1. Monte Carlo Simulation Presented by Megan Aldrich and Tiffany Timm

2. What is Monte Carlo?  Uses random numbers to generate a simulation to mimic real data  Helps find statistics for data that is really messy  Use of a computer is required

3. Discovery and First Use  First used by Enrico Fermi in 1930s for neutron diffusion  Documented by John von Neumann in the 1940’s during the Manhattan Project of World War II  Popular because gambling was a rising sport and was coined the name Monte Carlo by Neumann’s partner Stainslaw Ulam who loved poker

4. Pros  Easy to use  Can make the complex data simple  Does not take a lot of time to analyze  Inexpensive

5. Cons  Original expense to develop and operate simulations can be high  Not sufficient in dealing with small numbers and usually has the operator estimating when this happens

6. Outline for Monte Carlo 1. List all possible outcomes for each event. 2. Determine the probability of each outcome. 3. Determine subsets of the integers which have the same relative frequencies as the probabilities. 4. Set up a correspondence between the outcomes and the subsets. 5. Select a random number. 6. Using each random number to represent the corresponding event, perform the experiment and note the outcome. 7. Repeat until desired confidence.

7. Our Problem As the owner of a small grocery store you have a choice of hiring: Two cashiers who do their own bagging, and each of whom can check out a shopper in two minutes, or One cashier and one bagboy who, working as a team, can check out a shopper in one minute. We want to find the best scenario.

8. Our Problem continued Based on our experience for every one minute: Zero people get in line 30% of the time One person gets in line 40% of the time Two people get in line 30% of the time Using this system we can find the expected wait time per customer and the expected line length they will encounter.

9. Problem analysis  We generated random numbers in Excel and used a program written by Tiffany to run the experiment  We want to explore: Ho: Mx = My H1: Mx > My

10. Results  We reject the null hypothesis in favor of the alternative hypothesis. This shows that the average wait time for a one-lane system is longer than a two-lane system.  Therefore, we would choose a two-lane system to effectively lower the wait time for customers.

11. Questions  Under what circumstances would you use the Monte Carlo Simulation?  Name three ways you can generate random numbers.