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311_Session13_Simulation_Chen

# 311_Session13_Simulation_Chen - Session13:Simulation...

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Operations Management Session 13:  Simulation

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Session 14 2 Class Objectives Presenting a new type of a problem Generate random numbers. Simple Examples Portfolio Optimization New Product Development
Session 14 3 Why simulation? Methods to deal with randomness Build up models to have analytical solution Mimic the randomness, observe and analyze the  outcome Simulation

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Session 14 4 Portfolio Example What is the expected value, standard deviation and  coefficient of variation of the portfolio? Budget: \$1000 Stock t A B Current stock price 100 50 Portfolio composition 90% 10% # of share 9 2 Estimate a month later Distribution ~U[50,150] ~N(45, 3) Simulate the stock price a month later to observe the portfolio value. next
Session 14 5 Random Number Generator = RAND() generates a random variables between 0 and 1 ~  Uniform Distribution between [0,1] = 2*RAND() generates a random variable between 0 and 2 = 3 + RAND() generates a random variable between 3 an 4 = a + (b-a)*RAND() generates a random variable between a  and b ~ Uniform Distribution between [a, b]

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Session 14 6 Generating Normal Distribution = NORMINV(probability, mean, standard deviation) If we assign probability = RAND() then  NORMINV function generates a random variable that follows a  normal distribution with specified mean and standard deviation   =NORMINV(RAND(), mean, standard deviation)
Session 14 7 Portfolio Example What is the expected value, standard deviation and  coefficient of variation of the portfolio? Budget: \$1000 Stock t A B Current stock price 100 50 Portfolio composition 90% 10% # of share 9 2 Estimate a month later Distribution ~U[50,150] ~N(45, 3) Simulate the stock price a month later to observe the portfolio value. next

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Session 14 8 Portfolio Example Standard deviation of portfolio is less than  standard deviation of Stock A plus Stock B Why? Risk pooling Try portfolios: 30% Stock A + 70% Stock B 50% Stock A + 50% Stock B 70% Stock A + 30% Stock B Which one has a lower coefficient of variation.
Session 14 9 Product Development Example

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