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311_session_15_simulation_hiroshi (1)

# 311_session_15_simulation_hiroshi (1) - Simulation BUAD311...

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1 Simulation BUAD311 Session 15 Hiroshi Ochiumi

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2 Objectives Generate random numbers. Simple Examples Portfolio Optimization New Product Development Simulate waiting lines M/M/1 M/D/1
3 Random Number Generator = RAND() generates a random number 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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4 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
5 Portfolio Example Stock A: price follows a Normal Distribution with mean 100 and standard deviation 20 Stock B: price follows a Normal Distribution with mean 120 and standard deviation 30 Portfolio: 50% of Stock A and 50% of

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6 Portfolio Example Standard deviation of portfolio is less than standard deviation of Stock A and 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
7 Project Management Example Project with a deadline 100 days Project duration estimation: Normal with mean 110 and standard deviation 10 (days) Fixed fee (100K) plus an incentive plan: if the project is completed earlier than 100 days, earn bonus 1K / day if the project is late, pay penalty 4K / day You can reduce the expected project duration (now 110) by paying 2K / day up to 20 days What duration gives the highest net profit?

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8 More Data For the sake of simplicity, we only consider the following reduction plans: 90, 95, 100, 105 days First, make a decision based on expected values
9 Solution? Decision

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