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Operational Research
1.
2. ๏ ROY THOMAS
๏ SAM SCARIA
๏ SONU SEBASTIAN
๏ SHILPA MATHEW
๏ AMMU VIJAYAN
๏ SIJU JOSE
๏ SAJITH P S
๏ SCARIA JOSEPH
3. 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.
4.
5. โข Monte carlo method is a substitution for
the mathematical evaluation of a model.
โข Darker and Kac define monte carlo
method as combination of probability
methods & sampling techniques providing
solution to complicated partial or integral
differential equation.
โข In short, monte carlo technique is
concerned with experiments on random
numbers & it provides solutions to
complicated OR problems.
6. ๏ 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.
7. 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.
8. ๏ 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
9. ๏ Find solution of complicated mathematical
expressions.
๏ Difficulties of trial and error experimentation
are avoided by these method.
10. ๏ 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.
11. ๏ 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.
12. ๏ 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.
13. ๏ฑ 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.
14. ๏ 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.
15. ๏ 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.
16. ๏ 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.