Class_11_Simulation_Slides

# Analytical models simulation 2013 8 qso 510

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Analytical Models Simulation 2013 8 QSO 510 Simulation vs Analytical Models

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When not all the underlying assumptions set for analytic model are valid. When mathematical complexity makes it hard to provide useful results. When “good” solutions (not necessarily optimal) are satisfactory . When do we prefer to a simulation model over an analytic model? 2013 9 QSO 510 Simulation vs Analytical Models
Introduction Monte Carlo Simulation Random Number Mapping Simulation Procedure Simulation 2013 10 QSO 510

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Simulation in the presence of random variables in the decision-making situation. Relies on repeated random sampling to compute their results Used in computer simulations of physical and mathematical systems Applies to physical science, engineering, biology, statistics, finance and business, etc. To reflect the relative frequencies of the r.v., the random number mapping method is used. Monte Carlo Method 2013 11 QSO 510 Monte Carlo Simulation
Uses the probability function to generate random demand. The Probability Function Approach The Cumulative Distribution Approach Random Number Mapping Two Approaches 2013 12 QSO 510 Monte Carlo Simulation

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JEWEL VENDING COMPANY The vending machine holds 80 units of the product. The machine should be filled when it becomes half empty. Daily demand distribution is estimated from similar vending machine placements. P(Daily demand = 0 jaw breakers) = 0.10 P(Daily demand = 1 jaw breakers) = 0.15 P(Daily demand = 2 jaw breakers) = 0.20 P(Daily demand = 3 jaw breakers) = 0.30 P(Daily demand = 4 jaw breakers) = 0.20 P(Daily demand = 5 jaw breakers) = 0.05 2013 QSO 510 13 Bill would like to estimate the expected number of days it takes for a filled machine to become half empty.
The Probability Function Approach 2013 QSO 510 14 0.10 0.15 0.20 0.30 0.20 0.05 0 1 3 4 5 A number between 00 and 99 is selected randomly. 00-09 10-24 25-44 45-74 75-94 95-99 34 The daily demand is determined by the mapping demonstrated below. 34 34 34 34 34 34 34 34 2 25-44 Demand

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The Cumulative Distribution Approach 15 1.00 0.95 0.75 0.45 0.25 0.10 1 3 4 5 0 1.00 0.00 The daily demand X is determined by the random number Y between 0 and 1, such that X is the smallest value for which F(X) Y . F(1) = .25 < .34 F(2) = .45 > .34 Y = 0.34 2 2013 QSO 510
Simulation of the JVC Problem A random demand can be generated by hand (for small problems) from a table of pseudo random numbers.

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• Spring '13
• WenjunGu
• Randomness, Cumulative distribution function, Daily demand

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