POWELL Teaching Modeling in Management Science _____________________________________________________________________________________________
Teaching Modeling in Management Science Stephen G. Powell Amos Tuck School of Business Administration Dartmouth College Hanover, New Hampshire 03755, USA
[email protected]
A Radical Proposition The heart of Management Science is not the science of optimization or simulation, but the art of reasoning logically with models. Abstract This essay discusses how we can most effectively teach Management Science to students in MBA or similar programs who will be, at best, part-time practitioners of these arts. I take as a working hypothesis the radical proposition that the heart of Management Science itself is not the impressive array of tools that have been built up over the years (optimization, simulation, decision analysis, queuing, and so on) but rather the art of reasoning logically with formal models. I believe it is necessary with this group of students to teach basic modeling skills, and in fact it is only when such students have these basic skills as a foundation that they are prepared to acquire the more sophisticated skills needed to employ Management Science. In this paper I present a hierarchy of modeling skills, from numeracy skills through sophisticated Management Science skills, as a framework within which to plan courses for the occasional practitioner. ________________________________________ Management Science in the Business School A host of problems face teachers of Management Science in the business school (INFORMS Education Committee, 1995; Powell, 1998a). The subject itself has been removed from the core curriculum of the AACSB, and Management Science courses have been removed from the core in a number of highly-respected schools. No
accurate data are available, but it is widely accepted that Management Science plays a much smaller role in most business schools than it once did. These developments are particularly ironic at this time, since Management Science is enjoying a renaissance in practical applications, from revenue management at the airlines to financial engineering on Wall Street. Before we can determine how best to teach Management Science, we must ask what the discipline offers to the business school curriculum. Why should MBA students learn about Management Science, and how should they learn it? One difficulty, of course, is that Management Science is not a recognized functional area in most businesses, nor is it in the business school. Very few students will pursue careers in which Management Science plays a central role. In addition, Management Science is rarely used in other courses, and some, perhaps many of our faculty colleagues have negative images of the subject itself. (In many cases we need to educate our colleagues on the relevance of Management Science in the business world, its relevance in their own fields, and even on the value of using modeling in teaching their courses.) My thesis is that Management Science can, indeed, make a fundamental contribution to the education of business students, but it will not be by teaching them linear programming (although we should do that). Management Science can teach business students the essential skills of analytical reasoning, especially how to use models to think through business problems. I suggest that there are six categories of skills business school students need that management scientists are best equipped to provide: • basic quantitative reasoning skills (for example, order-of-magnitude estimation) • informal modeling skills (for example, identifying critical assumptions) • formal modeling skills (Excel skills, for example) • the ability to understand and learn from models in other disciplines (for example, the Black-Scholes model in finance, the ISLM model in macroeconomics, or the EOQ model in operations)
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end-user modeling skills; that is, the ability the build and analyze models on one’s own (Plane, 1994) the skills to understand and work with large-scale models (the traditional “intelligent consumer” rationale for teaching Management Science).
