1. Technical Note 8. Simulation • Definition of Simulation • Random Variables and Risk • Random Number Generators • Simulation Methodology • Data collection and distributions • Considerations When Using Computer Models • Types of Simulations • Desirable Features of Simulation Software • Advantages & Disadvantages of Simulation

2. Simulation • A simulation is a computer-based model used to run experiments on a real system. • Objective: To study, understand, and experiment with complex systems. • Computer simulation is the process of designing a model of a real system. • Allows study and experimentation without interrupting or damaging the real system • Determine reactions to different operating rules or change in structure • Variance in the system is represented by probability distributions. • We repeatedly sample from these distributions to generate outcomes. (This process is nick named Monte Carlo simulation.)

3. Model Input Output Random Variables & Risk • A random variable is any variable whose value cannot be predicted or set with certainty. • Future interest rates • The number of customer arriving at a restaurant between 6-7 p.m. • The number of air force pilots leaving the service • The profit margin • Generally the value of one or more of the “independent”(input) variables is unknown or uncertain (hence making them random variables) • Consequently, the value of the dependent (output) variable(s) will be uncertain, therefore making the output(s) random variables • The uncertainty in the outcomes represents the riskin the decision making process.

4. Random Number Generators • Need RNs to simulate randomly occurring events, outcomes, etc. • All spreadsheets (and compilers and …) include a function for creating uniformly distributed random numbers between 0.0 and 1.0. • Simulate the coin toss • Demonstrate the warm up (transient) period • Do we have to reach to steady-state always? • Simulate interest rate for the next quarter given: • P(rate cut) = 0.12, P(rate hike) = 0.55, and P(no change) = 0.33 • The trick used to generate random numbers for any given distribution is called the inverse transformation method.

5. Simulation Methodology

6. Data Collection and Distributions • Data collection (could be time consuming or costly) and analysis steps are always necessary • Suppose we capture the arrival times of calls coming to a help center. • Times are in minutes (decimals) • Compute the inter-arrival times • Develop a frequency chart • Determine if the distribution can be approximated by a known distribution or use the empirical distribution • Excel time!

7. Evaluate Results and Validate the Model • Simulation results (conclusions) depend on • the degree to which the model reflects the real system • design of the simulation (in a statistical sense) • Validation refers to testing the computer program (model) to ensure that the simulation is correct • To insure that the model results are representative of the real world system they seek to model • Print all calculations, verify manually (separately) • Simulate current real system conditions and compare the results using statistical tests. • The only true test of a simulation is how well the real system performs after the results of the study have been implemented

8. Units Demanded: 0 1 2 3 4 5 6 7 8 9 10 Probability: 0.01 0.02 0.04 0.06 0.09 0.14 0.18 0.22 0.16 0.06 0.02 Lead Time (days): 3 4 5 Probability: 0.2 0.6 0.2 Inventory Control Simulation – A mini Case • MCC is a retail computer store facing fierce competition. • Stock outs are occurring on a popular flat monitor. • The current reorder point (ROP) is 28. • The current order size is 50. • Daily demand and order lead times vary randomly, historical data is below: • MCC’s owner wants to determine the ROP and order size that will provide a 98% service level while minimizing average inventory. Develop a simulation model to determine the “optimal” order size and ROP. • Excel time!

9. The key Desirable Features of Simulation Software • Recently almost all are user-friendly and interactive and provide standard statistics such as cycle times, utilization, and wait times. • Have building blocks that contain built-in commands • Have macro capability, such as the ability to develop machining cells • Have material-flow capability • Allow users to write and incorporate their own routines • Allow a variety of data analysis alternatives for both input and output data • Have animation capabilities to display graphically the product flow through the system

10. Advantages of Simulation • Often leads to a better understanding of the real system • Years of experience in the real system can be compressed into seconds or minutes • Simulation does not disrupt ongoing activities of the real system • Simulation is far more general than mathematical models • Simulation can be used as a game for training experience • Simulation provides a more realistic replication of a system than mathematical analysis • Simulation can be used to analyze transient conditions, whereas mathematical techniques usually cannot • Many standard packaged models, covering a wide range of topics, are available commercially • Simulation answers what-if questions

11. Disadvantages of Simulation • Building a simulation model can take a great deal of time • Simulation, although allows for experimentation, does not easily lend itself for optimization (finding the best configuration) • Simulation may be less accurate than mathematical analysis because it is randomly based • A significant amount of computer time may be needed to run complex models • Less significant concerns are: • The technique of simulation still lacks a standardized approach • There is no guarantee that the model will, in fact, provide good answers • There is no way to prove reliability