Monte Carlo simulation is a statistical technique that helps calculate the probability of outcomes based on thousands of random samples. Some examples of Monte Carlo simulation application include risk analysis and forecasting in finance, manufacturing project management, designing components, pharmaceutical clinical trial design, and resource allocation planning in healthcare. @RISK risk analysis software runs powerful Monte Carlo simulation tools from within Microsoft Excel.
In any field where decision-making processes must account for uncertainty—from weather events to supply chain issues to stock market movements—Monte Carlo simulation-based risk models play a key role. While they may seem arcane when explained mathematically, the probabilistic calculations produced by Monte Carlo simulation have many practical applications. For example, Monte Carlo simulation models can help stakeholders understand how likely it is that a business will make money on a new venture or complete a construction project on time.
This article covers some Monte Carlo simulation examples within different working environments ranging from engineering and energy to finance and healthcare. By the end, you should have a broader understanding of how to use the Monte Carlo method in your projects.
First, a definition. Monte Carlo simulation is a statistical modeling technique that uses repeated random samples of numbers from a defined range to calculate the probability of different outcomes. It’s a powerful method for decision making and forecasting within complex systems that contain many variables.
Monte Carlo simulation algorithms emerged from the Los Alamos National Laboratory in the late 1940s, when researcher Stanislaw Ulam conducted a thought experiment about how he would calculate the chances of winning a hand of solitaire. The number of possible layouts for a 52-card pack is enormous—too enormous to calculate individually. Ulam realized that it would be possible to take a large sample of layouts, calculate the number of winning hands, and extrapolate probabilities from there. The name “Monte Carlo simulation” refers to the famous gambling destination: like gambling, this technique relies on random chance.
The development of computer systems allowed for further refinement of Monte Carlo simulation algorithms—ones that can use thousands of simulations to model the probability of certain events occurring. While the Los Alamos scientists originally used Monte Carlo simulation to understand high-energy physics, today, Monte Carlo simulations are used in industries from marketing to manufacturing. NASA even uses Monte Carlo simulation models to plan space missions.
Let's take marketing as one example for understanding how Monte Carlo simulation techniques can be applied in practice. If you’re launching a new product and you want to understand whether it will make back its costs, you could try to come up with a deterministic result—a single number—based on past launches.
Or, you could use the Monte Carlo method to calculate the probability of success instead. By running the simulation thousands of times with random numbers taken from within your range of values, you’ll calculate the probability of different outcomes for your product launch.
You’ll need to understand the variables—factors that can change at random. Variables for a new product launch could include:
Knowing the ranges in which these variables fall based on past records or market research can help you create a statistical model for your Monte Carlo simulation. After running thousands of simulations of the product launch, you will be able to understand how likely success is. If you work with a Monte Carlo-based risk analysis software like @RISK, you can also gain insight into which variables impact success most, which allows you to adjust your strategy accordingly.
It’s possible to develop sophisticated Monte Carlo method-based models within Microsoft Excel—one of the most common spreadsheet software programs in any industry. Lumivero’s @RISK risk analysis software runs as an Excel add-on, making it possible to quickly develop models without leaving your spreadsheets.
The procedure for building and running a Monte Carlo simulation in Excel will vary depending on what you are trying to model, but key steps could include:
Once you’ve run your Monte Carlo simulations, you’ll want to understand the results. @RISK makes it possible to visualize and interpret simulation results from very high-level overviews to granular, variable-by-variable scenario analyses.
You can conduct a sensitivity analysis to see how changes in each variable effect outcomes. With the use of tornado charts, scatterplots, histograms, and a wide range of other graphs, you can clearly communicate findings to stakeholders—all within minutes, and from within Excel.
Modern finance is an incredibly complex landscape. While there is no way to predict market activity, according to Investopedia, it is possible to determine the probability of certain events using Monte Carlo simulation methods that draw on accurate data. These can help identify potential opportunities and mitigate risks.
One Monte Carlo simulation example in finance is modeling the performance of investment portfolios. If an investor can clearly see the range of probable returns alongside risk, they can properly mitigate or take strategic risks with data backing their decisions. For example, when debating whether to buy or sell an option, an investor can model the probability of its future growth or decline.
Similarly, Monte Carlo simulation can be used to analyze risk in currency markets, allowing investors to hedge against volatile exchange rates. Strategic, data-driven risk analysis modeling allows financial planners to make more informed decisions for the short and long term.
It’s possible to apply Monte Carlo simulation in project management situations, including manufacturing and engineering. At a high level, Monte Carlo simulation can inform project managers about issues like cost estimations, scope changes, and scheduling. The method can also apply to quality control, design optimization, production line changes, and more.
For example, in complex manufacturing environments, Monte Carlo simulation can help plan maintenance costs. If you have data on how often (and under what conditions) a machine on the line breaks down, you can model those variables with a range of probability for each part. You can even conduct scenario or sensitivity analysis to determine system-wide impacts of a failure, lost revenue, and other factors.
You can also use @RISK to apply the Monte Carlo method to engineering and design. Our article “Manufacturing Supply Chain Management: Optimizing Production and Supplier Specifications Using Monte Carlo Simulation” covered a case study involving an Australian manufacturer of telecommunication infrastructure components. In this example, they used Monte Carlo simulation to conduct tolerance stacking—understanding to what degree different components of a product can deviate from specifications without impacting the quality of the finished piece.
Pharmaceutical clinical trials are traditionally a risk-filled process where the wrong decision could be costly in both time and money. By applying the Monte Carlo method to clinical trial models, you can optimize your trial design, improve efficiency, and more. Specific Monte Carlo simulation examples in pharmaceutical research include:
Monte Carlo simulation has other applications in healthcare contexts. For example, epidemiologists often use Monte Carlo simulations to model the spread of infectious diseases within populations, considering factors such as:
With the data from these models, policymakers can predict and plan for different responses to protect vulnerable populations.
During the COVID-19 pandemic, Monte Carlo simulations were a standard method for estimating the spread of the virus. By modeling a pandemic’s spread and health care surge capacity, hospitals were able to better plan for the availability of:
Data-driven decisions informed by Monte Carlo simulation can offer greater preparedness for day-to-day hospital operations, as well as in emergencies.
This article has provided just a basic overview of how Monte Carlo simulation modeling can empower robust, data-driven decisions—and how simple it can be to develop your own models with Lumivero’s @RISK. With an easy-to-use interface accessible from inside Microsoft Excel, our decision-making tools can support better strategies in virtually any industry.
Request a demo of @RISK today to begin exploring how Monte Carlo simulation can benefit you.
