## Monte Carlo Simulation

This page introduces Monte Carlo and explains why you might need it, and what you need to know (or learn) in order to use it.

- What is Monte Carlo Simulation?
- Why Should I Use Monte Carlo Simulation?
- What Knowledge Do I Need to Use It?
- How Will This Help Me in My Work or Career?

#### What is Monte Carlo Simulation?

The **Monte Carlo method** was invented by scientists working on the atomic bomb in the 1940s, who named it for the city in Monaco famed for its casinos and games of chance. Its core idea is to use **random samples** of parameters or inputs to explore the behavior of a complex system or process. The scientists faced physics problems, such as models of neutron diffusion, that were too complex for an analytical solution -- so they had to be evaluated **numerically**. They had access to one of the earliest computers -- MANIAC -- but their models involved so many **dimensions** that exhaustive numerical evaluation was prohibitively slow. Monte Carlo simulation proved to be surprisingly effective at finding solutions to these problems. Since that time, Monte Carlo methods have been applied to an incredibly diverse range of problems in science, engineering, and finance -- and business applications in virtually every industry.

#### Why Should I Use Monte Carlo Simulation?

Whenever you need to make an estimate, forecast or decision where there is significant uncertainty, you'd be **well advised** to consider Monte Carlo simulation -- if you don't, your estimates or forecasts could be **way off the mark**, with adverse consequences for your decisions! Dr. Sam Savage, a noted authority on simulation and other quantitative methods, says "Many people, when faced with an uncertainty ... succumb to the temptation of replacing the uncertain number in question with a single average value. I call this the **flaw of averages**, and it is a fallacy as fundamental as the belief that the earth is flat."

Most business activities, plans and processes are **too complex for an analytical solution** -- just like the physics problems of the 1940s. But you can build a spreadsheet model that lets you evaluate your plan numerically -- you can change numbers, ask 'what if' and see the results. This is straightforward **if** you have just one or two parameters to explore. But many business situations involve **uncertainty in many dimensions** -- for example, variable market demand, unknown plans of competitors, uncertainty in costs, and many others -- just like the physics problems in the 1940s. If your situation sounds like this, you may find that the Monte Carlo method is surprisingly effective for you as well.

#### What Knowledge Do I Need to Use It?

To use Monte Carlo simulation, you must be able to build a quantitative model of your business activity, plan or process. One of the easiest and most popular ways to do this is to create a **spreadsheet** model using Microsoft Excel -- and use Frontline Systems' **Risk Solver** as a simulation tool. Other ways include writing code in a programming language such as Visual Basic, C++, C# or Java -- with Frontline's **Solver Platform SDK** -- or using a special-purpose simulation modeling language.You'll also need to learn (or review) the basics of **probability and statistics**. To deal with uncertainties in your model, you'll replace certain fixed numbers -- for example in spreadsheet cells -- with functions that draw **random samples** from probability distributions. And to analyze the results of a simulation run, you'll use statistics such as the mean, standard deviation, and percentiles, as well as charts and graphs. Fortunately, there are great software tools (like ours!) to help you do this, backed by technical support and assistance.

#### How Will This Help Me in My Work or Career?

If your success depends on making **good forecasts** or **managing** activities that involve **uncertainty**, you can benefit in a big way from learning to use Monte Carlo simulation. By doing so, you can **Avoid the Trap of the Flaw of Averages.** As Dr. Sam Savage warns, "Plans based on average assumptions will be *wrong* on average." If you've ever found that projects came in later than you expected, losses were greater than you estimated as "worst case," or forecasts based on averages have gone awry -- you stand to benefit!

**Go Beyond the Limits of 'What If' Analysis.** A conventional spreadsheet model can take you only so far. If you've created models with best case, worst case and average case scenarios, only to find that the *actual* outcome was very different, you need Monte Carlo simulation! By exploring *thousands* of combinations for your 'what-if' factors and analyzing the full range of possible outcomes, you can get much more accurate results, with only a little extra work.

**Know What Factors Really Matter.** Tools such as Frontline's **Risk Solver** enable you to quickly identify the high-impact factors in your model, using *sensitivity analysis* across thousands of Monte Carlo trials. It could take you hours to identify these factors using ordinary 'what if' analysis.

**Give Yourself a Competitive Advantage.** If you're negotiating a deal, or simply competing in the marketplace, having a realistic idea of the *probability* of different outcomes -- when your opponent or competitor does not -- can enable you to strike a better bargain, choose the price that yields the most profit, or benefit in other ways.

**Be Better Prepared for Executive Decisions.** The higher you go in an organization, the more you'll find yourself dealing with uncertainty. Simulation or risk analysis might not be essential for routine day-to-day, low-value decisions -- but you'll find it invaluable as you deal with higher-level, more strategic -- and higher-stakes -- decisions.

Consult our **tutorial** to learn more. We'll take you step by step through the process of converting a simple spreadsheet model, that uses "flawed average" assumptions, into a risk analysis model that yields surprising insights with the aid of Monte Carlo simulation.