Operations Research in the Stewart School

Jan 1, 2012 | Atlanta, GA

Try this (if you have little else to do): Pick a buddy, then grab a dozen people off the street—okay, to make it a little more interesting, when you visit for homecoming, just select a dozen people on campus—and ask them to define the field of study known as “operations research” (OR). Before doing this, however, make a wager with your friend: If at least two responses are the same, you will purchase for him two season tickets to the Atlanta Thrashers next year; otherwise, he has to mow your grass and rake leaves for a full year. Assuming he takes you up, how do you like your chances? Well, as they say: You have nothing to lose and everything to gain (hint: there is a very good chance you’ll be staying out of your yard for a year, but, if on the off-chance that you lose the bet, you won’t have lost too much on the purchase of those hockey tickets, since the Thrashers became the Winnipeg Jets last spring).

What’s in a name?

No matter the stakes, your bet was pretty secure because there is a very high probability that those dozen responses to the query posed above will be all over the proverbial map; some will have to be tightened to even reach the level of “nebulous.” And, even if a couple of descriptions are the same, it is entirely likely that both are vague, outmoded, or simply nonsensical. So is there a punch line here—a resolution of a riddle? Actually, there is not (at least from this author), but there is an article, and its theme is this: We don’t really have an air-tight definition of OR either, but we do believe that in the H. Milton Stewart School of Industrial and Systems Engineering (ISyE), we do it at least as well as anybody and quite possibly better than any other academic program.

In order to have at least a fixed point, suppose we go straight to the description offered up by what many will argue is the flagship professional society representing this identity-conflicted field. The Institute for Operations Research and the Management Sciences (INFORMS) tells us on their website, www.informs.org, that “operations research is the discipline of applying advanced analytical methods to help make better decisions.” Paraphrasing the well-known sentiment expressed by Churchill regarding democracy as a system of government, this characterization of OR might well strike you as not so hot, but then none of the others we know about appear to be any better. Indeed, the professional society recently rolled out a somewhat slicker marketing version calling OR the “science of better.” Take your pick.

No matter one’s view on the definitional issue, it does remain that OR seems to occupy at least “brand name” status. Even if they can’t agree on a formal description (this is not a new frustration but rather one dating to at least the Second World War when the phrase was first introduced), most people queried will certainly know the name. Universities, after all, teach plenty of courses directly related to if not actually titled Operations Research, many award degrees (mostly graduate) specifically designated as OR, and some even have Operations Research in their academic program name.

If we return to the INFORMS- sponsored version stated above, we are also instructed that the section in the description referring to “advanced analytical methods” includes the following fundamental methodologies: simulation, optimization, probability, and statistics. Okay, let us check the fall 2011 roster of fifty-one academic faculty with full-time appointments in ISyE. From that list, let us apply a conservative, if not fairly stern test that counts only faculty members who either originated and/or teach an advanced course in statistics, optimization, or stochastics (probability/simulation).

Since you’re reading this, I ask that you trust me to count for you; I get thirty- three. This means that nearly two of every three ISyE faculty members are apparently “doing OR” under the INFORMS description. But then if you turn back and focus on the word “applying” from the INFORMS description, and add those faculty who are, by their own admission, demonstrable and routine users of the stated methodologies, I can easily identify at least ten additional faculty that can be counted.

So, thirty-three for sure and possibly as many as forty-five of fifty-one current ISyE faculty members are either teaching and conducting research directly in the methodologies of OR as defined by no less than the parent professional society or are doing work that routinely draws upon OR tools in their research applications. Would not even the most casual observer wonder: “Why isn’t it the Stewart School of Operations Research?” Well, it probably could be; however, tradition and history play a major role in negotiating that question and that’s how it should be. Indeed, it is quite common for industrial engineering (IE) programs to have much (or at least some) activity in operations research; to be sure, many ISyE faculty who are counted in the forty-five above have their educational backgrounds firmly rooted in modern industrial engineering and fully appreciate and respect that identity. On the other hand, many, especially from the gang of thirty-three, have their degrees in mathematics, statistics, and operations research. The larger point is, though, that the boundaries defining fields where operations research is done legitimately are blurred at best and without a doubt overlap substantially.

