Monte Carlo simulation is a powerful tool for modeling complex systems with uncertain inputs. It uses random sampling to generate a range of possible outcomes, helping businesses understand risks and make informed decisions.

By defining probability distributions for key variables and running numerous iterations, Monte Carlo simulation provides a comprehensive view of potential scenarios. This approach allows managers to quantify uncertainty and evaluate different strategies based on likely outcomes.

Introduction to Monte Carlo Simulation

Principles of Monte Carlo simulation

• Computational technique using random sampling to model and analyze complex systems with uncertain inputs
• Defines probability distributions for key input variables
• Generates random samples from these distributions
• Calculates corresponding outputs using a simulation model
• Quantifies risk by providing range of possible outcomes and associated probabilities
• Enables informed decision-making based on comprehensive understanding of uncertainty

Probability distributions for inputs

• Capture uncertainty in values of key input variables
• Common distributions: normal, uniform, triangular, beta, exponential
• Estimate parameters (mean, standard deviation, minimum, maximum) to fully define distribution

Random sampling and output calculation

• Develop simulation model capturing relationships between input and output variables
• Generate random samples from each input distribution using random number generator and specified distribution parameters
• Calculate corresponding outputs for each set of random input samples using simulation model
• Repeat process for large number of iterations to obtain distribution of output values

Analysis of simulation outputs

• Compile output values from all simulation iterations into distribution representing range of possible outcomes
• Calculate summary statistics (mean, median, standard deviation, percentiles) for output distribution
• Estimate probability of different outcomes by calculating proportion of iterations within specific ranges or meeting certain criteria
• Identify most likely scenarios by examining regions of output distribution with highest probability density

Interpretation for decision-making

• Assess risk associated with different decision alternatives using estimated probabilities and most likely scenarios from simulation results
• Compare simulation results with predetermined risk thresholds or performance targets to identify acceptable and unacceptable outcomes
• Conduct sensitivity analysis by varying input distributions or model parameters to understand impact on simulation results and robustness of decisions
• Communicate simulation results and implications to stakeholders, emphasizing range of possible outcomes, associated probabilities, and key drivers of risk and uncertainty
• Make informed decisions by selecting alternative aligning with organization's risk appetite and maximizing expected value or utility based on simulation results