Many of these skills are not recognized as fundamental to business students, yet at the same time many faculty colleagues complain about their student’s weaknesses in mathematics and quantitative reasoning. I believe we have an opportunity to substantially improve business school education (while creating more jobs for our profession) by articulating the need for learning these skills and then teaching them as part of the Management Science curriculum. Perspectives on Modeling When I refer to modeling or model-building I am referring to the fundamental activity of creating a simplified representation of reality in order to understand reality better, not necessarily to the sophisticated models built by Management Scientists. Model building is such a natural and familiar activity to most management scientists that many do not recognize its central role. Modeling is both an innate human capability and an arcane, specialized art. The role of those of us who teach Management Science is to build a bridge between the student’s innate abilities to simplify and abstract the world to improve their understanding, and the formal skills needed to build a useful computer model. In The Search for Solutions, a book on modeling in the sciences, Judson (1980) notes that “modelmaking is a profound and instinctual human response to understanding the world.” Children are modeling when they take on adult roles in their play. Adults are modeling when they use maps, when they use political labels (like “liberal”) to describe politicians, or when they choose insurance based on an informal assessment of risks. The important point for management scientists to understand is that many of the basic concepts necessary to build formal models, simplification, abstraction, and so on, are already present in some form in most people’s minds. In
fact the mind itself seems to be highly evolved to use models in many ways. But mental models are not as effective in many situations as are formal models, so the educational task is to help the student augment his or her existing skills with those needed to build explicit, formal models that (unlike informal, mental models) can be evaluated, critiqued, and improved upon by both the builder and others. Seymour Papert, whose 1980 book Mindstorms should be required reading for anyone teaching Management Science, is a computer scientist and the originator of the programming language Logo. Papert is an expert in childhood learning and has a vision of how well-developed computer software can help children learn fundamental thinking skills. Part of this vision involves the notion that programming a computer can help a child learn to think by forcing the child to reflect on his or her own thought processes: …in teaching the computer how to think, children embark on an exploration of how they think. The experience can be heady: Thinking about thinking turns the child into an epistemologist, an experience not even shared by most adults I see a similar role for modeling and Management Science in the business school: developing models can help students le arn how they think and can think better in the future (whether or not they are actually using models). Finally, the Systems Dynamics community has developed the notion of “microworlds,” computer software that helps the user learn about the dynamics of a typical business situation, such as the perils of exponential growth. Peter Senge, in The Fifth Discipline (1990), offers this vision of the role models, in this case models packaged as microworlds, can have on management: Now a new type of microworld is emerging. Personal computers are making it possible to integrate learning about complex team interactions with learning about complex business interactions. These new microworlds allow groups to reflect on, expose, test, and improve the mental settings for both
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crafting visions and experimenting with a broad range of strategies and policies for achieving those visions. Gradually, they are becoming a new type of “practice field” for management teams, places where teams will learn how to learn together while engaging their most important business issues. While I stress the importance of teaching students to build their own models (end-user modeling), Senge stresses the use of models in team building and group learning. Both activities are complementary, and build upon a basic understanding of what a model is and how to use one effectively. A Hierarchy of Modeling Skills My argument, in its simplest form, is that before we embark on teaching Management Science we should teach modeling. But what are the modeling skills we should teach, and how can we organize these skills from basic to advanced? I propose a four-part hierarchy, which starts with the most basic skills involving logic and numbers, then moves on to basic modeling skills every student should have, progresses to more advanced skills that some students can acquire, and ends with the most advanced Management Science tools we are likely to teach our students. These four categories are described below along with examples of specific skills in each class. Numeracy and logical skills Anyone who teaches Management Science has encountered students who can understand the rudiments of Management Science but cannot successfully build or analyze models because they cannot reason with numbers. What are some of these necessary numeracy skills? One fundamental skill is the ability to make rough numerical estimates quickly. For example, if we sell 1200 units at $495 will our revenues be about $600,000 or $6 million? This skill is basic to debugging a model and in general to avoiding mechanical mistakes in quantitative reasoning. It is also extremely useful in understanding and discussing model-based results.
Some other numeracy skills include • using special cases to test the limits of an argument or calc ulation • checking the consistency of units in a calculation to avoid errors • using the "sniff test," a quick intuitive evaluation of the plausibility of a result or conclusion, to detect unreasonable assumptions or other errors in reasoning. In addition to numeracy skills, modeling requires the ability to reason logically. For example, one must be able to recognize an assumption in one's own or another's argument. On another level, successful use of an "IF" statement requires a basic familiarity with logic.
I stress the importance of these foundational skills for two reasons: first, because they are important but are almost always taken for granted in graduate-level teaching, and second, because we must teach them if we are to prepare our students mentally for learning Management Science itself. Basic modeling skills Beyond basic numeracy and logical skills, the modeler-in-training needs to acquire basic modeling skills. These are skills that are used in building and analyzing any model, from the simplest spreadsheet model to the most complex integer program. Once again, they are often taken for granted by expert modelers who long ago acquired these skills. But an effective teacher above all can understand which skills students lack. And I have found that many students stumble in learning Management Science because they lack a basic understanding of the rudiments of creating a useful descriptive model and exploring that model to build intuition (see also Plane, 1997). Here is a sample of some basic modeling skills: • categorizing variables: distinguishing parameters, decisions, and outcome measures • modularization: decomposing a model into relatively independent parts
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isolating parameters: entering a parameter in one place in a model and referring to it wherever else it is needed establishing a base case: deciding whether to measure proposed changes against the most likely case, the current case, or the worst case backing in: using breakeven analysis to identify a critical level for a variable sensitivity analysis: learning which parameters have the most powerful effect on the outcomes pattern analysis: looking for patterns in the results to assist in translating model results into information useful to managers (Baker, 2000).
