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 ROY THOMAS
 SAM SCARIA
 SONU SEBASTIAN
 SHILPA MATHEW
 AMMU VIJAYAN
 SIJU JOSE
 SAJITH P S
 SCARIA JOSEPH
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.
• 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.
 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.
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.
 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
 Find solution of complicated mathematical
expressions.
 Difficulties of trial and error experimentation
are avoided by these method.
 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.
 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.
 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.
 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.
 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.
 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.
 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.
Operational Research

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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. • 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.