Introduction
Many business situations involve uncertainty. Such situations arise frequently when trying to do budgeting,
project planning, investment planning, etc. Whenever we have uncertainty, this implies some amount of risk in our
decisionmaking process. So business managers attempt to come up with a reasonable estimate or "best guess" for
uncertain outcomes (variable values).
There are several methods of risk analysis that managers could typically consider, e.g.:
 BestCase/WorstCase Analysis
 WhatIf Analysis
 Simulation Modeling
Let's examine each of these approaches.
BestCase/WorstCase Analysis
This method begins with a "most likely" or "base case" value that we might expect for a variable. And because we
recognize that the actual value may turn out to be somewhat different from what we believe is the most likely
value, we also try to specify "worst case" and "best case" values to give us a range of possible values around the
base case.
But there are problems inherent in this approach to risk analysis. Simply knowing the "best case" and "worst
case" outcomes doesn't give us any useful information about the distribution of possible values within
this range. It also doesn't tell us the probabilitity with which either the "best case" or "worst case"
outcome might occur. Shown below are just a few examples of how the distribution of probable outcomes might look,
depending on the underlying nature of the data.
Here are three different uniform probability distributions, in which all possible outcomes (on the X
axis) have equal probabilities:
Here are four examples of normal ("bell curve") probability distributions, in which the highest
probabilities occur nearest the horizontal center of the distributions, but then tail off as we approach the
extremes:
Here are five examples of the Gamma distribution, where higher probabilities are concentrated
asymmetrically somewhat more toward the left end of the horizontal axis, gradually tailing off as we move to the
right:
And here is an example of an asymmetric triangular distribution:
In addition to the above examples, there are many other types of probability distribution; and each type can
have many different shapes. So a bestcase/worstcase method of defining only two possible extreme outcomes is
a rather imprecise method that does not reflect reality very well. Knowing, or at least being able to surmise the
shape of the probability distribution, will tend to be a much more accurate and successful approach to assessing
and managing risk.
WhatIf Analysis
This method is still popular among many business managers. It typically involves the testing of many more
scenarios than just "base case," "worst case" and "best case" outcomes, so it tends to be somewhat more
accurate. But there are several problems associated with this approach. For example, the values of the
input variables are usually selected based on the manager's judgment, which may lead to a substantially biased
output variable. And managers simply don't have the time to select a large number of random values to test
manually for all of the input variables across the entire presumed ranges of the variables.
In addition, even if a manager could take the time to create a large number of scenarios, the resulting output
from all these scenarios would be difficult to interpret, explain and justify to management, who must make a
single, final decision. And finally, this approach suffers from the same limitation we saw in connection with
the bestcase/worstcase method: it doesn't provide a sufficiently formal way to estimate the probability
distributions of either the input variables or the output variable.
Simulation
Because of the severe limitations of the other two major approaches to risk analysis, managers are increasingly
turning to the more sophisticated and accurate simulation approach. Simulation allow us to factor in the
influences of many random input variables to determine the likely impact on a random outcome variable. This
method insures that the values of the input variables are assigned in an unbiased way, and without the manager's
having to spend a lot of time trying to decide what all these values should be.
With the use of modern computers, we can randomly generate a large number of sample values for each input
variable, and then determine the impact of these various values on the output variable(s), or "performance
measure(s)," of interest to us. This approach also provides us with useful statistics to help guide our
decision, e.g.:
 A probability distribution of the possible values of the performance measure
 An estimate of the mean and variance of the probability distribution
 An estimate of the probability that the value of the performance measure will be greater than or less than
a particular value
 A statistical confidence interval constructed around the expected value of the performance measure, that
shows us how much error there might be in our calculation, and what the true range of the performance
measure could be
All of these features of simulation analysis tend to provide managers with a much more realistic estimate of
risk and probable outcomes, and this tends to lead to more accurate and successful decisions.
This link takes you to an example demonstrating the application of Monte Carlo simulation risk analysis to a budgeting
problem.
And here is an example that combines Monte Carlo risk simulation with
Nonlinear Programming to optimize the assignment of management consultants to consulting projects and maximize
total expected profit.
Back to Top
Back to the Operations Research
and Analytics page
_______________
Images of probability distributions shown
above are used courtesy of
the Wikimedia Commons organization
(http://commons.wikimedia.org), and are used under the Creative Commons license agreement (http://creativecommons.org/licenses/bysa/3.0/).