I believe it is important to recognize that these kinds of skills are necessary in all modeling activities. Teachers of Management Science should at least be aware of these skills, and ideally should create explicit opportunities in their courses for students to learn these skills. Advanced modeling skills The craft skills of modeling do not end with the basic skills illustrated above. In fact, there is no reason to assume that modeling skills are finite. But what kinds of skills can advanced students learn, perhaps in a second-year MBA class in modeling? Here is a sample of some advanced skills: • prototyping: building a simple model first, testing its implications, and then expanding and improving it along lines that will improve the quality of the analysis • sketching a graph: using a simple generic graph to suggest properties of a relationship between two model variables • using families of mathematical relationships: using families of curves with a few parameters (such as the demand family Q=aP-b ) to support later sensitivity analysis • imagining the answer: working backward from the desired answer to known data • modeling the data: understanding that all data is a (possibly biased) sample from
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reality and explicitly modeling the process that gave rise to the data separating idea generation from evaluation: controlling one’s critical faculty by generating ideas in a uncritical fashion.
I have written more extensively elsewhere (Powell, 1995a, 1998b) on the importance of these skills to the practice of modeling. Their importance to us as teachers is that most students will not recognize or acquire these skills on their own. In fact, it takes most practitioners years of experience to develop just a few of these skills. Our task as teachers is to explicitly identify these skills, and to find ways to encourage our students to use them. Management Science tools and applications Finally, we come to the tools that form the accepted heart of Management Science: optimization, simulation, decision analysis, queuing, and so on. To reiterate what was said earlier, most students cannot successfully acquire and use these skills unless they have an adequate foundation. This foundation consists of the basic numeracy, logical, and modeling skills described above. In fact, the better a student is as a modeler the more effective use they can make of the Management Science tools. I believe as a profession we have underestimated the importance of these basic skills over the years and assumed that any motivated student can learn to use Management Science tools. In reality, these tools are more sophisticated than we sometimes realize, or at least using them presumes a basis in modeling that many of our students do not have. It is a far more effective pedagogical strategy to teach less of Management Science and more basic modeling, if that is what our students need, than to teach a full complement of Management Science tools to a student audience that is poorly equipped to use them. Importance of basic skills I have argued throughout this essay on the importance of teaching (or at least ensuring that our students have) basic modeling skills before we teach Management Science tools. There are a
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number of reasons why I believe this is so, beyond the obvious fact that many of our students do not possess these skills. First, basic modeling skills are used routinely, while advanced skills are used only occasionally. It is far more important for a student to understand basic sensitivity analysis than it is to understand shadow prices, since he or she will always do the former but may never encounter a linear program in the workplace.
teaching MBAs. In addition, as William Hogan has suggested to me, the spreadsheet is the second best way to do many things, and therefore the best way to do almost everything. We will simply have to accept that we may choose to build our research models in GAMS or GPSS, but teach our MBAs to use Solver and Crystal Ball.
A second reason is that sophisticated methods fail if basic skills are inadequate. I have seen students fail attempting to solve simple one- or twovariable nonlinear programs, when a simple grid search would have sufficed. In our desire to teach sophisticated algorithms we must not suppress our students’ common sense.
