Mitigate Risks
Calculate Many Different Outcomes and Their Probabilities of Occurrence with Monte Carlo Simulation Software.
Monte Carlo Analysis Probabilistically Assesses the Impact of Risk
As we are constantly faced with uncertainty and variability, risk and forecast analysis is part of every decision you make. And even though we have unprecedented access to information, we can’t accurately forecast the future. But with Monte Carlo simulation, we have the next best thing to a superpower.
Monte Carlo simulation (also known as the Monte Carlo method) lets you see all possible outcomes of your decisions, including the actual probabilities each will occur, by running simulations with random variables thousands of times. These variables are described by their probability distribution which can be estimated with historical data or defined using expert opinion. Then, with risk analysis software like @RISK, you can run sensitivity analysis to identify which variables have the largest impact on the outcome. This method lets you quantitatively assess the impact of risk, allowing for more accurate forecasting and, ultimately, better decision-making under uncertainty.
What is Monte Carlo Simulation?
The Monte Carlo method is a computerized mathematical technique that allows people to quantitatively account for risk in forecasting and decision-making. At its core, the Monte Carlo method is a way to use repeating random samples of parameters to explore the behavior of a complex system. A Monte Carlo simulation is used to handle an extensive range of problems in a variety of different fields to understand the impact of risk and uncertainty.
A Way to Account for Risk
Monte Carlo simulations have assessed the impact of risk in cost estimation, project management, portfolio optimization, and many other real-life scenarios. The Monte Carlo method provides many advantages over predictive models with fixed inputs, such as the ability to conduct sensitivity analysis or define correlation between inputs.
A Forecast Analysis Tool That Works in Many Fields
The technique is used for forecasting which takes into account risk and is used for demand forecasting, load planning, pricing, sales forecasting, portfolio allocation, strategic planning, Six Sigma and quality control, profit projects, and more. Using this method, one can easily take risks into account and assess the probability of completing a project on time and staying within budget.
Use cases run the gamut and include cash flow analysis, capital investments, reserves estimation, pricing, cost estimation, project management, product pipeline analysis, portfolio optimization, supply chain risk, and more.
The Monte Carlo Simulation is used in many different fields, including:
Environmental Conservation
Agriculture & Food Safety
Consulting & Legal
Entertainment, Sports & Media
Mining & Minerals
Technology & Telecom
A Range of Outcomes
Monte Carlo simulation furnishes the decision-maker with a range of possible outcomes and the probabilities they will occur for any choice of action. It shows:
The outcomes of going for broke and for the most conservative decision
Along with all possible consequences for middle-of-the-road decisions
History of Monte Carlo Simulation
The technique was first used by scientists working on the atom bomb; it was named for Monte Carlo, the Monaco resort town renowned for its casinos. Since its introduction in World War II, Monte Carlo simulation has been used to model a variety of physical and conceptual systems.
How Monte Carlo Simulation Works
Monte Carlo simulation performs risk analysis by building models of possible results by substituting a range of values—called a probability distribution—for any factor that has inherent uncertainty. It then calculates results over and over, each time using a different set of random values from the input probability distributions. Depending upon the number of uncertainties and the ranges specified for them, a Monte Carlo simulation could involve thousands or tens of thousands of recalculations before it is complete. The result of a Monte Carlo simulation is a range – or distribution – of possible outcome values. This data on possible results enables you to calculate the probabilities of different outcomes in your forecasts, as well as perform a wide range of additional analyses. Monte Carlo simulation software builds a spreadsheet model that lets you evaluate your plan numerically, allowing you to change the numbers, ask ‘what if’ and see the results.
By using probability distributions for uncertain inputs, you can represent the different possible values for these variables, along with their likelihood of occurrence. Probability distributions are a much more realistic way of describing uncertainty in variables of a risk analysis, making Monte Carlo simulation far superior to common “best guess” or “best/worst/most likely” analyses.
To use Monte Carlo simulation, you need to build a qualitative model of your business activity, plan, or process. The best way to do this is by creating a spreadsheet model using Microsoft Excel and using Lumivero's @RISK analysis software. Analyze your simulation results by using the mean, percentiles, standard deviation, in addition to charts and graphs. Lumivero's Monte Carlo simulation software will help you interpret your data and is backed by 24/7 technical support and assistance.
100% Microsoft Excel Integration
With PrecisionTree, you never leave your spreadsheet, allowing you to work in a familiar environment, and get up to speed quickly.
Full Statistics Reports and Graphs
See results in risk profile graphs, 2-way sensitivity, tornado graphs, spider graphs, policy suggestion reports, and strategy-region graphs.
