is how to compute or update this inverse at each step. Until 1972, the standard way of doing this update was the product form of the inverse, as suggested to George Dantzig by Alex Orden while both were working on Project SCOOP at the Pentagon around 1947. Around 1972, John Forrest and John Tomlin, while working at Scicon in the UK, developed a clever and generally faster way of doing this update (Forrest & Tomlin 1972). Forrest joined IBM in 1985, and Tomlin joined IBM in 1987. Around 1987, Forrest, with the help of Tomlin, developed a research LP code at Yorktown Heights, called YKTLP that incorporated the Forrest/Tomlin update. The product form inverse was well suited for sequential magnetic tape units because it could be done with just one pass through a magnetic tape for each simplex pivot. The Forrest/Tomlin update requires random access memory and is essentially incompatible with sequential storage devices. The Forrest/Tomlin update has been an option in most other commercial LP solvers since then. Around 1989 a large oil company was contemplating the purchase of an Amdahl computer, while IBM was trying to sell the company its new, rather more expensive IBM 3090 computer. One of the features of the 3090 was vector processing capability. Forrest and Tomlin, with suggestions from Fred Gustavson in the High-Performance Computing group, were able to generalize YKTLP to exploit the vector processing capability and IBM won the sale. As part of the process, YKTLP became an official software product and renamed OSL (Optimization Subroutine Library). OSL removed the upper limit of 32,000 constraints that was a limitation of MPSX. It was introduced commercially around the same time Bell Labs introduced the KORBX LP solver, which only sold three copies. OSL, by comparison was fairly successful in its role as an eventual popular replacement for MPSX into the 1990s. Though IBM eventually decided to stop marketing OSL, the software still lives on in a sense in the COIN-OR (Computational Infrastructure for OR) open-source optimization software initiative, launched at the 2000 International Symposium on Mathematical Programming as a three-year experiment by IBM Research. In 2004, a dedicated nonprofit corporation was formed to continue the initiative. Forrest was jokingly named the “benevolent dictator” of the resulting open-source initiative. Many young researchers in computational OR “learned the ropes” of software development thanks to IBM’s support of COIN-OR.

IBM researchers made notable contributions not only to the implementation of linear programming but also to the underlying theory. INFORMS Fellow and IBM researcher Nimrod Megiddo worked for many years on both the probabilistic behavior of the simplex method and on the performance of the interior point/barrier method. In 1992 he received the Lanchester Prize and the INFORMS Computing Society Prize. In 2014 he was awarded the John von Neumann Theory Prize.

IBM Fellow and researcher Ellis L. Johnson also made fundamental contributions to the theory and practice of integer programming and combinatorial optimization. He was aggressively recruited to Yorktown Heights by Hoffman and Gomory on the recommendation of his thesis advisor, George Dantzig. Johnson provided the theoretical underpinnings for the algorithm development, computational testing, and solution of hard real-world problems in industry and transportation. He and Manfred W. Padberg were jointly awarded the INFORMS John von Neumann Theory Prize in 2000.

IBM made advancements not only to linear and integer optimization but also to nonlinear optimization. One of the leaders in this effort was Andrew Conn. With the encouragement of Ellis L. Johnson, Conn moved from University of Waterloo to IBM Research in 1990 and became a member of the Center for Computational and Statistical Learning Group in the Mathematical Sciences Department at IBM Research. Motivated by problems in circuit design, and working closely with actual circuit designers for IBM computers, Conn developed notable methods for nonlinear optimization. His most well-known work is the Lancelot software for nonlinear optimization. He originated the CUTE (Constrained and Unconstrained Testing Environment) methodology + test problem library for evaluating nonlinear optimization algorithms. His book, *Introduction to Derivative-Free Optimization *(2009), with Katya Scheinberg and Luís N. Vicente, is a standard reference. He received the Lagrange Prize in Continuous Optimization, the Beale-Orchard-Hays Prize from the Mathematical Optimization Society, and the IBM Outstanding Technical Achievement Award.

** ****IBM and OR in Europe **

IBM Europe was very active in OR work in both optimization solver development and applications of optimization in industry and government in the 1960s, 1970s and 1980s. The OR applications basically started in the late 60s by using LP solvers, mainly MPS/360 for the 360 series and LPS/1130 for 1130 computer. The latter was a small (8Kbytes, 16Kbytes) but efficient computer where the optimization of simple blending problems was carried out jointly with teams of the oil refinery industry, and for preparing feed mix for dairy cattle. The IBM MPSX (Mathematical Programming System Extended) solver was developed in IBM White Plains in the late 1960s. Some of its first applications in Europe were related to one- and two-dimensional steel cutting stock problem in the steel industry, and production planning in the steel, oil, and petrochemical industries. Interesting OR applications were related to project scheduling of ships and the construction of buildings.

