operations research models-chapter 1-l1

8/22/2019 Operations Research Models-Chapter 1-L1

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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 inclass..


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Operations Research Models

A solution of a model is feasible if itsatisfies all the constraints.

It is optimal if it yields to the best value ofthe objectives.

OR models are designed to Optimize aspecific objective criterion.

Suboptimal solution: in case we can notdetermine all the alternatives.


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Solving the OR Model

In OR, we do not have a single generaltechnique to solve all mathematical models.

The type and complexity of the mathematicalmodels 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 byalgorithms.

The algorithm provides fixed computational rulesthat are applied repetitively to the problem.

Each repetition moves the solution closer to theoptimum.

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 studyof 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 scienceand an art.

The principal phases for implementing OR inpractice includes:

Definition of the problem.

Construction of the model.

Solution of the model.

Validation of the model.

Implementation of the solution.

operations research models-chapter 1-l1

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