#### General Methods for Solving OR Models

General Methods for Solving OR Models

Usually three types of methods are there for solving OR models

1. Analytic method
2. Monte- Carlo method
3. Iterative method

Analytic method

Analytic solutions are those when the OR model is solved by taking use of all the tools of classical mathematics like differential calculus and finite differences available for this job. Solutions of diverse inventory models are obtained through adopting the so called analytic procedure.

Iterative method

If classical methods fall short due to complexity of the constraints or the number of variables, then we are generally forced to take on an iterative method. This type of procedure begins with a trial solution and a series of rules for improving or enhancing it. The trial solution is then substituted with the improved solution and the process is repeated until either no additional improvement is possible or the cost of additional calculation cannot be justified.

Iterative method can be sub-divided into three groups

1. After a limited number of repetitions, there will no further improvement possible
2. Though successive iterations enhance the solutions, we are only guaranteed the solution as a limit of an infinite process
3. Lastly, include the trial and error method which however is possible to be long, tedious and costly even if electronic computers are used.

The Monte-Corlo method

The basis of Monte-Corlo technique is random sampling of variables values from a distribution of that variable. Monte-Corlo takes the use of sampling methods to approximate the value of non-stochastic variables.

The main steps of this method are listed below

Step 1 - To get a general idea of the system, firstly draw a flow diagram of the system

Step 2 - Then, take accurate sample observations to choose some suitable model for the system. In this step, calculate the probability distributions for the variables of our interest.

Step 3 - Then, change the probability distribution to cumulative distribution function

Step 4 - A series of random numbers is now chosen with the help of random number tables

Step 5 - Establish the sequence of values of variables of interest with the sequence of random numbers getting in step 4.

Step 6 - Lastly create standard mathematical function to the values obtained in step 5

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