Simulation Modeling Fundamentals

Model Validation

• The process of determining whether a simulation model is accurate and reliable
• Involves comparing the model's output with real-world data or experimental results
• Types of validation:
  • Face validation: checks if the model's assumptions and structure are reasonable
  • Internal validation: checks if the model's internal logic is correct
  • External validation: checks if the model's output matches real-world data

Model Calibration

• The process of adjusting a model's parameters to match real-world data or experimental results
• Involves finding the best-fit parameters that minimize the difference between the model's output and the real-world data
• Calibration methods:
  • Manual calibration: trial-and-error approach
  • Automatic calibration: uses optimization algorithms to find the best-fit parameters

Simulation Software

• Types of simulation software:
  • Discrete-event simulation software (e.g. Arena, Simio)
  • System dynamics simulation software (e.g. Stella, Vensim)
  • Monte Carlo simulation software (e.g. MATLAB, Python)
• Features to consider when selecting simulation software:
  • Ease of use
  • Flexibility and customization
  • Performance and scalability
  • Integration with other tools and software

System Dynamics

• A method for modeling and analyzing complex systems with feedback loops and nonlinear relationships
• Key components:
  • Stocks (accumulations of resources)
  • Flows (rates of change of stocks)
  • Feedback loops (positive and negative loops that affect the system's behavior)
• System dynamics is used to study complex systems, such as population growth, resource depletion, and supply chains

Sensitivity Analysis

• A method for analyzing how changes in a model's parameters affect its output
• Types of sensitivity analysis:
  • One-at-a-time (OAT) analysis: varies one parameter at a time
  • Multi-parameter analysis: varies multiple parameters simultaneously
  • Global sensitivity analysis: uses statistical methods to analyze the sensitivity of multiple parameters

Chi-Squared Goodness of Fit Test

• A statistical test used to determine whether a model's output is a good fit to a set of observed data
• The test calculates the chi-squared statistic and compares it to a critical value or uses a p-value to determine the significance of the fit
• The chi-squared test is commonly used in simulation modeling to validate the model's output

Calculating the Optimal Number of Simulations

• The number of simulations required to achieve a desired level of accuracy and confidence
• Factors to consider:
  • Desired level of precision
  • Model complexity
  • Computational resources
• Methods for calculating the optimal number of simulations:
  • Replication analysis
  • Confidence interval analysis

Calculating the Number of Runs or Replicas

• The number of times a simulation is run to achieve a desired level of accuracy and confidence
• Factors to consider:
  • Desired level of precision
  • Model complexity
  • Computational resources
• Methods for calculating the number of runs or replicas:
  • Replication analysis
  • Confidence interval analysis

Validation of Results

• The process of ensuring that the simulation results are accurate and reliable
• Involves checking the results for:
  • Consistency with the model's assumptions
  • Reasonableness of the output values
  • Robustness to changes in the model's parameters
• Methods for validating results:
  • Visual inspection of the output data
  • Statistical analysis of the output data
  • Comparison with real-world data or experimental results