Methods for solving Operation Research Models

            Solving a model consists of finding the values of the controlled variables that optimize the measure of performance or estimating them approximately. O.R models are generally solved by the following three methods:

1.      Analytic or Deductive Method. In this method only the mathematical equations with symbols (without actual values) are manipulated deductively to arrive at the final solution. This has an advantage of further simplification of variables by either eliminating some of them or combining a few of them into a more compact set. These involve use of graphs, elementary differential calculus and finite differences.

2.      Numerical or Iterative Methods. When classical methods fail to derive the solution due to complexity of the constraints or number of variables then we are usually forced to adopt an interactive procedure. Such a procedure starts with a trial solution and a set of rules for improving it. The trial solution is hen replaced by the improved solution, and the process is repeated until either no further improvement is possible or the cost of further calculation cannot be justified. In other words the method can take the form of either simple trial and error or complex iteration in a successive to arrive at the optimal solution.

3.      Monte Carlo Method. The solution of any problem in a system becomes complicated if the system is not representing by the theoretical methods. Then solution of any problem in a system becomes complicated if the system is not represented by the theoretical methods. Then by the knowledge of the important characteristics and rules of operation of a system we can visualize the typical behavior of the system. This is done by taking random samples from the mathematical model that represents the real life system. The random samples result in a probability distribution that imitates the real life system, and from which the value of the specified stochastic variables is to be estimated. Furthermore, by varying the values of certain parameters and independent variables and then repeating the random sampling process one can attempt to measure their effect of Monte Carlo Method:

The following are the main steps of Monte Carlo Method:

(i)     Draw a flow diagram of the system under study.

(ii)   Obtain probability distribution for each of the variable of interest.

(iii)  Find out cumulative probability distribution corresponding to each of the variable chosen for study in step (ii)

(iv)  Assign an appropriate set of random numbers to represent each value of range of values, of the variable of interest chosen in step (ii)

(v)   Fit a suitable standard mathematical function to the values obtained in step (iv)

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