1. Introduction to Simulation

2. What is simulation? A simulation is the imitation of the operation of a real-world system over time. It involves the generation of an artificial history of a system. The observations of the artificial history are used to draw inferences about the operating characteristics of the system.

3. Simulation Models A simulation model consists of a set of assumptions that describe the operation of a system. These assumptions are expressed in mathematical, logical, and symbolic relationships between the entities of the system.

4. Simulation Models The simulation model, once developed and validated, can be used to investigate a wide variety of “what-if” questions about the real- world system.

5. Monte Carlo Simulation

6. A Manual Algorithm 1.Calculate the relative frequency of occurrence of each possible outcome  relative frequency = number of times x occurs / total number of observations = Pr(outcome = x)

7. Spare Parts Example

8. A Manual Algorithm 2.Calculate the cumulative distribution of the possible outcomes - Pr(outcome <= x)

9. Spare Parts Example

10. A Manual Algorithm 3.Use random numbers to simulate the possible outcomes by associating these numbers with the intervals of the cumulative distribution.  random numbers = a set of numbers, each of which has the same probability of occurring

11. Spare Parts Example

12. A Manual Algorithm 4.Repeat step 3 a suitable number of times to generate the desired statistics.

13. Spare Parts Example

14. Simulation with Spreadsheets

15. Random Variable Generation RAND() - this function returns a uniformly distributed random number between 0.0 and 1.0. NORMINV(RAND,  ) - this function returns a normally distributed random variable with mean=  and standard deviation =  Some other distributions can be generated by formula.

16. Empirical Distributions Empirical distributions are distributions based on observed historical data that are not fit to any specific probability distribution.  Embedded ifs IF(logical_test,value_if_true,value_if_false)  Table lookups VLOOKUP

17. Replicating the Model Data Tables To set up a two-input data table  In a cell, enter the formula that will use the substituted values.  Starting in the cell below the formula, enter the values that you want substituted into one input cell. Enter these values in the same column as the formula.

18. Replicating the Model  Starting in the cell to the right of the formula, enter the values that you want substituted into the other input cell. Enter these values in the same row as the formula.

19. Data Analysis Descriptive Statistics Histogram Anova Etc.