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
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.
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.)
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:
quantitative reasoning skills (for example, order-of-magnitude estimation)
modeling skills (for example, identifying critical assumptions)
modeling skills (Excel skills, for example)
ability to understand and learn from models in other disciplines (for
example, the Black-Scholes model in finance, the IS-LM model in
macroeconomics, or the EOQ model in operations)
modeling skills; that is, the ability the build and analyze models on
one’s own (Plane, 1994)
skills to understand and work with large-scale models (the traditional
“intelligent consumer” rationale for teaching Management Science).
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
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
The Search for Solutions, a book
on modeling in the sciences, Judson (1980) notes that “model-making 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.
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
|…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
see a similar role for modeling and Management Science in the business
school: developing models can
help students learn how they think and can think better in the future
(whether or not they are actually using models).
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 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.
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
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
other numeracy skills include
special cases to test the limits of an argument or calculation
||checking the consistency of units in a calculation to avoid errors
the “sniff test,” a quick intuitive evaluation of the
plausibility of a result or conclusion, to detect unreasonable
assumptions or other errors in reasoning.
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
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
Basic modeling skills
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).
is a sample of some basic modeling skills:
parameters, decisions, and outcome measures
decomposing a model into relatively independent parts
parameters: entering a
parameter in one place in a model and referring to it wherever else it is
a base case: deciding whether
to measure proposed changes against the most likely case, the current
case, or the worst case
in: using breakeven analysis
to identify a critical level for a variable
analysis: learning which
parameters have the most powerful effect on the outcomes
analysis: looking for
patterns in the results to assist in translating model results into
information useful to managers (Baker, 2000).
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
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?
is a sample of some advanced skills:
a simple model first, testing its implications, and then expanding and
improving it along lines that will improve the quality of the analysis
a graph: using a simple
generic graph to suggest properties of a relationship between two model
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
the answer: working backward
from the desired answer to known data
the data: understanding that
all data is a (possibly biased) sample from reality and explicitly
modeling the process that gave rise to the data
idea generation from evaluation: controlling
one’s critical faculty by generating ideas in a uncritical fashion.
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
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 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
A second reason is that sophisticated methods fail
if basic skills are inadequate. I
have seen students fail attempting to solve simple one- or two-variable
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.
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 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
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.
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;
going back to the basics of modeling, as I advocate here, we can
||establish a firm foundation for the Management Science course
a coherent, general, and useful set of skills to students
skills that will be useful to students learning other disciplines
widely-applicable business skills
||reestablish the role of Management Science in the
business school curriculum.
K. (2000), Gaining Insight in Linear Programming from Patterns in
Optimal Solutions, INFORMS Transactions on Education, Vol. 1,
INFORMS Education Committee (1995), Report of a Survey of OR/MS Programs,
OR/MS Today, February, pp. 54-56.
H.F. (1980), The Search for Solutions, Holt, Rinehart, and Winston,
Liberatore, M. J. and R. L. Nydick
(1999), Breaking the mold: A new approach for teaching the first MBA Management Science course,
Interfaces, Vol. 29, No. 4, pp. 99-116.
S. (1980), Mindstorms, Basic Books,
D.R. (1994), Spreadsheet power, OR/MS Today, Vol. 21, No. 6, (December), pp. 32-38.
D.R. (1997), How
to build spreadsheet models for production and operations management,” OR/MS
Today, Vol. 24, No. 6, (December), pp. 50-54.
S.G. (1995a), “Teaching the Art of Modeling to MBA Students,” Interfaces, Vol. 25, No. 3, pp. 88-94.
S.G. (1995b), “Six Key Modeling Heuristics,” Interfaces, Vol. 25, No. 4, pp.
S.G. (1997), “From Intelligent Consumer to Active Modeler: Two MBA Success Stories,”
Interfaces, Vol. 27, No. 3, pp. 88-98.
S.G. (1998a), “Requiem for the Management Science Course?”, Interfaces, Vol. 28, No. 2, pp. 111-117.
S.G. (1998b), “The Studio Approach to Teaching the Art of Modeling,” Annals of Operations
Research, Vol. 82, pp. 29-48.
S. (1997), Weighing the pros and cons of decision technology in spreadsheets,”
OR/MS Today, Vol 24, No. 1 (January), pp. 42-45.
P. (1990), The Fifth Discipline, Doubleday, NY.
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.
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