# SIMULATION

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## SIMULATION

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1. SIMULATION SASIKARAN P. 051055A GUNASEKARA D.P.S.C 061021C NUWAN U.P.A. 061040H THAASAN S. 061053B

2. 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

3. 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

4. Applications • Production and manufacturing systems • Inventory management • Queuing problems • Capital investment and budgeting • Service operations

5. Purpose • Cost effective • Used before implementing the actual system • Modelling flexibility , ease in modelling • Provides a faster way of evaluating • Provides a better understanding of the system • Capability to analyze the results in the statistical terms

6. Simulation Process

7. Limitations • 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

8. Monte Carlo Simulation • 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 area • Used in computer simulations or computer experiments as well

9. The input distribution is known Random number generation Random sample generation provides approximate solutions to a variety of problems Process ofMonte Carlo Simulation

10. Identification of Input Distribution • Distribution fitting for historical data e.g. Chi-square Test, Nonlinear Optimization…etc • Possible distributions will be • Normal • Poisson • Exponential…etc

11. Random Number Generation • Different random number generating techniques for different distributions • Random number tables are commonly used

12. Random Sample & Solutions • Relative and cumulative probabilities are found according to the distribution • Define random number ranges

13. Random Sample & Solutions ctd.. • Find possible outcomes • Solutions are made according to the outcomes

14. Example of an Application of Monte Carlo • 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

15. A Recent Development of Simulation • Finite element method • Structures are divided in to finite elements • Data 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

16. THANK YOU.