Bayesian Revision
“Flip” one or more chance nodes to show probabilities calculated using Bayes’ Rule. This is valuable when the probabilities of a model are not available in a directly useful form. For example: You need to know the probability of an outcome occurring given the results of a particular test. The test’s accuracy may be known, but the only way to determine the probability you seek is to “reverse” a traditional decision tree in Microsoft Excel using Bayes Rule.
Advanced Features
Set up your decision tree in Microsoft Excel exactly as you need it with logic nodes, reference nodes, linked trees, custom utility functions, and influence diagrams.
Common Probability Distributions
Normal
Or “bell curve.” The user simply defines the mean or expected value and a standard deviation to describe the variation about the mean. Values in the middle near the mean are most likely to occur. It is symmetric and describes many natural phenomena such as people’s heights. Examples of variables described by normal distributions include inflation rates and energy prices.
Lognormal
Values are positively skewed, not symmetric like a normal distribution. It is used to represent values that don’t go below zero but have unlimited positive potential. Examples of variables described by lognormal distributions include real estate property values, stock prices, and oil reserves.
Uniform
All values have an equal chance of occurring, and the user simply defines the minimum and maximum because they have no knowledge of which values are more likely than others. Examples of variables that could be uniformly distributed include manufacturing costs or future sales revenues for a new product.
Triangular
The user defines the minimum, most likely, and maximum values. Values around the most likely value have a higher chance of occurring. Variables that could be described by a triangular distribution include past sales history per unit of time and inventory levels.
PERT
The user defines the minimum, most likely, and maximum values, just like the triangular distribution. Values around the most likely value have a higher chance of occurring. However, values between the most likely and extremes are more likely to occur than the triangular; that is, the extremes are not as emphasized. An example of the use of a PERT distribution is to describe the duration of a task in a project management model.
Discrete
The user defines specific values that may occur and the likelihood of each. An example might be the results of a lawsuit: 20% chance of positive verdict, 30% chance of negative verdict, 40% chance of settlement, and 10% chance of mistrial.
FEATURES LIST (not always shown)
Feature | Benefit | Professional Edition | Industrial Edition |
---|---|---|---|
Optimization under uncertainty | Combines Monte Carlo simulation with sophisticated optimization techniques to find optimal solutions to uncertain problems. Used for budgeting, allocation, scheduling, and more. | ![]() | ![]() |
Efficient Frontier Analysis | Especially useful in financial analysis, Efficient Frontiers determine the optimal return that can be expected from a portfolio at a given level of risk | ![]() | ![]() |
Ranges for adjustable cells and constraints | Streamlined model setup and editing | ![]() | ![]() |
Genetic algorithms | Find the best global solution while avoiding getting caught in local, “hill-climbing” solutions | ![]() | ![]() |
Six solving methods, including GAs and OptQuest | Always have the best method for different types of problems | ![]() | ![]() |
RISKOptimizer Watcher and Convergence Monitoring | Monitor progress toward best solutions in real time | ![]() | ![]() |
Overlay of Optimized vs Original Distribution | Compare original output to optimized result to visually see improvements | ![]() | ![]() |
Original, Best, Last model updating | Instantly see the effects of three solutions on your entire model | ![]() | ![]() |
Random Sampling Versus Best Guess
During a Monte Carlo simulation, values are sampled at random from the input probability distributions. Each set of samples is called an iteration, and the resulting outcome from that sample is recorded. Monte Carlo simulation does this process hundreds or thousands of times, and the result is a probability distribution of possible outcomes. In this way, Monte Carlo simulation provides a much more comprehensive view of what may happen. It tells you not only what could happen, but how likely it is to happen.
Monte Carlo simulation provides several advantages over deterministic, or “single-point estimate” analysis:
Probabilistic Results. Results show not only what could happen, but how likely each outcome is.
Graphical Results. Because of the data a Monte Carlo simulation generates, it’s easy to create graphs of different outcomes and their chances of occurrence. This is important for communicating findings to other stakeholders.
Sensitivity Analysis. Deterministic analysis makes it difficult to see which variables impact the outcome the most. In Monte Carlo simulation, it’s easy to see which inputs had the biggest effect on bottom-line results. This allows you to identify and mitigate factors which cause the most risk.
Scenario Analysis: Scenario analysis determines which input variables contribute significantly toward reaching a particular goal (called the target scenario or output scenario) associated with an output. For example, it can show which variables contribute to exceptionally high sales values or which variables contribute to negative NPV values.