Final thoughts
A third reason to teach the basics of modeling is that no one else in the business school is doing so, and management scientists have a strong comparative advantage. Furthermore, modeling skills are in increasing demand in the workplace. It may seem ironic that Excel skills are in demand by recruiters but very few ask for Management Science skills. This may be due to the fact that managers whose MBAs are ten or twenty years old do not realize that Management Science is now an eminently practical tool. I believe that the best way to educate these managers is to equip our students with excellent Excel, modeling, and Management Science skills, and let the graduating students show by example how powerful and practical these tools have become. For some examples of successful MBA model-building see Liberatore and Nydick, 1999; Sonntag and Grossman, 1999; and Powell, 1997. Finally, spreadsheets are a natural vehicle for teaching both basic modeling skills and Management Science (Savage, 1997). We could not have asked for a more helpful development than the evolution of the spreadsheet into a universal business language. There is still a residual feeling among some members of our profession that spreadsheets are not a legitimate modeling tool. I agree, of course, that many sophisticated models require more powerful or specialized software. But most managers will never work with software beyond the spreadsheet. And every manager has a spreadsheet. These reasons alone make it the platform of choice for
Managers are both decision makers and learners. Modeling (both mental and formal) is a fundamental human tool for learning about the world and for preparing to make decisions. As teachers of Management Science, our task is to help students augment their innate modeling skills with formal modeling skills, including the tools of Management Science. Friendly software, especially spreadsheets, has made this task easier than ever by dramatically reducing the costs of modeling. As a result, future managers can and will be model builders, model consumers, and active computer learners. This is a golden opportunity for management scientists. Successful use of Management Science requires a solid foundation in basic modeling skills. Many of our students do not possess these skills. Much of modeling is a craft, and should be taught in a manner appropriate to craft. While this requires a different approach than teaching the scientific aspects of Management Science, it can be done (Powell, 1995a; 1995b; 1998b). By going back to the basics of modeling, as I advocate here, we can • establish a firm foundation for the Management Science course • present a coherent, general, and useful set of skills to students • provide skills that will be useful to students learning other disciplines • provide widely-applicable business skills • reestablish the role of Management Science in the business school curriculum. References: Baker, K. (2000), “Gaining Insight in Linear Programs from Patterns in Optimal Solutions,”
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INFORMS Transactions forthcoming.
on
Education,
INFORMS Education Committee (1995), “Report of a Survey of OR/MS Programs,” OR/MS Today, February, pp. 54-56. Judson, H.F. (1980), The Search for Solutions, Holt, Rinehart, and Winston, New York. Liberatore, M. J. and R. L. Nydic k (1999), “Breaking the mold: A new approach for teaching the first MBA Management Science course”, Interfaces, Vol. 29, No. 4, pp. 99-116. Papert, S. (1980), Mindstorms, Basic Books, New York. Plane, D.R. (1994). “Spreadsheet power,” OR/MS Today, Vol. 21, No. 6, (December), pp. 32-38. Plane, D.R. (1997). “How to build spreadsheet models for production and operations management,” OR/MS Today, Vol. 24, No. 6, (December), pp. 50-54. Powell, S. G. (1995a), “Teaching the Art of Modeling to MBA Students,” Interfaces, Vol. 25, No. 3, pp. 88-94. Powell, S. G. (1995b), “Six Key Modeling Heuristics,” Interfaces, Vol. 25, No. 4, pp. 114125. Powell, S. G. (1997), “From Intelligent Consumer to Active Modeler: Two MBA Success Stories,” Interfaces, Vol. 27, No. 3, pp. 88-98. Powell, S. G. (1998a), “Requiem for the Management Science Course?”, Interfaces, Vol. 28, No. 2, pp. 111-117. Powell, S. G. (1998b), “The Studio Approach to Teaching the Art of Modeling, Annals of Operations Research, Vol. 82, pp. 29-48. Savage, S. (1997). “Weighing the pros and cons of decision technology in spreadsheets,” OR/MS Today, Vol 24, No. 1 (January), pp. 42-45. Senge, P. (1990), The Doubleday, New York.
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Sonntag, C. and T. A. Grossman (1999). “End User Modeling Improves R&D Management at AgrEvo Canada, Inc.” Interfaces, Vol. 29, No. 5, pp. 132-142. _____________________________________________________________________________________ 67 INFORMS Transactions on Education 1:2 (62-67)
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