MT235 Math for Management Science

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MT235 Math for Management Science
Chapter 1Introduction to Modeling
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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
• Verbal model written or oral representation
• Visual model - blueprints, schematics, maps
• Physical models - scale models and prototypes
• Mathematical models - symbols are used to
  represent decision variables which approximate a
  real system or decision problem

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A Modeling Approach to Decision Making

• Models are abstractions of reality
• They seek out and represent the major effects in
  a system
• Simplicity is their advantage
• Simplicity is their weakness

If a model doesnt faithfully represent reality
change the model.
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Benefits of Models

• Less costly to analyze than real system or
  problem
• Outcomes be analyzed more rapidly
• Provide insight about real problem or system
• Facilitate what if and whats best analysis

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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
  is the goal?
• 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?
• What can a manager change?
• What things are givens (for the current
  scenario)?

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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

• If the model is too simple the results may be
  unrealistic.
• If the model is too complex, it may be difficult
  if not impossible to solve.

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The Modeling Process

• Once a model is formulated an appropriate
  solution methodology must be identified.
• This will be based on the relationships embodied
  in the model.
• Data must also be collected to estimate the
  parameters of the model.
• Some information will be precise.
• The values of some parameters might have to be
  guesses.

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The Modeling Process

• Just because a solution might be 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 requires 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.
• Thus the modeling process is an iterative one

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Steps to Develop a Valid Model 1 of 2

• Determine the Goal what is being maximized or
  minimized.
• State the objective To determine. In order to
  (meet the goal).
• The goal involves those things over which the
  manager has control.
• The things enumerated in the statement of the
  objective become the objective variables

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Steps to Develop a Valid Model 2 of 2

• Determine the coefficients of the objective
  variables.
• The units must match the units in which the goal
  is measured.
• Identify the constraints.
• These values control the value of the decision
  variables
• These values are fixed for the given problem
  the manager cannot change them in the given
  scenario.
• Write the constraint equations (inequalities).
• Each constraint is written in terms of each
  objective variable.
• The coefficient of some obj. vars. may be zero
  (indicating that it has no effect on the
  constraint.