In fact, one of the reasons that your bet in the opening paragraph was pretty safe is that on the spectrum of academic programs at universities, there are a host of points where operations research is getting done, more or less. This easily includes programs in mathematics, statistics, computer science, various other engineering departments, and certain business schools. So, those dozen “random” people indicated above, chosen, and asked to define OR, might well know the discipline and offer honest descriptions of just what they think it is, at least what it involves, but those descriptions will likely be tailored or influenced by their respective domains and academic cultures.

Academics

If you’re a prospective student (at any level, but especially for those at the graduate level), and you want to avoid any coursework requirements covering OR methodology, you can save the cost of application to ISyE. In the current list of active courses taught by ISyE faculty, nearly forty-five are devoted explicitly to methodology in optimization, stochastics, or statistics. A half-dozen of these are at the undergraduate level, in support of the BSIE; the remaining courses are Master’s and doctoral-level courses.

At the master’s level, the School offers eight designated degree options, two of which are focused explicitly on OR and statistics (MSOR and MSStat, respectively) even though most of the other master’s (MS Industrial Engineering, MS Health Systems, etc.) also require OR methodology courses somewhere in their programs of study. At the doctoral level, the PhD in OR is (surprise) intensive in its requirements of advanced methodology courses, particularly in optimization and stochastics, but the PhD in IE, which breaks into four specializations, has heavy doses of the very same courses sprinkled throughout depending upon one’s chosen specialization, e.g., supply chain engineering, economic decision analysis, etc.

Again, these methodology courses are the hard-core, fundamental courses, taught almost exclusively by those thirty-three faculty members mentioned earlier. Naturally, we also teach many additional courses pertaining to the classic as well as contemporary application domains commonly identified with our fields and that apply these methodologies. Faculty whose primary responsibility is covering those courses constitute, by and large, the others that produced the larger estimate of forty-five “OR- related” faculty.

People and Research

In this section, we profile just some of the School’s senior faculty members who make us look particularly good in the world of OR as we have interpreted it. It needs to be stated that many not on this list have equally justifiable cases to have been included. As genuinely uncomfortable as this dilemma is for this author, it does serve to corroborate the exceptional strength of the OR faculty in the School.

The position that the School has risen to among the elites in the context of OR owes its origin to a small number of individuals who, upon their arrival, sent clear signals to the broader community that ISyE was ready not only to build upon existing competence but also to move to the next level. The obvious pioneer in this group would be George Nemhauser (PhD in Operations Research, 1961, from Northwestern). Attracted from Cornell in 1985, he came to Georgia Tech as the Russell Chandler Chair, the first endowed chair in ISyE. He also owns the remarkable distinction of being the first individual at Georgia Tech to be elected to the National Academy of Engineering while a sitting faculty member (1986). Long noted for basic work in integer programming and combinatorial optimization, a hallmark of much of his research career has been influenced by an attraction to interesting applications that validate his methodological work. Many claim such interests, of course—George Nemhauser actually does it. Working with generations of students and colleagues spanning more than forty years, he has done impactful work in a broad spectrum of practical settings, including vehicle routing, production, transportation, and even sports scheduling.

Insisting that work in applied areas possess serious research content, he routinely attracts doctoral students who come from strong, theoretically rounded backgrounds (and who are recruited precisely because they do), but who also are interested in seeing their methodological work validated in practical settings. Always supported from sources typically aligned with funding basic/theoretical work (e.g., NSF, ONR, etc.), he is one of our most successful faculty in attracting industrial sponsorship. Bridging the divide between theory and applications in a program of our stature and at the level exhibited by George Nemhauser is a rare feat.

A giant in integer programming, Ellis Johnson (PhD in Operations Research, 1965, from Berkeley) has been directly associated with no fewer than three of the most famous and influential names in the entire history of methodology fundamental to Operations Research. His PhD advisor was George Dantzig, the father of linear programming. While at IBM (and beyond) and working with Ralph Gomory, he of cutting plane theory that bears his name, Ellis produced elegant results pertaining to so-called corner polyhedra. Finally, with Jack Edmonds, the person who probably more than anyone is responsible for creating the prominence associated with the discipline of combinatorial optimization, Ellis authored fundamental results pertaining to the storied Chinese postman problem that still stand as seminal in the field.