New theory development and solver implementation for mixed integer linear optimization (MILO) by academia, competitors, and IBM USA / Europe in the late 1960s and early 1970s allowed users to carry out more realistic projects in various fields. The implementation of several releases of the mixed integer programming (MIP) module in MPSX by the IBM Paris Development group converted the system into the de-facto standard MILO in the optimization field. The group was first headed by Gerard Hentges (coming from IBM White Plains) and later by Jean-Michel Gauthier, who with Michel Benichou and Gerard Ribière were the architects of the MIP module, (Benichou et al. 1971). The development of improved branch-and-bound (B&B) strategies for selecting the branching nodes and branching variables allowed the solution of problems of up to 16383 constraints and 4095 integer variables. Based also on the developments in academia and by competitors, the version MPSX/370 included advancements in B&B strategies, mainly refining the estimation of the solution value of the problem and the pseudo-costs of the integer variables criteria for branching node and branching variable selections, respectively. Some advances were made for handling models with special structures, special ordered sets of type 1 (SOS1), and others. The development of the latter benefited from innovations in the literature and competitors, see the seminal papers by Beale and Tomlin (1970), Beale and Forrest (1976), Forrest, Hirst and Tomlin (1974), and Escudero (1988). The first developments and results obtained by the IBM Paris group for solving MILO problems with MPSX/370 are shown in Gauthier and Ribière (1977). Besides the MIP developments mentioned above, the key feature that made MPSX the most influential MILO solver in the 1970s and 1980s was ECL (the Extended Control Language, written in PL/I). It allowed users to write their own functions and strategies for problem solving based on partial results in the status of the B&B tree.

The iteration between the user and the system, made possible by ECL, made MPSX a precursor of later standard approaches to tackle difficult MILO problems. The influential feature of SOS1 in MPSX/370 is reported in Escudero (1979), where a relevant application is reported. The usefulness of exploiting these features was shown in a multistage planning problem that was carried out to optimize the dimensions of warehouses and piers for maritime fleets in a big Spanish steel company for the decade 1974-1983. The MILO model had 1000 constraints, 568 continuous variables and 432 binary ones. Without exploiting the SOS1 structure, the quest for the optimal solution in MPSX/370 (where the optimality gap limit was set to 2%) was interrupted after 100 hours of branching on an IBM 360/65 computer. The optimality gap of the incumbent solution was 20%. Grouping the binary variables in 72 SOS1 sets, considering the mentioned dimensions as weights of the variables in the sets, and choosing an appropriate SOS1 branching ordering, a feasible solution was found in 7 minutes of branching, satisfying the 2% optimality limit).

Theoretical and practical contributions on MILO model tightening by valid inequalities generation and by considering different separation procedures have been made by IBM researchers working in IBM Yorktown Heights, New York Scientific Center, Philadelphia Scientific Center, IBM Development Centers in Paris and Rome, and IBM Scientific Centers in Heidelberg, Madrid, Pisa and Rome, among others; see the works of Guignard and Spielberg (1977), Crowder, Johnson and Padberg (1983), Johnson, Kostreva and Suhl (1985), Dietrich and Escudero (1992), and Dietrich, Escudero and Chance (1993), among others. The technical responsibility for MPSX/370 was moved from Paris Development Center to Rome Development Center in 1979, where it remained until 1985 when IBM stopped development of MPSX. During that period, new features were added to the MPSX solver related to probing, variable fixing, constraint redundancy, tightening, as well as valid cut inequalities generation.

Independently of the MPSX solver, IBM researchers in Europe were active in the 70s and 80s on developing OR algorithms for scientific reasons as well as for helping customers on nonlinear programming, see e.g., Escudero (1984a, 1984b, 1986) for hydro-thermal energy generation planning. They also provided specific MILO algorithms for problem solving in industry and government. It is worth noting the work carried out in the 1970s, by the IBM Madrid Scientific Center, located at that time in a Spanish university, on linear and nonlinear multispectral image classification by modeling and solving the problem in MPSX/370. For testing the accuracy and efficiency of the model, named DISMIP, one of the testing environments was the following: The classification of an agricultural area in several land use categories (rice, water, swamp, dry land, bare soil, sand beach, and irrigation) in the Spanish Ebro Delta river, by considering data from a satellite Landsat-1 image of Northeastern Spain, (Rebollo and Escudero 1977).