Correlation of Inputs. In Monte Carlo simulation, it’s possible to model interdependent relationships between input variables. It’s important for accuracy to represent how, in reality, when some factors go up or down, others go up or down accordingly.
An enhancement to Monte Carlo simulation is the use of Latin Hypercube sampling which samples more accurately from the full range of values within distribution functions and produces results more quickly.
How PrecisionTree Is Used
PrecisionTree has a multitude of applications, including:
Oil, Gas, & Mineral Reserves:Map out sequential, probabilistic exploration plans of prospective sites containing oil, natural gas, or other minerals. Estimate uncertain reserves to make wise drilling decisions.
Litigation & Bidding Strategy:Plan step-by-step strategies in complex legal or business negotiations, or when bidding on contracts. Map what could happen at each stage and your response to, along with probabilistic chance events.
Real Options Valution:Quantify the value of real options, or the right to undertake an investment or not, in the face of uncertainty future outcomes.
Supply Chain Management: Develop multi-stage plans for complex supply chains, incorporating probabilities of failures and other chance events.
Medical Treatment Planning: Establish sequential, multi-stage treatment plans for complex medical conditions given uncertain outcomes at each stage.
Resources about Monte Carlo Simulation
How Teacher Education Programs are Leveraging Student Personalized Placement Software
Creatingan elevated, personalized experience for their students Higher education institutionsare continuouslybusy coordinating field placement for students studying health, education, and otherpractice-based majors. This detailed process...
Using Monte Carlo Simulation in Excel to Understand Possible Outcomes in Manufacturing
Identifying possibilities and actioning on strategic scenarios in manufacturing Welcome to a fascinating expedition into Monte Carlo simulation use in manufacturing, a powerful method for...
Monte Carlo Magic: Accurate Football Tournament Probabilities
Join this webinar to learn about the “magic” of Monte Carlo simulation through the modeling of the uncertainties involved in the outcomes of matches in...
Predictive Neural Networks
Sophisticated, predictive neural networks imitate brain functions to identify patterns in historical or new, incomplete data sets – letting you intelligently predict the future and...
10 Project Manager Issues Addressed by Using Monte Carlo Simulation
Anticipating Project Manager Issues with Monte Carlo Simulation to Meet Deadlines and Plan Contingencies Project management is a multifaceted endeavor that involves careful planning, resource...
@RISK New Version: Enhanced Communication and Modeling for Gantt Charts, Time Series, and ScheduleRiskAnalysis
Effortlessly improve your decision making through risk modeling and analysis with @RISK software – a powerful add-in tool for Microsoft Excel. By using the Monte...
Optimizing Reliability Engineering in Manufacturing with Monte Carlo Simulation
As 2023 progresses, manufacturing companies continue to focus on supply chain management issues. In an April 2023 survey conducted by CNBC, only 36% of supply...
Optimizing Manufacturing Operations with Monte Carlo Simulation for Supply Chain Risk Management
The increased costs, lack of reliable transportation, and scarcity of supplies all clearly tell the story that’s reigned on news feeds since 2020; The global...
Manufacturing Supply Chain Management: Optimizing Production and Supplier Specifications Using Monte Carlo Simulation
How to Optimize Production and Inventory and Improve Tolerance Stacking Through Risk Analysis and Forecasting Supply chain management issues continue to be top of mind...
Optimizing Manufacturing Supply Chains with Monte Carlo Simulation
How to Keep Supply Chains Flowing Amid Global Threats with Risk Analysis for Optimizing Manufacturing For manufacturers, COVID-19 revealed many vulnerabilities in today’s complex global...
The Analytics Pyramid: Why Analytics are Critical for Defensible, Objective Decision-Making?
Organizations of all types use analytics to approach decision-making more objectively, accurately, and confidently. These techniques help decision-makers at all levels to be better-informed and...
Getting Started with ScheduleRiskAnalysis in 10 Steps
Managing uncertainty in project schedules has never been easier thanks to DecisionTools Suite’s newest feature, ScheduleRiskAnalysis (SRA). SRA lets you perform risk analysis using Monte...
Hedge Against Volatile Oil Prices Using Monte Carlo Simulation
Updated: Sept. 1, 2023 The escalation of Russian’s invasion of Ukraine and the ongoing response to the COVID-19 pandemic contributed to crude oil price volatility...
Cost Estimating: Triangular vs PERT
Continuing with this series of articles introducing cost estimating with @RISK, we will compare the use of the most popular distributions of this technique: the...