In 1988, he began a substantive collaboration with George Nemhauser and others in ISyE, including several long-term faculty visits. Then upon retirement from the mathematical sciences group at IBM's Watson Research Center, he joined the School as a permanent faculty member, taking the Coca-Cola Chair in 1993. If there is a “double-play combination” most responsible for sending a message that ISyE was ready to join the major leagues in OR, it would be the early presence of the Nemhauser-Johnson tandem.

But as renowned as his work in fundamental integer programming theory is, Ellis Johnson’s name also resounds in an application area that he, almost single-handedly, invented: airline operations research. His research, applying the tools from linear and integer programming and network flows, has enjoyed enormous success in modeling and treating myriad, hard transportation and scheduling problems specific to the airlines; his influence in passing this expertise on to numerous students and younger colleagues is well known. His stature is corroborated as the recipient of a number of research awards of the first rank; he was elected to the National Academy of Engineering in 1988.

The traveling salesman problem (TSP) is arguably the most celebrated example in combinatorial optimization. Required is that one find a minimum-distance itinerary that visits all of the cities in a set exactly once before returning to the starting point. While particularly easy to state, the problem is notoriously difficult. In fact, its position as one of the hardest of hard problems has been formalized by being named one of the so-called Millennium Problems by the Clay Mathematics Institute. Still, much work continues on and around this perplexing problem.

Its applications are myriad in the real world and research on the problem itself, while not close to a formal resolution, spawns important results in related areas along the way; this is what forms good science, and ISyE has the MVP in this game.

Bill Cook (PhD in Mathematics, 1983 from the University of Waterloo), holder of the Chandler Family Chair in the School, combines knowledge of and a personal research record pertaining to the TSP that may have no rival anywhere in the world. He has written the definitive book on the subject and was awarded the prestigious Lanchester Prize for the effort. Importantly, he, along with research colleagues elsewhere, have been able to verify optimal solutions for the largest known instances of a special but important class of TSPs. Bill is one of the world’s ranking researchers in computational optimization. Because of his reputation, he is an in-demand speaker in prestigious, public scientific forums and provides great visibility not only for ISyE but for Georgia Tech and across boundaries that span OR, mathematics, and computer science. He was elected to the National Academy of Engineering in 2010.

If anyone in academia can stake a claim as the ranking engineering statistician in the country if not the world, a safe bet is that it is likely to be Jeff Wu (PhD in Statistics, 1976, from Berkeley). Luckily for us, he holds the Coca-Cola Chair in Engineering Statistics in the Stewart School. Following distinguished careers at Wisconsin-Madison (Statistics), Waterloo (Statistics), and the University of Michigan (Statistics/ Industrial and Operations Engineering), he has continued to conduct cutting- edge research in applied statistics that increasingly blends in and interacts with the activities historically prominent in OR, i.e., optimization and stochastics.

That this is noteworthy follows because if we are to be true to the characterization of OR from  INFORMS, statistics is a staple in the portfolio of methodologies that support the discipline; with Jeff Wu’s role, the strength of that staple is more than secure in ISyE. As a research advisor, he routinely attracts the best doctoral students seeking work in statistics. Importantly, through his personal power of attraction coupled with a judicious hiring policy, he has added a marvelous group of young statisticians who, when added to existing strength, have made the engineering statistics group in ISyE an exceptionally strong one, certainly the best in the country.

With particular expertise in experimental design, he too represents the School in prestigious, international forums. In August of this year, he was honored by giving the famed R. A. Fisher Lecture, named for the legendary statistician. In 2008, he was awarded a prestigious, honorary doctorate in mathematics from the University of Waterloo; he was elected to the National Academy of Engineering in 2004.

The British scientist and writer Jacob Bronowski said: “A genius is a man who has two great ideas.” Now, we know that Bronowski hung out with the great physicists and mathematicians in the first half of the last century, so the application of his claim to that population assumed a pretty lofty bar on what constituted a “great” idea. Still, we can surely understand what his rule implies in general, and in that regard, if there is a candidate in ISyE who would meet the test, it would be Arkadi Nemirovski (PhD in Mathematics, 1974, from Moscow State University).

