# Monte Carlo Method – Steps involved with example

## Monte Carlo Method

The Monte Carlo method of simulation owes its development to the two mathematicians, John Von Neumann and Stanislaw Ulam, during World War II when the physicists were faced with the puzzling problem of behavior of neutrons i.e. how far neutrons would travel through different materials. The technique provided an approximate but quite workable solution to the problem. With remarkable success of this technique on neutron problem, it soon became popular and found many applications in business and industry and at present forms a very important tool of operation researcher too.

Monte Carlo method is a simulation technique in which statistical distribution function are created by using a series of random numbers. This approach has the ability to develop many month or years of data in a matter of a few minutes on a digital computer. The method is generally used to solve problems which cannot be adequately represented by mathematical models, or where the solution of the model is not possible by analytical method.

Monte Carlo simulation yields a solution which should be very close to the optimal, but not necessarily the exact solution. However, it should be noted that this technique yields a solution that converges to the optimal or correct solution as the number of simulated trials lead to infinity.

### Steps involved in Monte Carlo Method

1. Establishing Probability Distribution

In case of this method the values of the variables have to be generated. There are number of variables in  real world system that are probabilistic in nature and that we want to simulate e.g. the no. of variables may be :

• inventory demand on daily basis.
• Lead tiem for inventory/order to arrive.
• Time between machine breakdown.
• Time between arrivals and users.
• Service time etc.

For the above variables it is important to determine the probability distribution to examine historical outcome. Probability distribution need not be based solely on historical observation. It may be based on judgment  and experience.

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