IBM had divisions and development centers devoted to helping improve the efficiency of its own manufacturing plants. One of those initiatives was the German Manufacturing Technology Center (known as GMTC) aiming to provide service to German plants; one of them was in nearby Boeblingen (about 1 km distance). The IBM Montpellier (France) plant had its own highly reputed OR department.

**Contributions to Related Fields**

IBM researchers also pioneered various database management systems that contributed to the success of many OR projects. Edgard Frank “Ted” Codd proposed the relational model for database management while working at IBM San Jose in 1970. This model went on to become the standard of most database systems. In 1973, the San Jose Research Laboratory (today’s Almaden Research Center) developed a database system called System R (“R” for relational) to provide the relational theory with what is called an “industrial-strength implementation.” The project produced an extraordinary output of inventions that became the foundation for IBM’s success in the field. The following year, Don Chamberlin and Ray Boyce at IBM San Jose invented SQL (Structured Query Language), the most widely used computer language for querying relational databases to this day.

Another field IBM contributed to was intelligent management of transportation systems. When Denos C. Gazis joined IBM in 1961, he began using computer systems for traffic control. This work led to IBM selling a computer to the Traffic Commissioner of New York City. Gazis compiled his research in the 1974 book *Traffic Science *(Gazis 1974) and again in 2002’s *Traffic Theory* (Gazis 2002). Around the same time (1967-1972), IBM’s Jerrold Rubin provided software called TPACS to the airline industry for airline crew scheduling. General purpose integer programming-based optimizers applied to crew scheduling began to replace TPACS in the 1980s. In the 1980s and 1990s, IBM encouraged its researchers to get more involved with customers. One such example in this space was John Forrest’s works on crew optimizations with Ranga Anbil at American Airlines. Anbil eventually joined IBM Research before setting up a company supporting the airline industry.

While the computer industry had grown to include significantly more players, such as Cray, HP, and Dell, and start-up culture enabled disruptive custom silicon firms, IBM has maintained a key presence entering the new millennium. This is exemplified by the recognition the company and its employees has received from INFORMS, the successor organization to ORSA and TIMS. In 1999, the Company was awarded the INFORMS Prize “for its innovative and effective use of operations research and management science (OR/MS) methodology throughout the company”, acknowledging “the widespread application of OR/MS studies, models and software [that] has resulted in significant performance improvement (INFORMS n.d.b).” That same year, a team with IBM’s Personal Systems Group was awarded the Franz Edelman Award “in recognition of their global supply chain re-engineering effort to improve customer responsiveness with minimal inventory (INFORMS n.d.a).” Furthermore, thirteen INFORMS Fellows spent significant portions of their careers as permanent employees of IBM (see Table 1). No fewer than ten other INFORMS Fellows had early career and consulting stints with the company. IBM was a founding member of the INFORMS Roundtable. Delegates have included Chacko Abraham, Brenda Dietrich, and Arnold Greenland. Corporate engagement with the organization remains strong as IBM has sponsored the INFORMS Service Science Section’s Student Best Paper Award since 2018 to celebrate high-quality research generated by PhD students. Additionally, the company was an early and frequent sponsor of the Women’s Forum and the Minority Issues Forum at conferences.

Ralph Gomory (2002) | Alan Hoffman (2002) | Ellis L. Johnson (2002) |

Peter Norden (2002) | Philip Wolfe (2002) | Grace Lin (2006) |

Harlan Crowder (2006) | William Pulleyblank (2007) | John Forrest (2007) |

Nimrod Megiddo (2009) | John Tomlin (2009) | Brenda Dietrich (2010) |

Peter Haas (2016) |

Table 1: IBM-affiliated INFORMS Fellows

**Author**: Reed Devany

**Note**: The author would like to thank Richard Cottle, Harlan Crowder, Brenda Dietrich, and John Forrest for their helpful contributions and comments.

The section on IBM and OR in Europe was contributed by Laureano Escudero.

**Edited by**: Mark Eisner, Douglas Shier and Linus Schrage

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### Associated Historic Individuals

Crowder, HarlanFisher, Marshall L.

Gass, Saul I.

Gazis, Denos C.

Gomory, Ralph E.

Hearn, Donald W.

Hoffman, Alan J.

Hu, Te Chiang

Johnson, Ellis L.

Karp, Richard M.

Kimball, George E.

Kleinrock, Leonard

Markowitz, Harry

Montroll, Elliott W.

Nahmias, Steven

Norden, Peter V.

Pierskalla, William P.

Shubik, Martin

Takács, Lajos

Thompson, Gerald L.

Tomlin, John

Veinott, Jr., Arthur F.

von Neumann, John

Wolfe, Philip