Simulation Part 1: Simulation with Discrete Random Variables

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Presentation transcript:

Simulation Part 1: Simulation with Discrete Random Variables EMIS 7300 Simulation Part 1: Simulation with Discrete Random Variables Updated 04 October 2006

Flow Chart of Monte Carlo Simulation method Input 1: Statistical distribution for each component variable. Input 2: Relationship between component variables and system performance Select a random value from each of these distributions Calculate the value of system performance for a system composed of components with the values obtained in the previous step. Output: Summarize and plot resulting values of system performance. This provides an approximation of the distribution of system performance. Repeat many times

Example 1: News Vendor Newspapers cost $0.10 each to stock in a vending machine and sell for $0.25. Any papers left unsold at the end of the day are sent for recycling. Demand for papers each day is either 15, 16, or 17 P(Demand = 15) = 0.4 P(Demand = 16) = 0.4 P(Demand = 17) = 0.2 Use simulation to determine the optimal number of papers to stock each day.

Cumulative Probability Distribution 1.0 Demand = 17 0.8 0.6 Demand = 16 0.4 0.3 0.2 Demand = 15 0.18 0.05 0.0 15 16 17

Simulation with Excel

=if(b3<0.4,15,if(b3<0.8,16,17)) =rand() =min(16,c7)*0.25-(16*0.1)

Simulation with Excel: Run 1 This simulation run suggests stocking 16 papers.

Simulation with Excel: Run 2 This simulation run suggests stocking 15 papers.

Simulation with Excel: Average of Multiple Runs The results of multiple simulation runs suggest stocking 16 papers to maximize expected profit.

How Accurate is the Simulation? The simulation estimates the expected profit as follows: E[Profit |15 papers] = 2.25 E[Profit |16 papers] = 2.31 E[Profit |17 papers] = 2.24 Analytical solution:

Comments If we run more trials the estimates from the simulation will be closer to the true values calculated analytically In many situations a simulation is used because It is very difficult or impractical to calculate the expected values analytically It is very difficult or impractical to calculate the variance analytically

Using the VLOOKUP Function =vlookup(b3,$f$2:$h$4,3,true)

Data Analysis Package

Data Analysis Package

Discrete Random Variables

Discrete Random Variables