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

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