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.