MonteCarlo - 2.90 2.95 3.00 3.05 3.10 3.15 3.20 3.25 3.30 1...

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MONTECARLO (STATIC) SIMULATIONS
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Examples Monte-Carlo (Static) Simulation Estimating profit on a sale promotion Newsvendor problem Estimating π value Approximating integrals
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Profit on a Sale Promotion Furniture Store Unit cost: $175 Demand distribution : TRIA(500, 2000, 3500) Unit price distribution : UNIF(200, 300) 50% off sale Determine the order amount for maximizing profit. Estimating profit on a sale promotion
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Newsvendor Problem Wholesale price : $0.55 Retail price : $1.00 Scrap price : $0.03 Demand distribution : NORM(135.7, 27.1) Determine the order amount for maximizing profit Newsvendor Problem
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Estimating π value 4 ) 1 Pr( 2 2 π = + Y X 0 1 1 π/4 X, Y ~ uniform (0,1) Estimate π value by simulation
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Convergence to π Point Estimates for Pi
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Unformatted text preview: 2.90 2.95 3.00 3.05 3.10 3.15 3.20 3.25 3.30 1 , 2 5 Replications Estimate Approximating Integrals Consider the integral Making the substitution we get where x a dx y dy b a b a-= =-- = b a dx x g ) ( ( 29 =--+ = 1 1 ) ( ) ( ) ( dy y h dy a b y a b a g ( 29 y a b a g a b y h ) ( ) ( ) (-+-= Approximating Integrals Let Y ~ uniform(0,1) Approximate the integral by simulation = = = -1 ) ( ) ( ) ( )] ( [ dy y h dy y f y h Y h E Y dx x x + + 3 1 2 1 3...
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MonteCarlo - 2.90 2.95 3.00 3.05 3.10 3.15 3.20 3.25 3.30 1...

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