Operations Research ModelsOperations Research Models OR Dated back to World War II.OR Dated back to World War II. Mathematical modeling, feasible solutions, Mathematical modeling, feasible solutions,

optimization, and iterative search.optimization, and iterative search. Defining the problem correctly is the most Defining the problem correctly is the most

important thing.important thing. Solution to a decision-making problem Solution to a decision-making problem

requires answering three questions:requires answering three questions: What are the decision alternatives? What are the decision alternatives? Under what restrictions is the decision made?Under what restrictions is the decision made? What is an appropriate objective criterion for What is an appropriate objective criterion for

evaluating the alternatives?evaluating the alternatives?

ExamplesExamples

Discussion of two important Discussion of two important examples in class…..examples in class…..

Operations Research Operations Research ModelsModels

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

Solving the OR ModelSolving the OR Model In OR, we do not have a single general In OR, we do not have a single general

technique to solve all mathematical models.technique to solve all mathematical models. The type and complexity of the mathematical The type and complexity of the mathematical

models dictate the nature of the solution models dictate the nature of the solution method (e.g. the previous examples).method (e.g. the previous examples).

The most prominent OR technique is linear The most prominent OR technique is linear programming.programming.

Integer programming.Integer programming. Dynamic programming.Dynamic programming. Network programming.Network programming. Nonlinear programming.Nonlinear programming.

Cont ..Cont ..

Solution to OR model may be determined Solution to OR model may be determined by algorithms.by algorithms.

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

Each repetition moves the solution closer Each repetition moves the solution closer to the optimum.to the optimum.

Some mathematical models may be so Some mathematical models may be so complex.complex.

In the above case we may use some other In the above case we may use some other methods to find a good solution.methods to find a good solution.

Queuing and Simulation Queuing and Simulation ModelsModels Queuing and simulation deal with the Queuing and simulation deal with the

study of waiting lines.study of waiting lines. They are not optimization technique.They are not optimization technique. They determine measures of They determine measures of

performance of the waiting lines, such performance of the waiting lines, such as:as: Average waiting time in queue.Average waiting time in queue. Average waiting time for service.Average waiting time for service. Utilization of service facilitiesUtilization of service facilities

The use of simulation has drawbacks.The use of simulation has drawbacks.

Art of ModelingArt of Modeling The previous examples are true The previous examples are true

representation of a real situation.representation of a real situation. That is a rare situation in OR.That is a rare situation in OR. Majority of applications usually involve Majority of applications usually involve

approximation. approximation. Figure 1.1 in your textbook.Figure 1.1 in your textbook. The assumed real world is derived using The assumed real world is derived using

the dominant variables in the real system.the dominant variables in the real system. In order to design a model we should In order to design a model we should

consider the main variables in the real consider the main variables in the real system.system.

Example: A manufacturing company that Example: A manufacturing company that produce a variety of plastic containers.produce a variety of plastic containers.

Phases of an OR StudyPhases of an OR Study

As a decision-making tool, OR is both a As a decision-making tool, OR is both a science and an art.science and an art.

The principal phases for implementing OR The principal phases for implementing OR in practice includes:in practice includes: Definition of the problem.Definition of the problem. Construction of the model.Construction of the model. Solution of the model.Solution of the model. Validation of the model.Validation of the model. Implementation of the solution.Implementation of the solution.