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
reect 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 signicantly 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,
dierent distributions require dierent 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
risk ManageMent
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, reecting
the aggregate of the cost risks associated with all individual WBS
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 specied 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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