The optimization routine considers the locational parameters of
the polluting facility as parameters to be optimized and
minimizes the function f as defined above. As outlined in
Chapter 1, the decision variables for the
optimization process are: the location of the facility,
the stack height of the pollutant emitter, and the stack diameter of the
pollutant emitter. Usually, constraints on 
are natural
results of the modeling process. They include representations of engineering
restrictions on stack height resp. diameter as well as locational
constraints representing coastlines, jurisdictional boundaries,
etc. As a consequence, almost all optimization problems to be solved are
constrained ones. We can, however, assume that all constraints are
written in standard form
or
with functions 
,
, 
.
Moreover, both functions can be assumed to be continuously differentiable.
This is usually considered as a strong assumption in locational analysis,
especially if one wants to model regions forbidden for placement of
the smokestack. However, recent research [8] has shown that
a corresponding problem formulation is not necessarily more complicated
than other locational models, provided that the right modeling tools are
used.