Operations Research Models

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Operations Research Models

• OR Dated back to World War II.
• Mathematical modeling, feasible solutions,
  optimization, and iterative search.
• Defining the problem correctly is the most
  important thing.
• Solution to a decision-making problem requires
  answering three questions
• What are the decision alternatives?
• Under what restrictions is the decision made?
• What is an appropriate objective criterion for
  evaluating the alternatives?

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Examples

• Discussion of two important examples in class..

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Operations Research Models

• A solution of a model is feasible if it satisfies
  all the constraints.
• It is optimal if it yields to the best value of
  the objectives.
• OR models are designed to Optimize a specific
  objective criterion.
• Suboptimal solution in case we can not determine
  all the alternatives.

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Solving the OR Model

• In OR, we do not have a single general technique
  to solve all mathematical models.
• The type and complexity of the mathematical
  models dictate the nature of the solution method
  (e.g. the previous examples).
• The most prominent OR technique is linear
  programming.
• Integer programming.
• Dynamic programming.
• Network programming.
• Nonlinear programming.

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Cont ..

• Solution to OR model may be determined by
  algorithms.
• The algorithm provides fixed computational rules
  that are applied repetitively to the problem.
• Each repetition moves the solution closer to the
  optimum.
• Some mathematical models may be so complex.
• In the above case we may use some other methods
  to find a good solution.

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Queuing and Simulation Models

• Queuing and simulation deal with the study of
  waiting lines.
• They are not optimization technique.
• They determine measures of performance of the
  waiting lines, such as
• Average waiting time in queue.
• Average waiting time for service.
• Utilization of service facilities
• The use of simulation has drawbacks.

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Art of Modeling

• The previous examples are true representation of
  a real situation.
• That is a rare situation in OR.
• Majority of applications usually involve
  approximation.
• Figure 1.1 in your textbook.
• The assumed real world is derived using the
  dominant variables in the real system.
• In order to design a model we should consider the
  main variables in the real system.
• Example A manufacturing company that produce a
  variety of plastic containers.

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Phases of an OR Study

• As a decision-making tool, OR is both a science
  and an art.
• The principal phases for implementing OR in
  practice includes
• Definition of the problem.
• Construction of the model.
• Solution of the model.
• Validation of the model.
• Implementation of the solution.