Research at MIT
The Operations Research Center
This coming April twenty-fourth, the MIT Operations Research Center (OR Center) will celebrate its fiftieth anniversary. We will commemorate our anniversary with two speakers from each of the past five decades, providing their perspectives and memories of their time in the OR Center and the events in OR that helped shape the decade. The following day, we will continue our celebration by holding a joint meeting with the INstitute for Operations Research and the Management Sciences (INFORMS), which is our professional society in the United States.
In this article, I will discuss the beginning of the OR Center, the OR Center today, some research at the OR Center, and more information about the anniversary. But first, "What is Operations Research?"
What is Operations Research?
This question haunts many of us who refer to ourselves as Professors of Operations Research, because we don't have a satisfying answer. I remember trying to explain it to my mother so many times when I was an assistant professor, that I wrote up a 25-word description that she carried around in her wallet in case anyone would ask.
The difficulty of defining Operations Research is evidenced from a brief discussion that took place on the SCI.OP. Website in 1999 [SCI.OP-RESEARCH Digest V6 #37. http://mat.gsia.cmu.edu/ORCS/JUN1700/0890.html ], which is a site for discussions of topics in OR. One student from Italy wrote: "[Can] somebody tell me the definition of Operations Research?" The first response was "No, because there really isn't such a thing as THE definition of OR . . .. " The second respondent to the query quoted from the 4th Edition of Hillier and Lieberman's text on Operations Research, which says the following:
"In summary, operations research is concerned with optimal decision making in, and modeling of, deterministic and probabilistic systems that originate from real life. These applications, which occur in government, business, engineering, economics, and the natural and social sciences, are largely characterized by the need to allocate limited resources. In these situations, considerable insight can be obtained from scientific analysis such as that provided by operations research."
The third respondent to the query said:
"Defining OR exactly is probably an NP-complete problem, requiring an exponentially expanding number of qualifications and exceptions. So . . . [I will give] you a close approximation . . .. 'OR is the mathematics of decision-making.' "
While the phrases from Hillier and Lieberman are quite useful, I agree with the third respondent, and like his approximate definition, except that it omits any mention of the practice of decision making. I also like the following definition at the INFORMS Website: "Operations Research (OR) is the professional discipline that deals with the application of information technology for informed decision-making." Unfortunately, this definition omits the mathematics of decision making. I think a combination of the previous two definitions would offer a better description, and so offer the following:
Operations Research is the professional discipline that develops and applies mathematics and scientific approaches to support informed decision-making and to improve processes.
Incidentally, it's fewer than 25 words long, and there is no way that my mother would remember it without having it written on a piece of paper.
The Operations Research Center
Professor Philip Morse, the founder of the Operations Research Center, played a pivotal role in the development of operations research in America. Morse's role in the development of operations research dated back to 1942, when he recruited a group of scientists to recommend actions for the U.S. Navy on antisubmarine warfare. This group's recommendations on resetting detonation depth for air-dropped depth charges, combined with better search tactics, increased the sinking of enemy submarines by a factor of five [J.D.C. Little, "Philip M. Morse and the Beginnings" Operations Research 50 , (2002), 146-148]. Subsequently, the group expanded its role and became known as the Operations Research Group (ORG), the first group with that name in the U.S. By the end of the war the ORG had over 100 analysts. Morse was awarded the Presidential Medal of Merit in 1946, the nation's highest civilian award.
Morse helped found the Operations Research Society of America (ORSA) in 1952, and served as its first president. ORSA was later merged with The Institute of Management Science (TIMS) in 1995 to form INFORMS. He also helped establish the International Federation of Operational Research Societies (IFORS) in 1953, the same year in which he started the OR Center at MIT. Morse's first doctoral student was John Little, who among his many honors, was the first president of INFORMS, and is one of 13 current MIT Institute Professors.
The OR Center is MIT's oldest running interdepartmental program, and has both a doctoral and an SM program. Today, it has more than 45 affiliated faculty, approximately 40 doctoral students, and 10 masters students. Most people agree that it has one of the best doctoral programs in OR in the world, and is arguably the best. (There are no official ratings.) The OR Center students are passionate about the field of operations research, and they genuinely support each other in their striving for academic excellence and their efforts to create community. To get a better sense of the OR Center students, I highly recommend reading some of their comments at http://web.mit.edu/orc/www/letters.html .
Research at the OR Center
The OR Center is interdisciplinary, and our graduate students develop OR methodologies to advance research in many different disciplines. The fields of study to which OR students contribute is almost unlimited. Over just the past five years, OR Center students have written theses that contribute to each of the following areas: (1) Auctions and Pricing, (2) Finance, (3) Health Care Management, (4) Machine Learning, Statistics, and Data Mining, (5) Marketing, (6) Music, (7) Operations Management, and (8) Telecommunications. In addition, our students have developed methodologies that are not field specific.
Here are four examples of Ph.D. research carried out over the past five years. I chose them because they help give a sense of the breadth of research in the OR Center.
Clustering is a fundamental and widely applied methodology used to understand structures in large datasets. Clustering techniques generally assume (unrealistically) that there is no measurement error, or uncertainty, associated with data. Mahesh Kumar, in his PhD thesis entitled "Error-based Clustering and Its Application to Sales Forecasting in Retail Merchandising," developed a new clustering method that explicitly incorporates error information associated with data in cluster analysis. His technique outperforms traditional methods such as k-means and hierarchical clustering on simulated data. Kumar further demonstrated the effectiveness of the new clustering method in producing improved sales forecasts in retail merchandising.
Revenue Management for Telecommunication Networks
Airlines have made billions of dollars through the development of the science of yield/revenue management, viewing seats as perishable inventory and controlling fares intelligently based on available capacity. Can this experience be applied to telecom networks? Pundits believe "yes," but have yet to develop a framework for doing so.
In his PhD thesis entitled "Yield Management for Telecommunication Networks: Defining a New Landscape," Salal Humair (i) argues for basing telecom yield management on "innovative" services explicitly designed to use only spare capacity; (ii) proposes a framework to simplify related decision modeling; and (iii) articulates several "innovative" telecom services and models illustrative of decision problems arising in their operation.
Optimal Influenza Vaccine Strain Selection
In recommending which strains of influenza to include in annual vaccines, the World Health Organization (WHO) attempts to match the vaccine strains with forecasted epidemic strains. This strategy does not take into account expectations that a vaccine may be rejected by a vaccinee's immune system because of previous exposures to influenza. In his PhD thesis entitled "Optimization of Influenza Vaccine Strain Selection," Joseph Wu formulates the annual vaccine strain selection problem as a stochastic dynamic program while incorporating information on residual immunity. The optimal solution outperformed the WHO policy, but only marginally, and demonstrates that the WHO policy is nearly optimal.
Pricing a Derivative Security Using Partial Information
How should one estimate a random quantity when only partial information on its distribution is known? In her PhD thesis entitled "Moment Problems in Probability and Finance," Ioana Popescu addresses this estimation problem when only means, variances, or possibly other "moments" of the distribution of the random quantity are known. She develops efficient techniques for solving these moment problems using convex and semidefinite optimization. Her results answer important questions in financial economics such as how to price a derivative security given partial information on the underlying asset.
The symposium is expected to be accessible to all MIT faculty, and there is some extra space available for faculty who want to attend. If you are interested, please contact me.