Keys to Expanding O.R. Discipline

 For many years members of our profession have been concerned over the general lack of awareness of and appreciation for our discipline. Clients in the private and government sectors, upon hearing descriptions of how I propose to address their issues and concerns, frequently respond that they are impressed with my mathematics skills (even though I go to great lengths to keep these discussions and presentations at a very nontechnical level). Despite our attempts to explain otherwise, students frequently refer to their introductory OR/MS courses as advanced statistics (somewhat understandable in my case since I also teach a doctoral-level sequence in linear models and so am closely associated with statistics by my students, but I frequently hear of this occurring at universities around the world). I constantly need to remind my academic colleagues from other disciplines that while I frequently write code and create algorithms to solve problems, I did not earn my Ph.D. in computer programming.

Of course, we would be better understood and appreciated if the public were better educated about what OR/MS is and what it has to offer. Gary Lorden, who gave a terrific plenary talk at the 2005 INFORMS Conference in San Francisco on his role as the mathematical consultant to the CBS prime time television series “NUMB3RS”[Cochran, 2005], has encouraged the show’s writers to incorporate the phrase “operations research” into a script. The writers have come tantalizingly close (I watch the show regularly and recall hearing references to network analysis, game theory and risk analysis) but have never asked a character to utter the simple phrase “operations research.” While Lorden does discuss operations research (pp. 164-165, 169) and management science (p. 164) in his book, “The Numbers Behind NUMB3RS: Solving Crime with Mathematics” (which he coauthored with Keith Devlin – NPR’s Math Guy), something he shared one evening during the 2005 INFORMS conference put this problem into perspective for me.

The writers of “NUMB3RS,” he confided, look for mathematics terms and phrases that sound scientific and intriguing. Phrases such as “Markov Chains,” “Bayesian Inference” and “machine learning” intrigue general audiences, while phrases such as “operations research”and “management science”sound mundane and vague. Ironically, I came away from this conversation believing that the writers are convinced the viewing public likes to view us as obtuse and inaccessible.

I came away believing that the writers are convinced the viewing public views us as obtuse and inaccessible.

I know of several interviews given by operations researchers (including myself) during which the interviewee used the term “operations research” or “management science” only to find when reading, watching or listening to the final version of the interview that this portion had been edited out. Again, the interviewer and producer have likely determined that these phrases are too ordinary sounding or are too difficult to explain sufficiently in a short amount of time or space.

So what are we, as teachers and practitioners of operations research and/or management science, to do? Why has operations research failed to gain the level of awareness and appreciation it deserves outside of the discipline? I believe the answer is comprised of three interrelated elements (none of which I can lay claim to have realized independently):

1. The difficulty in succinctly defining operations research. The breadth of our discipline is remarkable and stunning; this is a primary reason I was attracted to operations research, and I suspect many of you share my feelings. I cannot think of another branch of mathematics that is so deeply involved with the deterministic, stochastic and statistical worlds. The difficulty in defining our discipline contributes substantially to the second issue on my list.
   
   
2. Lack of general awareness by potential users – the general public, private industry, government agencies, and our colleagues from other disciplines – of operations research and its potential. I know of very few members of the operations research community who initiated their undergraduate studies with the objective of studying or earning degrees in operations research. Most of us had little or no awareness of operations research at that point in our lives but were fortunate to eventually be exposed to the discipline. If we, those who have chosen to make operations research the center of our professional lives, were naïve about or entirely unaware of the discipline upon initiating our undergraduate studies, what can we expect of others? This lack of public awareness/ understanding of our discipline leads directly to the third issue on my list.
   
   
3. Intimidation of many potential users by operations research. This is, of course, inadvertent – we don’t try to intimidate potential users. I have consistently been impressed with the great patience most members of the operations research community demonstrate when trying to explain “what we do” and “how we do it” to people outside the community. More often then not, we work with individuals and groups who become anxious as soon as they have some awareness of what we do. We are also still coping with a generation of students who recall from their single operations research course (which they took in the 1970s or 1980s) that operations research is appropriate for problems of very large scale and requires tremendous investments in time and computing power. Most of these former students are now in the mid and latter portions of their careers, and many have naturally worked their way into positions of authority over and responsibility for decision-making.

As the next several sections of this article indicate, education can be an important tool in addressing these problems.

