What is Monte Carlo simulation?
Monte Carlo simulation is a method for estimating how uncertain inputs combine into an uncertain result. Each input, such as a task duration, a price, or a default rate, is described by a probability distribution instead of a single number. The model runs thousands of times, and each run draws a random value for every input and records the outcome. Together, the runs form a distribution of results that shows, for example, the probability of going over budget. It is one form of simulation, and it often generates the scenarios used in stochastic optimization.
Monte Carlo simulation in practice
A law firm is asked to quote a fixed fee for a commercial litigation matter. Partners estimate low, likely, and high hours for each phase, from pleadings through discovery to trial preparation, using records from similar past matters. The model draws hours for every phase, includes the chance of an early settlement, and repeats the calculation ten thousand times. The firm then sets a fee that covers most of the simulated outcomes. Adding up the likely estimates would have understated the total, because overruns on legal work tend to be larger than underruns.
What to watch for
- Link inputs that move together, such as fuel and freight prices, or the simulation will understate extreme outcomes.
- Record where each input distribution came from, since an invented range produces precise-looking but unfounded results.
- Report ranges and the probability of key thresholds, because the average of the runs hides the risk the method exists to show.