**2. Monte Carlo simulation**

Monte Carlo simulation (MCS), or probability simulation, is a technique used to understand the impact of risk and uncertainty cost, time, and other forecasting models [4]. MCS estimates the expected value based on historical data, or expertise in the field, or experience. While this estimate is useful for creating a model, it contains some intrinsic uncertainties, because it is an estimate of unknown values [4].

In project management, you could use expert knowledge to estimate the time it will take to complete a particular job, you can also estimate the maximum time it might take, in the worst possible case, and the minimum time, in the best possible case. The same could be done for project costs. The Monte Carlo simulation method is used for estimating the output Y of a function (M) with random input variables (R1, R2, … , Rn) (**Figure 1**).

**Figure 1.** *The output Y of a function M with random inputs can be calculated using Monte Carlo simulation.*

**Figure 2.** *A probability density function (PDF) developed based on historical data.*

*Fuzzy Monte Carlo Simulation to Optimize Resource Planning and Operations DOI: http://dx.doi.org/10.5772/intechopen.93632*

In a Monte Carlo simulation, an arbitrary value is selected for each of the activities, based on the range of estimates. The model is calculated based on this arbitrary value. The result of the model is recorded, and the process is repeated [6]. A traditional Monte Carlo simulation calculates the model hundreds/thousands of times, each time using different randomly selected values. When the simulation is complete, we have a large number of outcomes, each based on random input values. These outcomes are used to describe the likelihood, or probability, of reaching various results in the model [6] (**Figure 2**).