Draw Students in with Active Learning

MOST STUDENTS initially perceive operations research to be uninteresting and irrelevant; my experience suggests that this perception results largely from their feelings that operations research is unapproachable and inaccessible. Fortunately we have colleagues who have developed many clever and imaginative ways to make operations research extremely accessible, which in turn stimulates student interest in operations research that otherwise would not be kindled.

Many articles on effective active learning exercises have been published in OR/MS Today’s “Issues in Education” column. The first of these that I recall reading is Judith S. Liebman’s “Promote Active Learning During Lectures.”Liebman espouses the virtues of active learning exercises, discusses her use of these exercises and makes a very convincing case for the effectiveness of simple but thought-provoking active learning exercises.As with many truly effective teaching methods, Liebman’s suggestions are also inexpensive, easy to use and extend, and transfer effortlessly across cultures.

I have also found Norman Pendegraft’s “Lego of My Simplex” to be extremely useful. Pendegraft discusses his use of a simple child’s toy (Legos™), made up of small interlocking plastic rectangles of various dimensions, to teach basic linear programming concepts. His classroom exercise makes superb use of the toy’s simplicity to illustrate model building, algebraic representation, the geometry of linear programming and shadow costs. His exercise is also inexpensive, easy to use and extend, and transfers effortlessly across cultures.

INFORMS Transactions on Education (ITE) has also published many articles on various active learning exercises. Brimberg and Hurley [2007], Cochran [2001], DePuy and Taylor [2007], Talluri [2009], Taras and Grossman [2003] and Teich, Wallenius and Wallenius [2005], as well as others, have contributed articles that detail very effective active learning exercises. ITE has also published an entire special issue on educational games (Volume 8, Number 1) that was guest-edited by Paul Griffin in September 2007, and Martin Chlond contributes a regular series of articles on puzzles and operations research to the journal.

An instructor must invest time in order to incorporate active learning exercises into her/his classroom, but the potential return on this investment is tremendous. If a student’s interest in operations research has been stimulated through effective active learning exercises, s/he will naturally develop a much stronger understanding of what operations research is as her/his introductory O.R. coursework progresses and be far more receptive to the enormous potential of operations research.

The Case for Cases

ONCE A STUDENT’S INTEREST in operations research has been aroused and s/he has begun to understand what operations research is, the student is prepared to begin developing an appreciation of what one can do with the tools (including the mindset) of our discipline. I have found cases to be extremely useful for accomplishing this pedagogical goal [Cochran, 2000]. By starting with relatively simple and straightforward cases and progressing to more technically demanding cases with greater ambiguity, the instructor can provide students with a tremendous opportunity to apply operations research to real problems in a relatively low risk classroom environment.

There are, of course, several impediments to integrating cases into an introductory course. These include:

• Initial student anxiety – most undergraduate students have little experience with case analyses and even less with the analysis of quantitatively oriented cases.
  
  
• The instructor’s lack of experience teaching with cases – many operations research instructors have little experience selecting cases to support their pedagogical objectives, facilitating case discussions or assessing student performances on cases.
  
  
• The cost of obtaining quality cases and associated teaching notes – other than cases that are available in some operations research textbooks – are too expensive for many universities and colleges to afford.

During my term as editor-in-chief of ITE, I have discussed these issues with many instructors who have expressed interest in using cases in their classrooms. Most of these instructors have indicated to me that they believe they could overcome the first two of these issues if not for the third issue (cost). In response to these concerns, ITE has increased its efforts to publish cases. In support of these efforts, last year the journal has established a password protected site from which only an instructor who has applied for access (and provided evidence that s/he is a college or university instructor) can download the teaching notes associated with any case published by ITE. Because ITE is an open access journal, this effort is generating a rich collection of highly affordable (i.e., free) operations research-oriented cases.

The issues that comprise the journal’s most recent volume include the following cases:

• Assigning regions to sales representatives at Pfizer Turkey [Köksalan and Batun, 2009]
  
  
• Bidding on Priceline [Anderson, Wilson and Zhang, 2008]
  
  
• MotherLand Air: Using Experiential Learning to Teach Revenue Management Concepts [Metters, Vargas and Weaver, 2009]
  
  
• Introductory Integrative Cases on Airline Revenue Management [Shumsky, 2009]
  
  
• Revenue Management at Harrah’s Entertainment, Inc. [Agrawal, Cohen and. Gans, 2009]
  
  
• Starting with Good Inputs: Unconstraining Demand Data in Revenue Management [Ferguson and Queenan, 2009]

The last four cases on this list were part of ITE’srecent special issue on “Teaching Revenue Management” (Volume 9, Issue 3, May 2009) that was guest edited by Ioana Popescu.

