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9.3
What-If Modeling
P
urpose
The role this topic plays in quantitative reasoning
Mathematical models produce output that is dependent on the input parameters. During the validation
process, we have seen that variations in the input result in corresponding changes in model output. In
real world applications, the input quantities have values that are likely but are often not certain. What-
If modeling examines the plausible alternatives that arise in a situation of interest and translates these
to different sets of input conditions. With a mathematical model, we can then calculate the outputs
corresponding to these varying scenarios. The answers to many interesting questions come to fruition
when we formalize this approach.
One of the goals of what-if modeling is to determine the effects due to changes in one or more of the
input variables. Perhaps the addition of a toll on an established route will cause a decrease in the traffic
flow, but how much of a charge is necessary to see this effect and how will the locations of the toll affect
the number of cars using the road? Using a mathematical model of the traffic flow on this road we can
predict the effects of different toll locations. In order to see this relationship clearly it is common to
analyze the model one factor at a time (OFAT); Fixing other input variables used by the model so that
any changes in the amount of traffic are attributed solely to the toll. Proceeding in this manner we can
quantify the range of uncertainty produced by the sample space.
When many factors are susceptible to fluctuation then it is possible our analysis of them individually is
insufficient. What-if modeling can then be used to apportion priority to the various changes influencing
an outcome or situation and then determine the maximum deviation likely to occur in the output.
Government agencies such as the EPAfrequently make use of impact assessment to delineate complicated
issues. When modeling the environmental effects of a proposed development the use of what-if analysis
is employed as a standard part of the evaluation. Naturally, this allows for the identification of the
quantities that contribute the most to the variation of the model’s results. Once identified these variables
may be the focus of future research.
L
earning Goals
What you should learn while completing this activity
1. Apply the process of constructing a model when the goal is what-if modeling
2. Describe the effects of changing individual input quantities on the resulting output of a mathematical
model.
3. Use what-if modeling to assess a situation where inputs are uncertain
4. Improve ability to provide recommendations based on what-if analysis
D
iscovery
Finding out for yourself
Access and run the mathematical model “Eating and Exercise” available from the companion website.
Using your own physiological data, record the results of the model for your range of different eating
habits while keeping the exercise input fixed. Now fix the diet and capture the changes in your
exercise routine, recording the output from the model.