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Life-cycle costing: Analysis of biofuel production systems 229

environmental impact caused by emissions through an appropriate valuation
procedure. Pollutants like reactive nitrogen may have a “cascade” of impacts
as the nitrogen emission transforms from different types of molecules of
varying reactivity and moves through the environment (Galloway et al.,
2003). The total cost to the environment thus changes as the nature of
the pollutant changes and thus the characterization problem is always
changing.
Conceptually, the eLCC is the closest to LCA. Heijungs et al. (2013)
proposed a unified framework to integrate both the established computa-
tional structure of LCA (Heijungs and Suh, 2002) and that of LCC. By
adopting the structure of LCA, the risk of double counting is avoided,
since the value added is accounted for in each individual process, and
not in subsequent processes. Note that, since the eLCC follows the com-
putational structure of LCA, the implied assumption that the entire system
is at steady state is also adopted (R€odger et al., 2017). This systematic
approach also makes it easier to scale up the computations for complex,
large-scale product systems. This approach makes the basic assumption that
the production chain or network adds value to the product, while its end
use consumes this accumulated value. Moreau and Weidema (2015)
proposed the reinterpretation of eLCC as the “sum of the value added
for each activity in the product life-cycle for each and every actor involved,
including externalities which are foreseen to be internalized in the
decision-relevant future.”
Once the different processes included in the LCA have been identified, it
is then possible to generate the technical coefficient matrix, A p , which rep-
resents the fixed proportions of material and energy flows for each process in
the system. Matrix A p consists of rows which represent economic streams,
and columns which represent the processes within the system. By conven-
tion, a negative entry in the matrix represents an input to a process, while a
positive entry indicates an output or a production. The streams may be tan-
gible physical products (e.g., material or energy streams) or intangible out-
puts with appropriate units of measure (e.g., services). It is then possible to
scale the different processes to achieve the desired functional unit as repre-
sented in the functional unit vector, f p , as indicated in Eq. (8.1). For systems
with zero degrees of freedom, it is then possible to solve for the scaling vec-
tor s p by using Eq. (8.2).

A p s p ¼ f p (8.1)
1
s p ¼ A f p (8.2)
p