The collection of freely available cases and associated teaching being accumulated and published by ITE will support instructors in their efforts to incorporate cases into their operations research courses. Again, this will require an investment of time by an instructor who wants to incorporate cases into her/his classroom, but the potential return on this investment is tremendous. Once a student has developed (through case analyses) a strong understanding of how to use operations research to solve real problems, s/he will be ready to use her/his tools to solve complex problems for real organizations outside of the relatively low risk classroom environment.

The Benefits of Project Based Learning

A STUDENT NEARING THE COMPLETION of her/his degree program is usually eager to move beyond the classroom and apply what s/he has learned; most students (correctly) perceive this as an important step toward establishing a career in their field of study. Operations research-oriented projects can provide students with such an experience.

Instructors who teach in urban areas or for universities with strong reputations or close relationships with corporations have several alternatives for developing capstone projects in cooperation with commercial organizations. However, a large proportion of operations research instructors are not so fortunate. Where are these instructors to go when looking for projects for their students?

One possible answer is to look to NPOs and government agencies. Over the past decade universities have put an increasing emphasis on community service, and many media sources report that the value placed on community service opportunities by incoming classes of college freshmen is rapidly increasing. Such projects have the potential to make both university administration and students happy – how often do we have a chance to do something that simultaneously accomplishes those two feats?

While sufficient opportunities for student projects may be available with local government agencies and NPOs, an instructor could do well to consider less local alternatives. As chair of the Operations Research Practice for Africa (ORPA) 4 conference last October [Cochran, 2009], I was overwhelmed by the number of NPOs I learned of that are working on resolving various water issues in Africa. Groups such as the Nuba Water Project, which sends its members to dig wells that provide convenient potable water in the Nuba Mountain region of Sudan, are routinely confronted by problems that beg for quantitative approaches. Agencies of governments in developing nations are also in need of such assistance.

These opportunities would certainly be attractive on their own merits. However, an instructor can simultaneously enhance both the likelihood of the project’s long-term success and her/his students’ educational experience by working with academicians and students who live and study in the area where the results will be implemented.

I am finishing this article during a break between sessions of the 5th Annual Operations Research Society of East Africa (ORSEA) conference in Dar es salaam, Tanzania. While participating in this conference I have met many colleagues from Tanzania, Kenya, Uganda, Rwanda and Burundi who are anxious to partner with colleagues from the United States and Canada. Instructors who engage these colleagues and their students (or colleagues and students from other parts of the world) will provide their students with opportunity to learn about working across cultures and develop professional and personal relationships that could benefit them for the rest of their lives.

Anything Else?

INSTRUCTORS CAN TAKE THREE additional steps to provide momentum through increasing awareness of these opportunities and efforts among other operations research instructors, students, colleagues from other disciplines, private industry and the general public.  These steps are:

• Submit articles on the results of these projects to journals such as Interfaces and ORiON, that focus on applications of operations research. In addition to documenting the instructor’s and students’ efforts, these articles will serve as examples to others in the operations research community (both at home and abroad).
  
  
• Submit cases based on these projects to journals such as INFORMS Transactions on Education, that focus on operations research pedagogy. Such cases will provide instructors with classroom tools that can motivate, excite and inspire students.
  
  
• Publicize these efforts in the media. The public may not fully understand our tools, but they will be fascinated by stories of how operations research is being used to improve the quality of life for others in developing regions.

I have only identified the investment that this approach will demand of instructors. However, this will require a strong commitment by the entire operations research community. Practitioners can contribute by identifying promising opportunities, volunteering to supervise/mentor some student groups working on these projects, and encouraging their organizations to provide financial support for instructors and students who are working on these projects. While the necessary level of commitment is high, the potential rewards, both professional and personal, are tremendous.

