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# Operational Research

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### Operational Research

1. 1.  ROY THOMAS  SAM SCARIA  SONU SEBASTIAN  SHILPA MATHEW  AMMU VIJAYAN  SIJU JOSE  SAJITH P S  SCARIA JOSEPH
2. 2. The process of designing a mathematical or logical model of a real-system and then conducting computer-based experiments with the model to describe, explain, and predict the behavior of the real system.
3. 3. • Monte carlo method is a substitution for the mathematical evaluation of a model. • Darker and Kac define monte carlo method as combination of probability methods & sampling techniques providing solution to complicated partial or integral differential equation. • In short, monte carlo technique is concerned with experiments on random numbers & it provides solutions to complicated OR problems.
4. 4.  Where one is dealing with a problem which has not yet arisen.  Where the mathematical and statistical problems are too complicated and some alternative methods are needed.  To estimate parameters to a model.
5. 5. Steps of Monte Carlo method  A Flow diagram is drawn.  Then correct sample observations are taken to select some suitable model for the system.  Then the Probability distribution is converted to cumulative distribution function.
6. 6.  Sequence of random numbers is selected .  Sequence of values of the variables of our interest is determined with the sequence of random numbers obtained.  Some standard mathematical functions is applied to the sequence of values obtained
7. 7.  Find solution of complicated mathematical expressions.  Difficulties of trial and error experimentation are avoided by these method.
8. 8.  These are costly way of getting a solution of any problem.  These method do not provide optimal answer to the problems. The answers are good only when the size of the sample is sufficiently large.
9. 9.  It is applied to a wide diversity of problems such as queuing problems, inventory problems, risk analysis concerning a major capital investment.  It is very useful in budgeting.
10. 10.  Under this method operating environment is produced and systems allows for analysing the response from the environment to alternative management actions.  The method is complicated and costly.
11. 11.  Random numbers It is a number in a sequence of numbers whose probability of occurrence is same as that of any other number in that sequence.
12. 12.  Pseudo-random Numbers: Random numbers are called pseudo random numbers when they are generated by some deterministic process. But they qualify the pre determined statistical test for randomness.
13. 13.  For solving simulation problems, there is the need of generating a sequence of random numbers.  Random numbers may be found by computer ,by random tables, manually etc.
14. 14.  Most common method to obtain random numbers is to generate them by a computer programme.  These numbers lie between 0 and 1,in conjunction with the cumulative probability distribution of a random variable including 0 but not 1.