Announcing ScheduleRiskAnalysis for Project Schedules in the DecisionTools Suite!
Manage uncertainty in project schedules like never before with Monte Carlo simulation. Perform risk analysis on Primavera P6 or Microsoft Project models in the @RISK...
Hedge Against Volatile Exchange Rates with Monte Carlo Simulation
Originally Published: Nov. 1, 2022 Updated: Sept. 1, 2023 At the time of this article's publication in November 2022, the U.S. dollar was at its...
Basic Cost Engineering with @RISK
This article offers a simple and concise explanation of the Monte Carlo simulation, a technique that combines statistical concepts (random sampling) with the ability of...
Project PMO
Jim Aksel, Principal atProjectPMOin Anaheim, California, has consulted for several major aerospace companies in project and schedule management. In this case study, he discusses how...
PCM Consulting
PCM Consulting, a project, contract, and engineering management consulting company based out of South Africa, used @RISK to determine the financial viability of biogas plants...
Bolster Your FIFA World Cup Bracket with @RISK
The 2022 FIFA World Cup is right around the corner and the tournament predictions are pouring in. While checking team rankings and relying on gut...
Monte Carlo vs Latin Hypercube Sampling
A model that compares Monte Carlo and Latin Hypercube sampling.
Identifying Profitable Housing Development Opportunities with Risk Analysis
Real estate investment opportunities come in all shapes and sizes – from new developments that traditionally provide reliable, predictable income, to troubled properties that could...
Monte Carlo Simulation as a Force for Good
Many who have been exposed to Monte Carlo simulation learned about it in the context of financial modeling such as asset management, cash flow analysis,...
Improving Legal Case Outcomes with @RISK and PrecisionTree, Part IV
A common first step in litigation strategy is to calculate the case’s settlement value. As discussed in our past legal blog series, settlement calculations can...
Improving Legal Case Outcomes with @RISK and PrecisionTree, Part I
In litigation, you often get stuck in inefficient negotiations. Between 95-97% of patent lawsuits settle before trial, but not before amassing an average of more...
Rotman School of Management Students Learn to Make Key Financial Decisions Using Monte Carlo Simulation
Asher Drory of the University of Toronto’s Rotman School of Management uses @RISK in his graduate-level Financial Management course. Understanding how to use Monte Carlo...
UK Ministry of Defence Completes Projects Within Time and Cost Budgets Set With Risk Analysis Forecasts
UK Ministry of Defense projects can be large and complex, including major equipment procurement projects. A Project Risk Maturity Model incorporating @RISK has increased the...
Unilever Uses DecisionTools Suite Software to Inform Decisions on Innovation
To better inform decisions, Unilever selected Lumivero’s DecisionTools Suite as the principle analysis software to support its Decision Making Under Uncertainty process and decision-focused culture...
Students at Cornell University's Dyson School use @RISK to evaluate capital budgeting, investments, random walks, derivatives pricing and real options
Offered by the Charles H. Dyson School of Applied Economics and Management at Cornell University, Dr. Calum Turvey’s Risk Simulation and Optimization course introduces students...
Deloitte Uses @RISK to Advise Clients on Risk-Heavy Insurance Partnerships
Global consultancy Deloitte uses @RISK to help insurers determine the risks that they may be exposed to when considering cell captive insurance policies. The insurance...
Using @RISK and Principal Component Analysis (PCA) for Valuing a Portfolio of Natural Gas Futures
The use ofcustom Excel programmingand @RISK APIs allows the automated analysis of historical data and construction of sophisticated risk models. Here, we present an application...
Monte Carlo Simulation Provides Insights to Manage Risks
Palisade's former CEO, Randy Heffernan, was featured in the May 2021 issue of Risk Management Magazine. In this article he shared, in part: Monte Carlo...
Struggling with Your NCAA Bracket? Try Monte Carlo Simulation, with Help from the Pros
Each March, office productivity is greatly impacted by theNCAA Men’s Basketball Tournament. Just about everyone—regardless of their passion for college basketball—fills out a bracket in...
Contingency Calculation in Cost Risk Analysis
When performing a cost risk analysis study, one of the key results is the amount of extra monetary resources that is to be added to...
The Efficient Frontier and Monte Carlo Software – Part II: Resampling
Let’s move on from Part I of this blog series on the Efficient Frontier, formulated over half a century ago by Harry Markowitz, to the...
The Efficient Frontier and Monte Carlo Software – Part I: Background
Thisarticle from IndexUniverse.comdetails just one of the ways Monte Carlo simulation can be tuned to the combined unfolding of time and risk. First, a little...