A world leader in continuous optimization for more than thirty years, he has made three major breakthroughs in the field: the ellipsoid method for convex optimization, the extension of modern interior-point methods to convex optimization, and most recently, the development of a theory of robust optimization. He has won three of the most prestigious scholarly prizes in operations research and applied mathematics: the Fulkerson Prize, the Dantzig Prize, and the John von Neumann Theory Prize. In fact, he was the first individual to have won all three of these awards. Interestingly, when he was awarded the Fulkerson Prize in 1982, he was not permitted to leave his native Russia to accept the honor.

Fortunately, in time, such barriers were dissolved. After some years on the faculty of the Technion in Israel, he was attracted to ISyE in 2005 and presently holds the John Hunter Chair. In 2006, he was honored with an invitation to give a plenary talk at the International Congress of Mathematics. To underscore this achievement, he is the only sitting faculty member from Georgia Tech ever to have been so honored. He was awarded an honorary doctorate in mathematics from the University of Waterloo in 2009.

It takes a certain level of “wizardry” to invent and ultimately present effective algorithms for hard problems that impress the user with their near- primitive level of simplicity, e.g., “How can something this simple, actually work so well?” Meet Manhattan Associates Chair of Supply Chain Management John Bartholdi (PhD in Operations Research, 1977, from the University of Florida), and you’ll likely get some insight. Working often with his students as well as colleagues, John Bartholdi mines deeply for problems of great practical value—notably, ones arising in common manufacturing and logistics domains but that are, nonetheless, inherently difficult at their core. Yet, he manages to produce approaches that yield good quality solutions coupled with efficacy not by taking liberties that dismiss analytical or mathematical insights but to the contrary, by applying them.

His work, employing some old and fairly sophisticated notions from geometry pertaining to space-filling curves in order to produce approximate solutions to various classes of routing problems, is well known and has been applied in a host of practical settings such as Meals on Wheels. Similarly, his “bucket- brigade” notion, which induces a self- organizing phenomenon for assembly lines based on fundamental results in stochastics, is so simple that even ants can appreciate it.  The models have been and still are being used in such real world settings as Subway, Readers Digest, Radio Shack, McGraw-Hill, and many others.

With little debate, most observers (at least those who have been around long enough) would agree that in the early 1980s, the most highly regarded doctoral programs in OR resided at Stanford and Cornell; Berkeley and MIT were close, but maybe a notch below. Lumped together, the four formed something of a closed set in that graduates from those programs tended to join the faculties of those programs. Moreover, honesty compels one to admit that we were simply not competitive in the recruitment of those graduates to ISyE.

However, in 1981, then-School Chair Mike Thomas made a concerted effort to change that state of affairs and convinced Craig Tovey (PhD in Operations Research, 1981, from Stanford) to come to Georgia Tech. Like Ellis Johnson, Craig conducted his work under the icon George Dantzig (who had moved from Berkeley to Stanford). Importantly, he brought a talent and scholarly depth to the School that was influenced by the culture from his Stanford experience and that took root in ISyE through his presence in teaching and research. Earlier in this piece, reference was made to various core OR courses that PhD students endure early in their programs; more advanced versions follow, of course. These are fundamental and quite rigorous courses that cover deterministic optimization as well as courses in applied probability and stochastics. If there is a list of ISyE faculty who could legitimately teach, at the level our best  doctoral students demand, more than two or three of these courses, that list would not be very long indeed, and it would most certainly include Craig Tovey.

This breadth of rigorous, technical talent coupled with genuine depth carries over to his research, the span of which may also be unrivaled in the School, ranging from mathematical models of voting systems to formalisms of graph algorithms, from circuit board assembly to polyhedral combinatorics. He is the only ISyE faculty member to have an Erdös number of 1.

Jim Dai (PhD in Mathematics, 1990, from Stanford) came to Georgia Tech in 1990 as a new assistant professor holding a joint appointment in the School of Mathematics and ISyE. He continued to hold the joint appointment all the way through his promotion to the rank of full professor after a remarkably short period of only eight years beyond graduation. In 2001, he reconstituted his appointment to only ISyE, and in 2007, he was named the Edenfield Professor in the School.

Trained in applied probability and stochastics, one of his major research specializations is in the area referred to as heavy-traffic queuing theory (think of a large call center or a dense roadway network subjected to rush- hour traffic jams). Jim Dai has studied such problems for twenty years.

