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Monte caRlo siMulations

is technique not only considers cost and schedule risk for indi-

vidual activities but also for the entire project. In many cases, there

is the temptation to assume that all project risks must be accounted

for in the worst case. e Monte Carlo analysis technique, however,

takes a more holistic approach. As such, the total project cost risk

and the total project schedule risk are usually expressed as a cumu-

lative probability distribution of total project cost and total project

schedule, respectively. Such distribution information can be used to

reect project risk by computing the probability that the project will

be accomplished within particular cost or schedule targets. It can also

be used to assess what level of funding or schedule would be required

to virtually guarantee success.

A computer is necessary to use this technique because the analysis

requires repetitive computations. Most of the software packages (for

example, Barbecana Full Monte, and @Risk) conduct both cost and

network analysis simultaneously, whereas some tools (@Risk for Excel,

for example) can perform only cost analysis. Input data requirements

for such models are signicantly less than cost and schedule analyses.

Technique Description

e technique uses simulation analysis to establish relative levels of

risk. In Monte Carlo analysis, uniform, normal, triangular, and beta

distributions are used to assign risk values to cost and schedule targets

for each work package within the work breakdown structure (WBS).

e type of distribution applied depends on the nature of the work

as well as the nature of the comprehension of that work. However,

dierent distributions require dierent levels of understanding.

A uniform distribution, for example, requires only that one knows

what the highest and lowest possible costs and durations are. A beta

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distribution, on the other hand, requires a far greater depth of data

and understanding.

Monte Carlo analysis uses a random-number generator to simu-

late the uncertainty for individual WBS elements. Some Monte Carlo

tools will use Latin Hypercube sampling, rather than random number

generators. In a Latin Hypercube, the analysis takes into account the

outcomes of earlier analyses, rather than truly random outputs. Most

analysts believe that Latin Hypercube achieves acceptable outcomes

with fewer samples.

After costs and schedules are simulated for each WBS element,

they are aggregated to establish a critical path, a total project dura-

tion, and a total project cost estimate. is process is repeated many

times. Each time that a new set of WBS element costs and durations

are developed is referred to as an experiment. e results of many such

experiments provide a frequency distribution of total costs, reecting

the aggregate of the cost risks associated with all individual WBS

elements.

When Applicable

is technique applies when the project manager needs to know the

probability that a project can be completed successfully at a given

funding level or within a given time frame. It is also appropriate to

use when there is a need to know what funding level is required to

achieve a specied probability of completing a project. To ensure that

this technique can be applied, the project manager must obtain sound

estimates of the cost uncertainty plus the schedule uncertainty associ-

ated with each WBS element. After cost and schedule estimates are

already in place at the work package level, this becomes a relatively

quick analytical procedure.

Inputs and Outputs

With Monte Carlo simulations, inputs and outputs vary depending

on the models used. As an example of inputs and outputs information,

Barbecana’s Full Monte and @Risk (as well as Primavera’s PERTMaster)

can apply various types of cost uncertainty against each individual

WBS element and then generate a variety of information types.

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