SASIKARAN P. 051055AGUNASEKARA D.P.S.C 061021CNUWAN U.P.A.061040HTHAASAN S. 061053B

OR Model Classification

• Optimization models:– Derive optimal parameter values directly

from mathematical representation of the model

• Prediction models:– Derive predicted output from math.

Representation

• Experimentation models: – Simulation

Simulation is a powerful tool for modeling processes and systems to evaluate choices and opportunities

Process of modeling reality to gain a better understanding of the phenomena or system being studied

Simulation can be used in conjunction with other initiatives such as Lean and Six Sigma to enable continuous improvement of systems and processes

Production and manufacturing systemsInventory managementQueuing problemsCapital investment and budgetingService operations

Cost effectiveUsed before implementing the actual systemModelling flexibility , ease in modellingProvides a faster way of evaluatingProvides a better understanding of the

systemCapability to analyze the results in the

statistical terms

Are not precise and exact replication of reality

Required large number of experimentations and provides a unique solution

With increase in parameters becomes very complex

One of the largest and most important classes of numerical method

Modern application of Monte Carlo methods date from the 1940s during work on the atomic bomb

Applications in a wide areaUsed in computer simulations

or computer experiments as well

The input distribution is known Random number generation Random sample generation provides approximate solutions to a variety

of problems

Distribution fitting for historical datae.g. Chi-square Test, Nonlinear Optimization…etc

Possible distributions will be NormalPoissonExponential…etc

Different random number generating techniques for different distributions

Random number tables are commonly used

Relative and cumulative probabilities are found according to the distribution

Define random number ranges

No of machine breakdowns per day

Frequency

Relative Frequency

Cumulative Relative Frequency

Random Number Range

0 30 0.3 0.30-29

1 45 0.45 0.7530-74

2 25 0.25 175-99

Find possible outcomes

Solutions are made according to the outcomes

Day Random No

Simulated Breakdowns

1 18 0

2 25 0

3 73 1

4 12 0

5 54 1

6 96 2

For a type of brain cancer that affects about 7,000 Americans each year

The Boron Neutron Capture Therapy was the solution

Radiation dosimeter and treatment planning calculations was required for the therapy

Identical calculation required 6,800 minutes

Could complete its calculations in 19.35 minutes by using 1,024 processors in Monte Carlo simulation

Finite element methodStructures are divided

in to finite elementsData of the material,

boundary conditions and forces are given

Behavior of the structure are simulated and analyzed

Visualization of how a car deforms in an asymmetrical crash using finite element analysis