Monte Carlo Simulation(MCS) in Project Management  demystified
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Simulation
As per Wikipedia simulation is defined as the imitation of some real thing, state of affairs, or process. It can also be described as an emulation of reality using a mathematical model. The act of simulating something generally entails representing certain key characteristics or behaviors of a selected physical or abstract system. This can help examine a given system’s behaviour in a virtual computational world taking into account different scenaria before applying it to the real world. Here we will be talking about simulation to elicit some key characteristics related to Project Management, using specifically the Monte Carlo technique.
Monte Carlo
Monte Carlo as a simulation method is used to iteratively evaluate a deterministic model using sets of random numbers as inputs. The basic principle behind this method, which has been used in many disciplines, is to randomly generate vales of uncertain and independent variables that make part of a model representing a system and make a computation of the model with the values of the variables. The larger the number of iterations (generated random values) the more reliable the outcomes will be, in coherence with the theory of large numbers of statistics. A histogram representing the values of the model against the frequency of happenings will be used to make a proper analysis.
The steps to be followed in using the Monte Carlo simulation in all circumstances are:

Identify key parameters x_{i}, i=1 to n,

Identify the range limits for the variables x_{imin}, x_{imax},

Specify probability weights for this range of values p(x),

Establish the relationships for the correlated variables, here is where a parametric model is created , y = f(x_{1}, x_{2}, ..., x_{q}).

Determine the optimal number of random inputs to be generated, n

Generate a set of random inputs, x_{i}_{1}, x_{i}_{2}, ..., x_{iq}.

Evaluate the model for the generated inputs and store the results as y_{i}.

Statistically analyze the results of the simulation run using histograms, summary statistics, confidence.
The parametric model can be simple or complex depending on the number of independent and uncertain parameters and the model.
The number of random inputs (n) will depend on an accepted error tolerance(ϵ) in percentiles and the standard deviation(Ϭ) of the random variable x_{i}.
N = (3 Ϭ/ ϵ)^{2}
Project Management & Uncertainties
Project management as a discipline that helps achieve the goals of a project using resources, knowledge, tools and techniques deals with an environment full of uncertain parameters. The major Project Management knowledge areas that can benefit from the MCS technique are: time management, cost management and risk management. The range of values of variables and the respective probability weights of the values of the parameters in all the mentioned knowledge areas are determined either by expert judgement or using historical data. The processes in which MCS technique can efficiently be used in relation to the mentioned knowledge areas are : Estimate activity durations, Estimate costs and Perform quantitative risk analysis.
Supposing we use the MCS to estimate activity durations following the above steps and the analysis is complete, we don’t obtain a single end date. We do have a probability curve showing expected outcomes and the probability of achieving each one.
For the purposes of scheduling, we would look at a cumulative curve showing the probability of completing the project between the best case, and the worst case.
MCS in PM
MCS can be very helpful to justifying the addition of reserves in cost , time duration or other key values of variables. In risk management one has to do a qualitative analysis of risks which will help identify the ones to be quantitatively analyzed using different methods but mostly the MCS technique. There exist quiet a number of efficient packages on the market for this purpose , but there exist also plugins to Microsoft excel which can do the job without much of a limitation in terms the number of random values to be generated using Excel 2007 and latter versions.
The key to the use of MCS for Project Management are : identification of the variables with their correlations(model), the identification of the distributions to be used for each of the variables, determining the optimal number of random values to be generated, compute the function and do the statistical analysis to determine the probabilities with which different values can be achieved.
One has to be cautious in determining the probability distributions of the variables and certainly the ranges on which the whole computation will be based. These criteria will determine the quality of the analysis and its outcome.