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Technical Note 8. Simulation

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

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Technical Note 8. Simulation

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  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

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