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7.2 How Do We Classify Models?
There are ways to classify models other than by the circumstances within which they
exist. For example, earlier we discussed the circumstances of data rich and data poor
models. Another fundamental classiﬁcation for models is as either deterministic or
probabilistic . A deterministic model will generally ignore, or assume away, any
uncertainty in its relationships and variables. Even in problems where uncertainty
exists, if we reduce uncertain events to some determined value, for example an aver-
age of various outcomes, then we refer to these models as deterministic. Suppose
you are concerned with a particular task in a project that you believe to have a 20%
probability of requiring 2 days, a 60% probability of 4 days, and a 20% probabil-
ity of 6 days. If we reduce the uncertainty of the task to a single value of 4 days,
the average and the most likely outcome, then we have converted an uncertain out-
come into a deterministic outcome. Thus, in deterministic models, all variables are
assumed to have a speciﬁc value, which for the purpose of analysis remains constant.
Even in deterministic models, if conditions change we can adjust the current
values of the model and assume that a new value is known with certainty, at least
for the purpose of analysis. For example, suppose that you are trying to calculate
equal monthly payments due on a mortgage with a particular term (30 years or
360 monthly payments), an annual interest rate (6.5%), a loan amount ($200 K),
and a down-payment ($50 K). The model used to calculate a constant payment
over the life of the mortgage is the PMT() ﬁnancial function in Excel. The model
returns a precise value that corresponds to the deterministic conditions assumed
by the modeler. In the case of the data provided above, the resulting payment is
$948.10, calculated by the function PMT ( 0.065/12,360,150,000 ) . See Exhibit 7.2
for this calculation.
Now, what if we would like to impose a new set of conditions, where all PMT()
values remain the same, except that the annual interest rate is now 7%, rather than
6.5%. This type of what-if analysis of deterministic models helps us understand the
potential variation in a deterministic model, variation that we have assumed away.
The value of the function with a new interest rate of 7% is $997.95 and is shown in
Exhibit 7.3. Thus, deterministic models can be used to study uncertainty, but only
through the manual change of values.
Unlike deterministic models, probabilistic models explicitly consider uncer-
tainty; they incorporate a technical description of how variables can change and the
uncertainty is embedded in the model structure. It is generally the case that prob-
abilistic models are more complex and difﬁcult to construct because the explicit
consideration of the uncertainty must be accommodated. But in spite of the com-
plexity, these models provide great value to the modeler; after all, almost all
important problems contain some elements of uncertainty.
Uncertainty is an ever present condition of life and it forces the decision maker
to face a number of realities:
1. First and foremost, we usually make decisions based on what we currently know,
or think we know. We also base decisions and actions on the outcomes we expect