К оглавлению
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 
17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 
34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 
51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 
68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 
85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 
102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 
119 120 121 122 123 

The real use of Monte Carlo Simulation in support of a project or program

is risk control. You want to control schedule risk or cost risk and usually both.

Monte Carlo Simulation almost demands the use of a computer because of the

nature of the process. The utilization of an available software package that supports

all these objectives is highly desirable. Fortunately, such things exist.

In times past, we made use of the ‘‘wet-finger-in-the-wind’’ technique to

establish risk, and therefore contingency, in programs. If you have a small project

and the overall risk is not perceived as great, you can still use this technique.

Simply, the technique is to do a ‘‘bottom up’’ estimate of task cost and task

schedule. Assign a value factor to your estimate. I have always used the value

factors 10/90, 50/50, and 90/10. The factors go from more risk (10/90) to less

risk (90/10). If you are involved in a proposal, the proposal manager will probably

insist on a 50/50 (most likely) estimate based on the assumption that 10/90

is too risky and 90/10 is too costly. You can then estimate the variance of what

it will take to get the task from 50/50 to 90/10. That estimate is the amount of

risk money or time that should be included with your bid along with a statement

of the task to be accomplished. Note: When I say ‘‘Included with your bid,’’

you need to follow the directions of your proposal manager. I insist that the time

and money allocated to risk be kept separate so that it can be collected at the

program level. Risk is then summarized, apportioned, and calculated at the program

level. If you include risk money at the task level you will end up with a bid

that will never win because of excessive cost.

Even though Monte Carlo techniques have been around for centuries, they

were not used extensively until the 1940s. History has it that Metropolis, associate

of Stan Ulam, brought the technique to the fore during the Manhattan

Project of World War II mainly to support Ulam’s penchant for gambling—

hence the name Monte Carlo. Ulam used the technique to solve mathematical

problems using statistical sampling in the development of the hydrogen bomb.

Monte Carlo techniques were not used too often in project planning until

the last ten or so years. There are two reasons for this: First, projects are more

expensive today and profit and schedule sensitivities are critical. Second, software

is now available to be used independently or in conjunction with other

software that makes the job of planning much simpler and faster, not to mention

more accurate.

The concept of the Monte Carlo technique is to assign Probability Density

Functions (PDFs) to outcomes. For example: Assume you have established a

task that is thirty days in duration. What is the probability that the task will be

four days late? What is the probability that the task will be done on time? What

is the probability that the task will be accomplished four days ahead of schedule?

The probability figure is the traditional 0–1 where 1 is the equivalent of 100

percent. Note that each of the figures is independent and the sum of all the

figures do not add up to one. Now, you don’t have to run too many projects or

programs to realize that, in the real world, the probability of schedule occurrence

grows with time. In other words, the later the estimate, the more likely it

is that the task will be completed. If the original estimate is anywhere near

correct, you will get a distribution that looks something like:

_4 days .1

0 days .7

_4 days .9

These are the PDFs that you run. It’s clear that, even with all the objectivity

of the computer and its processes, the basic data is subjective. In other words,

you established the original thirty days and you established the PDFs that apply

to each of the variances. That selection was, at least to some degree, subjective.

The computer will now select some random numbers and run the probabilities

over and over. You will end up with a high probability that the task will be

completed near the originally scheduled date but will be skewed slightly forward.

The early/late probabilities will center on this highest probability and

create a traditional bell curve or standard distribution curve. This foregoing has

been an extremely simplified example of what you might encounter in the field.

As promised at the outset of this book, I will not go into the math involved

in this process. If you are interested, I suggest you get a copy of any of the books

dealing with the Monte Carlo method. There are many, many of them out there.

You might consider the following books:

Rubenstein, Reuven Y. Simulation and the Monte Carlo Method. New York:

John Wiley, 1981.


Fishman, George S. Monte Carlo. New York: Springer-Verlag, 1996.

Sobol, Ilya M. A Primer for the Monte Carlo Method. Boca Raton: CRC Press,


Software, compatible with Microsoft products to provide Monte Carlo Simulation,

is available as ‘‘@RISK for Project’’ from:

Technology Associates

The Mansley Centre


Warwickshire CV37 9NQ


Worldwide Sales Office:

Phone: _44 (0) 1789 297000

Fax _44 (0) 1789 292191

E-mail: info@techassoc.com

U.S. Office

Phone: 917-210-8120

Fax: 917-210-8182

Voice mail: 206-374-2154