# Chapter 14 Simulation. Monte Carlo Process Statistical Analysis of Simulation Results Verification of the Simulation Model Computer Simulation with Excel.

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Chapter 14 Simulation

Monte Carlo Process Statistical Analysis of Simulation Results Verification of the Simulation Model Computer Simulation with Excel Spreadsheets Areas of Simulation Application Chapter Topics

Simulation replaces physical systems A system is replaced with a mathematical model that is analyzed with the computer Simulation offers a means of analyzing very complex systems that cannot be analyzed with other OR techniques Overview

Many applications of simulations are for probabilistic models Monte Carlo technique: a technique for selecting numbers randomly from a probability distribution Generate the random variable, demand, by sampling from the probability distribution P (x) Example: Demand data for an item selling for \$100 over a period of 100 weeks Monte Carlo Process Demand/ Week Freq. of Demand ProbabilityCumulative Probability Corresponding RN 0123401234 20 40 20 10 0.2 0.4 0.2 0.1 0.2 0.6 0.8 0.9 1.00 0-19 20-59 60-79 80-89 90-99

Select number from a random number table: Monte Carlo Process Use of Random Numbers

Repeat selection of random numbers to simulate demand (say for 15 week) Calculate average demand = 31/15 = 2.07 units per week Estimated average revenue = \$3100/15 =206 Expected average demand (analytically): Monte Carlo Process Use of Random Numbers

More periods simulated, the more accurate the results Have to have enough trials in order to have identical results (reach steady state) Often difficult to validate results of simulation When reaches the steady state, simulation model truly replicates reality When analytical analysis is not possible, there is no comparison; validation even more difficult Monte Carlo Process Use of Random Numbers

Random numbers are typically generated using a numerical technique Thus are not true random numbers but pseudorandom numbers Random numbers must have the following characteristics: Must be uniformly distributed Numerical technique used for generating the numbers must be efficient Sequence of random numbers should not reflect any pattern Computer Simulation with Excel Spreadsheets Generating Random Numbers (1 of 2)

Simulation with Excel Spreadsheets (1 of 3)

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