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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:
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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?
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.