The document discusses Monte Carlo simulation, which involves using a computer to conduct experiments with a mathematical model of a real system to describe, explain, and predict the behavior of the real system. It provides steps of the Monte Carlo method and notes that it uses random numbers and probability to solve complicated problems. The document also discusses advantages and disadvantages of the Monte Carlo method.

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.

5. • 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.

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.  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.