Theoretical Research at ISyE


Barbara Christopher

Stewart School of Industrial & Systems Engineering


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Summary Sentence:

A significant amount of theoretical research in ISyE takes place within the fundamental methodologies that are core to our discipline: mathematical optimization, stochastics and simulation, and statistics.

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  • ISyE's Titans of Theory: Santosh Vempala, Jeff Wu, George Nemhauser, Alex Shapiro, Arkadi Nemirovski ISyE's Titans of Theory: Santosh Vempala, Jeff Wu, George Nemhauser, Alex Shapiro, Arkadi Nemirovski

By Santanu S. Dey and R. Gary Parker

The academic concentrations supported by the H. Milton Stewart School of Industrial & Systems Engineering are myriad. Its graduates at all levels reflect this variety by making substantive contributions in a broad span of important practical settings, such as supply chain logistics, manufacturing, health care, finance, natural systems, energy, and others.

It is also the case that ISyE places great value in maintaining a strong theoretical research presence in our fields, and, in parallel, strives to educate the next generation of scholars so that they are well-positioned to thrive as contributors to that effort. The concrete value of our emphasis on theoretical work and, by extension, the profession we serve, deserves a closer look.

Sliding into pedantry is easy when it comes to defining theoretical research. The term by its very nature describes a relative concept. What could be considered “theoretical” by a software engineer might easily be declared “very applied” by a number theorist. Here we have used the “you-know-it-when-you-see-it” rule-of-thumb. Accordingly, a significant amount of theoretical research in our school takes place within the fundamental methodologies that are core to our discipline: mathematical optimization, stochastics and simulation, and statistics.

Theoretical research is often motivated by applications

Engineering, by definition, is an applied field; its practitioners solve important and real- world problems, often in incredibly creative and ingenious ways. Engineers draw their most effective technical skills from the hard sciences, most prominent among which are physics and chemistry. In the final analysis, engineers are users, doers. This certainly includes industrial engineers, with the exception that their core science base tends to be mathematics and statistics.

As is the case in most fields, the easy systems-level industrial engineering problems get solved routinely, and the genuinely hard ones ultimately prove resistant to existing methodological tools. Those hard problems don’t go away, leaving shakier options for their treatment, including the design of ad hoc fixes or approximations that may be clever and work in some cases but that may also fail miserably in others. But seeking ways to solve — or at least handle effectively — the hard problems is where the need for advances in existing theory most clearly reveals itself. Necessity, it’s true, is the mother of invention.

A commonly cited example — one that contributed directly to the development of what became the field known as Operations Research (OR) — relates to efforts by the British, in the years just prior to the outbreak of World War II. A multidisciplinary team of scientists, including many Nobel laureates, was assembled to conduct experiments on how fighter aircraft could be better deployed, based on radar-generated information. The need for success was obvious, and the groundbreaking work ultimately produced proved to be an important factor in winning the Battle of Britain. Similar teams helped to break enemy codes, optimize troop deployments, and even understand nuclear chain reactions.

Our methodological fields — the theory-oriented ones identified in the introduction, and that are prominently identified with ISyE — are also rife with similar stories where this scenario has played out. Typical are settings that benefit, sometimes in very practical ways, from results focused on seemingly abstract research pursuits such as understanding deeply how known methodologies work, generalizing and extending what is known, and, possibly, establishing formal limits regarding what can be known.

Some examples of famous outcomes of theoretical research include the well-known work of George Dantzig, conducted shortly after WWII, including his invention of the simplex algorithm for solving linear programs; John von Neumann’s anticipation of duality theory, actually motivated by discussions with Dantzig during this same period; Stan Ulam’s development in the late 1940s, following work related to the Manhattan Project, of the process that became Monte Carlo simulation; Ralph Gomory’s circa 1960 work that set the basis for a theory of cutting planes that played a pioneering role in initiating the field of integer programming; Jack Edmonds who in the mid-1960s coined the phrase “good algorithm,” and demonstrated the relevance of its formalization by presenting an ingenious solution for the so-called matching problem — which in turn ushered in the field that would became combinatorial optimization; and Richard Karp who, in the early 1970s, showed how apparently different problems were fundamentally equivalent in that either they all were solvable by a good algorithm or none were.

Common to all of these iconic contributions and developments that derived from theoretical research efforts is that they were authored by people educated and trained in mathematics. That this level of formal mathematical expertise was applied in producing these fundamental results is, of course, not a requirement, but neither should it be a surprise; such is the nature of the mathematical machinery and rigor needed to make substantive progress. And, no one should find it peculiar that some of the most productive theoretical research success stories affiliated with ISyE have been authored by faculty trained at a certain level of applied and even pure mathematics.