Using advanced, multidimensional Brownian motion approximations to estimate performance characteristics for such systems, his research has led to important results that yield keen insights into attributes such as queue waiting times, expected lengths of queues, as well as various anomalous outcomes, e.g., is it possible for expected lengths of lines that form to drift off to infinity, yet for servers to have an abundance of idle or free time? (The answer is yes.) He tackles deep, subtle real-life problems with sophisticated mathematical machinery and enjoys unquestioned recognition as one of the top world leaders in the field of applied queuing theory.

Distinction

This is a short section; don’t expect any chants of “We’re number one.” Indeed, there are no formal rankings of OR programs akin to ones read about every spring in U.S. News & World Report.

On the other hand, you can always just ask around and the bet is that a very, very short list will emerge that more or less defines the elite programs in the discipline; the claim is that the OR done in ISyE will be firmly rooted on that list. The eight profiles listed in the prior section could easily have been altered with several substitutes without missing a beat or diminishing the point that is being made. We could have spotlighted younger faculty who are poised or are already starting to earn world-class recognition, colleagues such as Shabbir Ahmed and Santanu Dey in optimization, Ton Dieker in stochastics, and Ming Yuan in statistics. They, and several others like them, represent our future; they would not come to a program like ours were it not for the attractiveness of working alongside world-class scholars already here. Name a major prize or award in or related to OR and applied statistics and somebody on this faculty has probably won it; many will have won several.

This program is simply exceptional and the assemblage of faculty expertise and reputation is arguably second to none anywhere.

Summary

Within the set of similarly constituted or named academic programs,11  ISyE is far and away the largest. But far more relevant, it’s also an exceptionally strong program. Derived directly from the quality of its faculty, this level of strength spans a broad expanse of areas, many of which are unambiguously and fundamentally aligned with the field of Operations research. We began this article on a light-hearted but hopefully somewhat instructive note; we finish with a similar exercise: suppose every academic unit at Tech (schools and departments) was asked to ascertain where its faculty members would relocate at the Institute if their unit were eliminated.  Now, there are some rules: a valid case has to be made that a faculty member actually fits in somewhere else, i.e., where they can teach real courses, sit on committees, and such. However, let us also require that they have to land at a place where their tenure is legitimate, where they could have been hired in the first place, and if not tenured, can earn it within the new unit’s guidelines and standards; that their presence at the new place actually makes the latter better not just that it adds to the workforce. This is a pretty tough litmus test. Against this backdrop, suppose we define the “width” of a unit to be the number of distinct colleges at Tech where at least one member of the evaporating academic unit’s faculty can be taken in legitimately as defined by the test just described. A program with a high- width number implies great breadth and strength that is deep, not cosmetic; those with a lower width, less of both.

So what’s the width of ISyE? At Georgia Tech, there are six distinct Colleges: Engineering (CoE), Sciences (CoS), Computing (CoC), Management (CoM), Architecture (ARCH), and the Ivan Allen College of Liberal Arts (IAC). If we are to compute the width for ISyE, we pull out the current roster and start down the list: where could this faculty relocate (if anywhere)? For sure some would stay in CoE; likely homes would probably be mechanical engineering (for manufacturing) or civil engineering (for logistics or transportation) and maybe others. Some would land in CoM (for operations management, strategic planning, etc.). We even have a couple who could find a home in IAC (for public policy). This calculation gets our width to three, not bad. Now here’s what’s impressive. We have, within our exceptionally strong OR group, faculty members who would be welcomed in the School of Mathematics (CoS) and others, some of whom are interchangeable with the mathematics candidates, in CoC. You’ve seen the profiles of some of these above.

So, ISyE has a pretty solid argument that its width is at least five (who knows, there may be somebody who would make a case for Architecture, but let us not push it). Given that the width of any unit at Tech is bounded from above by six, this is no small thing, but neither do we intend for this illustration to be gratuitous. If you can argue that another school or department at Tech rivals our width, that they can legitimately argue that its faculty could be placed in other college’s units without the latter holding their noses or having the dean twist their arm, then so be it. In fact, you might be hard-pressed to name another IE or OR academic program in the country that betters the Stewart School width at their respective institution. Here, we are only paying attention to the Stewart School, your School, and how it can continue to thrive, knowing that much of its reputation rises and falls with regard to its presence in the field of OR—no matter whose definition is applied.

For More Information Contact: 

Barbara Christopher
Industrial and Systems Engineering
404.385.3102