MT235 Math for
Management Science
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Chapter 1
Introduction
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Decision Analysis
Decision Science, Management Science,
Operations Research, Operational Research
 Applying the methods of science to
management decision making
 Methods of Science - logic, mathematics,
computers and the use of models

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A Modeling Approach to Decision
Making
Mental model - picturing in your “minds eye”
 Visual model - blueprints, schematics, maps
 Physical models - scale models and prototypes

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A Modeling Approach to Decision
Making

Mathematical models - mathematical symbols
are used to represent decision variables which
are then related by the appropriate math
functions to describe a real system or decision
problem
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Benefits of Models
Less costly to analyze than real system or
problem
 Can be analyzed more rapidly
 Facilitate “what if” and “what’s best” analysis
 Provide insight about real problem or system

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Benefits of Models
“By modeling various alternatives for future
system design, Federal Express has, in effect,
made its mistakes on paper. Computer
modeling works; it allows us to examine many
different alternatives and it forces the
examination of the entire problem.”
Frederick W. Smith, Chairman and CEO
Federal Express Corporation
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Benefits of Models
“Think of every enterprise, whether it is Intel or
a hotel, involved in adjusted capacity-demand
pricing. … If this can be done computers-tocomputers in real time, you’ll see another
power of 10 increase in the efficiency of the
work in the economic system. Now how do we
get there? … Bits and pieces of it exist in
decision theory and operations research.”
Andy Grove, CEO Intel Corp.
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Benefits of Models
“Level 3, at its heart, is a technology-based
company and frankly, the central technology is
operations research and optimization, which I
tend to think is going to revolutionize all of
business over the next 20 years.”
James Q. Crowe, CEO Level 3
Communications
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Benefits of Models
“Based on Eastman Kodak Company’s records
for 1990 to 1999, we estimate that decision
analysis contributed around a billion dollars to
the organization over time. The data also
reflect the many roles decision analysis can
play. Aside from the monetary benefits, it
promotes careful thinking
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Benefits of Models
about strategies and alternatives, improved
understanding and appreciation of risk, and use
of systematic decision-making principles.”
- from Robert T. Clemen and Robert C. Kwit, “The value of decision
analysis at Eastman Kodak Company, 1990-1999”, Interfaces, Vol. 31,
No. 5, September - October 2001.
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The Modeling Process

The process of building a model begins with an
understanding of the real world system.
Management must be able to answer questions
such as:
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The Modeling Process
What drives the system under consideration?
 What are the key factors which predict the
behavior of the system?
 What problems are relevant to management?
 What are the appropriate measures of success?

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The Modeling Process

The next step in the modeling process involves
simplifying and abstracting from the real world
system. This model formulation step is
exceptionally important.
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The Modeling Process

Should the model be too complex it may be
difficult if not impossible to solve.

If the model is too simple management may not
be willing to trust results obtained with the
model fearing that the model is unrealistic.
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The Modeling Process
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Once a model is formulated an appropriate
solution methodology must be identified. Data
must also be collected to estimate the
parameters of the model.
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The Modeling Process

That solutions are available at this point does
not mean that the managerial questions have
been answered. These solutions must be
interpreted. Interpretation may be thought of as
a reversal of the formulation step.
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The Modeling Process

Formulation required that the broad description
of the real world system be narrowed and
abstracted.

Interpretation requires that the narrow meaning
of the solution be broadened and applied to the
actual situation.
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The Modeling Process

This set of steps; understanding, formulation,
solution and interpretation should provide new
insights on the real world system. This insight
may well provide new understanding of the
problem and restart the modeling process.
Thus, the modeling process should be an
iterative one.
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