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?
Examples

Discussion of two important examples in
class…..
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.
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.
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.
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.
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.
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.