REFERENCES

1. Agrawal, Narendra, Cohen, Moris A., and Gans, Noah, 2009, “Case: Revenue Management at Harrah’s Entertainment, Inc.,” INFORMS Transactions on Education, Vol. 9, No. 3, www.informs.org/site/ITE/article.php?id=101.

2. Anderson, Chris K, Wilson, John G., and Zhang, Gouren, 2008, “Case: Bidding on Priceline,” INFORMS Transactions on Education, Vol. 9, No. 1, www.informs.org/site/ITE/article.php?id=75 .

3. Brimberg, Jack and Hurley, Bill, 2007. “Solving the U2 Brainteaser With Integer and Dynamic Programming,” INFORMS Transactions on Education, Volume 7, Number 3, http://archive.ite.journal.informs.org/Vol7No3/BrimbergHurley/ .

4. Camm, Jeffrey D., 2008. “O.R. in the Classroom – Get Real!,” OR/MS Today, Vol. 35, No. 4, www.lionhrtpub.com/orms/orms-8-07/frreal.html .

5. Cochran, James J., 2000, “Successful Use of Cases in Introductory Undergraduate Business College Operations Research Courses,” The Journal of the Operational Research Society, Vol. 51, December 2000.

6. Cochran, James J., 2001, “Who Wants To Be A Millionaire®: The Classroom Edition,” INFORMS Transactions on Education, Vol. 1, No. 3, http://ite.informs.org/Vol1No3/Cochran/

7. Cochran, James J., 2005, “All-Star Line-Up of Speakers,” OR/MS Today, Vol. 32, No. 4, www.lionhrtpub.com/orms/orms-10-05/fr-specrep-sb3.html .

8. Cochran, James J., 2009, “Water, Transportation & O.R. in Africa,” OR/MS Today, Vol. 36, No. 2, www.lionhrtpub.com/orms/orms-4-09/frafrica.html .

9. DePuy, Gail W. and Taylor, G. Don, 2007, “Using Board Puzzles to Teach Operations Research,” INFORMS Transactions on Education, Vol. 7, No. 2, http://archive.ite.journal.informs.org/Vol7No2/DePuyTaylor/ .

10. Devlin, Keith and Lorden, Gary, 2007, “The Numbers Behind NUMB3RS: Solving Crime with Mathematics, Plum.

11. Ferguson, Mark and Queenan, Carrie, 2009, “Case: Starting with Good Inputs: Unconstraining Demand Data in Revenue Management,” INFORMS Transactions on Education, Vol. 9, No. 3, www.informs.org/site/ITE/article.php?id=102 .

12. Köksalan, Murat and Batun, Sakine, 2009, “Case: Assigning regions to Sales Representatives at Pfizer Turkey,” INFORMS Transactions on Education, Vol. 9, No. 2, www.informs.org/site/ITE/article.php?id=87

13. Metters, Richard, Vargas, Vincente, and Weaver, Sherry, 2009, “Case: MotherLand Air: Using Experiential Learning to Teach Revenue Management Concepts,” INFORMS Transactions on Education, Vol. 9, No. 3, www.informs.org/site/ITE/article.php?id=99 .

14. Pendegraft, Norman, 1997, “Lego of my Simplex,” ORMS Today, Vol. 24, Number 1, www.lionhrtpub.com/orms/ORMS-archive.html .

15. Taras, Daphne and Grossman, Thomas A., 2003, “Stay or Switch: An Organizational Behavior and Management Science Joint Classroom Exercise,” INFORMS Transactions on Education, Vol. 3, No. 2, http://archive.ite.journal.informs.org/Vol3No2/TarasGrossman/

16. Shumsky, Robert A., 2009, “Case: Introductory Integrative Cases on Airline Revenue Management,” INFORMS Transactions on Education, Vol. 9, No. 3, www.informs.org/site/ITE/article.php?id=100 .

17. Talluri, Kalyan, 2009, “The Customer Valuations Game as a Basis for Teaching Revenue Management,” INFORMS Transactions on Education, Vol. 9, No. 3, http://ite.pubs.informs.org/ .

18. Teich, Jeffrey E, Wallenius, Hannele, and Wallenius, Jyrki, 2005, “The Bread/Flour/Grain Trading Game: Bidding In and Designing Auction Events,” INFORMS Transactions on Education, Vol. 5, No. 3, http://archive.ite.journal.informs.org/Vol5No3/TeichWallenius/index.ph