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

2. 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

3. 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.

4. 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

5. Simulation with Excel

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

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

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

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

10. 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:

11. 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

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

13. Data Analysis Package

14. Data Analysis Package

15. Discrete Random Variables

16. Discrete Random Variables