Lecture 9 - Monte Carlo Simulation Basic Definitions/Pros...

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Monte Carlo Simulation • Basic Definitions/Pros and Cons • Random Number Generation • Monte Carlo Simulation • Verification and Validation
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Simulation "designing a model of a real system and conducting experiments with the model to better understand system behavior and evaluate operating strategies" Simulation involves: 1.) the imitation of the operation of a random process 2.) generation of an artificial history of that process 3.) observation of that artificial history to draw inferences concerning the operating characteristics of the simulated process
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Optimization Accuracy Data Reqts. Sensitivity Analysis Robustness/Flexibility Effort Validity Conceptualization Tradeoffs in Using Simulation versus Analytical Modeling
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Random Number Generation: Random Numbers are Used Extensively in Simulation Random Number Generators are Evaluated With Respect to: Degree of Fit String Length Computational Efficiency
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RN Generator Performance Measures Degree of Fit: “Chi Square” Test: f 01 ... f 0n (observed) f e1 ... f en (expected) Σ j=1…n {(f 0i –f ei ) 2 / f ei }
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- String Length Number of unique u(0,1)’s obtained for a given RN seed e.g. “Mid-Square Method” .84 3844 .62 4624 .50 2500 .68 1681 .50 2500 .41 441[0] .50 25[00] .21 121[0] .05 7056 .11 211 2 6 .46 46 2
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- Computational Efficiency Computer Codes Usually Generate RN’s in a Two-Step Procedure: 1. Unif(0,1)’s via coding logic 2. Alternative Probability Distributions using a (cumulative) distribution function
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Variable Value 0 f(x) 1.0 Î 0.57 x P(x) Variable Value P(x y)=u(0,1) e.g. for N( μ , σ ) Î P(Z .18)=0.57, so x= μ +0.18 σ Distribution Function: pdf:
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Monte Carlo Simulation: - Risk Analysis - Optimization -Design - Economic/Investment Analysis
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Monte Carlo Procedure Generate RN Sample Observation Compute Response Variable Characterize/Apply Response Variable Distribution in Decision Making Iteration Limit yes no
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Pallet Ordering Example: In the month of August, the manager of a warehousing facility must make a decision on the number of returnable pallets to purchase for circulation among retail sites during the upcoming holiday season.
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This note was uploaded on 04/08/2008 for the course ENGR 2600 taught by Professor Malmborg during the Spring '08 term at Rensselaer Polytechnic Institute.

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Lecture 9 - Monte Carlo Simulation Basic Definitions/Pros...

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