Environmental Engineering Reference
In-Depth Information
concepts are not equipped to deal with the issue of fairness, and often, various
aggregations of criteria are applied in order to select suitable solutions. However,
such aggregations force comparability of criteria (as in the weighted-sums
method). In their paper, Kostreva et al. present criteria aggregation methods that
can be used to derive equitably efficient solutions to both linear and nonlinear
multiobjective problems. As methods for achieving equitable efficiency continue
to be developed, they may be used in the context of environmentally conscious
SCO, where issues of fairness and equitable use of resources abound.
5.6
Selecting an Appropriate Method
NLP methods should be employed when nonlinear dependencies exist among
decision variables, or when problem parameters are governed by nonlinear func-
tions. MOP methods are appropriate when the SCO exercise involves several,
possibly conflicting, objectives. A point to note here is that if the various criteria
are not comparable and an AOF method is chosen, then each criterion must be
scaled appropriately (Feyzan and Zulal 2007). The dynamic nature of environ-
mental factors can be accounted for by carefully choosing time-horizon lengths
and modeling interdependencies among variables and time. Stochastic program-
ming and robust optimization are designed to explicitly deal with uncertainty;
however, the complexity involved can lead to tractability and computational
issues. Lastly, “optimal” SCO decisions are materially impacted by the choice
of optimality criteria (e.g., an “equitably efficient” solution does not necessarily
result in the greatest profit or value).
In concluding this section, we note that the suggested optimization approaches
are not intended to serve as an exhaustive list. As SCO problems continue to
increase in complexity, decision makers may have to reach for meta-heuristic
solution techniques such as genetic algorithms, tabu search, and simulated anneal-
ing (Michalewicz and Fogel 2000).
6
SUMMARY
Economywide surveys unequivocally indicate that the costs of engaging in envi-
ronmental efforts — mandated as well as voluntary — are indeed significant. A
recent survey by the U.S. Census Bureau (April 2008) shows that capital expen-
ditures for pollution abatement and control in the United States totaled $5.91
billion in 2005, of which $3.88 billion was attributed to air emissions, $1.35
billion to water discharge, and $0.68 billion to solid waste. Operating costs for
pollution abatement and control totalled $20.68 billion. Of this, $8.63 billion was
attributed to air emissions, $6.73 billion to water discharge, and $5.32 billion to
solid waste.
The significance of these costs reinforces the need for an SCO effort to
appropriately incorporate the factors identified in this chapter. Evidently, envi-
ronmental considerations introduce fair levels of subjectivity in SCO, such as in
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