The short historical list of work we’ve identified above accurately reflects the complexion of what constitutes fundamental research efforts as they would be viewed and practiced by many who conduct their scholarly work in methodological areas directly supported by ISyE. With this deep emphasis on theoretical research, traced largely from the early to mid-1980s, the School is among the elites in terms of its theoretical research activity and its corresponding impact on our fields. We are in the company of such institutions as MIT, Stanford, Berkeley, Columbia, and Cornell.

By any measure, at least a third of ISyE’s full- time academic faculty are active in theory-based research as their primary focus — a remarkable number for industrial and systems engineering programs. In some facets of our methodological disciplines, our respective faculty have few (if any) peers.  The ISyE faculty boasts some very famous scholars. In particular, the contributions to discrete optimization by George Nemhauser, convex optimization by Arkadi Nemirovski, stochastic optimization by Alex Shapiro, graph theory by Robin Thomas, design and analysis of algorithms by Santosh Vempala, and industrial statistics by Jeff Wu are unparalleled in the world.

Theoretical research breeds new application areas

Why even bother with something as obscure as theoretical research? The answer is that not much gets done without it. In fact, one of the outcomes of basic theoretical research is that  it very often produces valuable and important practical results as spin-offs, especially as the work progresses. New questions often arise that open new avenues for fundamental research; much of this occurs along the way, even if the original problem being pursued remains elusive or resistant. It’s not at all uncommon for these so-called spin-off results to sometimes rival, ifnot overshadow — in both elegance and utility — the anticipated outcome when the research was initiated

Sometimes knowing that a tool has been invented for solving a problem in one context facilitates the search for related ones, where the newly discovered methodology can be applied. For instance, similar to the research group working on behalf of the British military, groups of interdisciplinary scientists in the U.S. army were formed to protect convoys, improve anti- submarine warfare, and increase success with bombers during the war. Then, by the 1950s, the methodological tools developed explicitly to solve military problems began to be useful in addressing many other postwar applications.

The typical paradigm is as follows: A scientist trained in various theoretical methodologies is introduced to a new and complex (and perhaps pressing) practical problem. The setting in which the problem arises need not be familiar  to the scientist. Usually, the first step is to state this problem in a familiar mathematical form. Once this possibly difficult feat is accomplished, known algorithms, mathematical techniques, and theoretical results can take over to solvethe problem. Indeed, the theoretical research accomplishments mentioned in the previous section, along with significant contributions by faculty at ISyE, are used daily to solve new problems for industry, business —  and humanity in general.

The above described process often involves heavy lifting; there are no easy problems anymore, and seldom does the resolution of these problems follow as a routine or obvious application of what is known, even if the latter is a newly discovered outcome of an arduous theoretical effort. And, even knowing that a problem is solvable in theory does not mean that the solution will be instantaneously useful in business and industry. Often a gap needs to be bridged in moving from theory to practice, which can require some effort and time. Still, knowing that a problem is solvable, even in a theoretical sense, is a major hurdle to overcome if any hope for practical impact is to ultimately be realized.

Naturally, when the progression from theory to algorithm-creation to practical application plays out, limits inevitably will be reached. Sometimes, known theoretical methodologies will be stymied. But then the investigative cycle repeats, and ultimately progress is made. This understanding is what motivates the research efforts of many of the aforementioned faculty in ISyE. That the School has attained its elite status as a center of serious theoretical research validates their efforts.

Final remarks

The intent here has not been to claim, or even suggest, that all theoretical research in our methodological fields can be painted with the same colors. The quality of theoretical work, no matter the field or discipline, can sometimes only be judged by experts, and certainly, its true worth is often gauged over time. Above all, since theoretical research is basic research, its value — or the justification of its worthiness for pursuit — cannot be exclusively influenced by utilitarian requirements or prospects of immediate payoff. For the payoff to become obvious and substantial can take time.

Theoretical research of the sort that we’ve been addressing here requires a great deal of support for its development. It’s true that much of this support involves material resources such as time and money, but equally important is the need for support in terms of a strong institutional commitment in the endeavor—a genuine belief that a serious engagement in theoretical research is valuable and important. While ISyE has been a proud producer of strong, applications-focused research, it has also been enormously successful in building a strong and visible presence in the extremely competitive field of theoretical research. It is crucial that the School continues to solidify its place among those few, highly regarded academic programs with which it has earned the right to be considered a peer. The strongest evidence serving to corroborate this intention to stay at the theoretical forefront, in terms of quality and level of activity, can be gleaned from ISyE continuing to add young  and exceptionally talented faculty to its roster. Many of these young stars were attracted by the heritage of excellence in fundamental research that has evolved in ISyE over the last 30 years, and it will be up to them to continue it.

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School of Industrial and Systems Engineering (ISYE)

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isye, theoretical research
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  • Created On: Nov 10, 2015 - 8:17am
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