The Efficient Frontier and Monte Carlo Software – Part III: Huang Litzenberger
In Part II of this series, we mentioned the existence of an analytic method to calculate the Efficient Frontier of a portfolio. Here we provide...
Calculation of Pi using Simulation and Other Approximations
Just for fun, here we talk about using Monte Carlo simulation to estimate the value of π (3.14159…). A circle of radius one will have...
Predicting the World Cup Winner with Monte Carlo Simulation
Soccer fans around the world are gearing up for the 2014 World Cup in Brazil. Many will be putting money on the various matches—basing their...
Ensuring Food Safety with Monte Carlo Simulation
The article shines light on the fact that the U.S. Food and Drug Administration has launched an interactive web-based tool called iRISK, to combat the...
Monte Carlo and Manufacturing: Learn more about simulation software and Monte Carlo simulation in the manufacturing industry.
A recent article written Randy Heffernan explores a variety of applications of Monte Carlo simulation in the manufacturing sector, such as: minimizing pilot programs, enterprise...
Super Bowl Prop Bets and Monte Carlo Simulation
The Super Bowl brings a significant amount of speculation on a multitude of outcomes—from who will win the match, to what color Gatorade will be...
Simulation City: Simulation software can improve decision making - and the manufacturing process
Monte Carlo simulations, named for the city in Monaco, were developed during the 1940s with the Manhattan Project. But today’s simulation software can be used...
Monte Carlo Simulation Means Quantifying Logistics Risks Doesn't Have to Be a Gamble
The expansion of global supply chains has meant an exponential growth of the risk of disruptions to those networks. Organizations around the world are turning...
When Calculating Risk for Reinsurers, Consider Monte Carlo
In the world of reinsurance, accurately determining risk is critical. The application of Monte Carlo simulation is being considered more often in order to better...
Monte Carlo…Or Bust?
The reinsurance industry has endured numerous larger than expected losses in the last decade or so -- everything from Hurricane Katrina to the global financial...
Getting the Full Picture Combining Monte Carlo Simulation with Decision Tree Analysis - Part I
@RISK is available with companion product PrecisionTree in the DecisionToolsSuite. PrecisionTreecreates decision trees in Excel to allow you to map and understand the complex decision...
Analysis Placebos: The Difference Between Perceived and Real Benefits of Risk Analysis and Decision Models
The authors examine decision analysis methods that merely make people feel better about their decisions with those that produce measurable improvements over time. They find...
Getting the Full Picture – Combining Monte Carlo Simulation with Decision Tree Analysis Part II
In Part I, combining simulation and decision tree analysis techniques was introduced. But what does that actually give you? What meaningful results are created to...
Monte Carlo Simulation Provides Advantages in Six Sigma
First of all, what is Monte Carlo simulation? Monte Carlo simulation is a computerized mathematical technique that allows people to account for variability in their...
Tornado Graphs: Basic Interpretation
When using @RISK (risk analysis software for conducting Monte Carlo simulations in Microsoft Excel), one of the output graphs is a tornado graph. Such graphs...
Enterprise Licensing
Better Research, Insights, and Outcomes for All
Whether your organization’s focus is qualitative, quantitative, or mixed methods data analysis, we can help your whole team work better together — collaborating to aggregate, organize, analyze, and present your findings. Lumivero’s enterprise licensing options offer volume pricing for teams and organizations needing nine (9) or more licenses.
Enterprise licenses allow the flexibility to install Lumivero software and solutions on multiple computers (up to the maximum number of licenses that your site has purchased) with a centralized management solution.
Lumivero’s team-based solutions allow you to:
Stay up-to-date with free upgrades to the latest releases
Reduce IT costs with one platform deployed across your organization
Reassign licenses to different users as teams evolve
Centralize license and subscription management in one place
Streamline budget allocation, especially for smaller groups and consultancy firms
Enjoy a Dedicated Customer Success Manager and pro-rated rates for new users
Monte Carlo Simulation
with Lumivero
Lumivero’s @RISK software puts this powerful technique within reach for any Excel user faced with uncertainty in their analyses. @RISK makes it easy to graphically define risk models, run simulations, and analyze the results, all with the click of a mouse. @RISK is 100% integrated with Excel, adding hundreds of new functions to Excel so that users can quickly understand their risks without learning a new application. First introduced in 1987 for Lotus 1-2-3, @RISK has a long-established reputation for computational accuracy, modeling flexibility, and ease of use, making it the dominant Monte Carlo simulation software in the market today.