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230 Biofuels for a More Sustainable Future

This framework can then be extended to calculate for the life-cycle cost
of a system by evaluating the scaled technology matrix, A p,scaled as shown in
Eq. (8.3) where diag(s) is the diagonalized scaling vector. The associated
costs for the system are then obtained using Eq. (8.4) where diag(α)is
the diagonalized price vector which contains the market value for the rel-
evant streams identified. Finally, the value added vector, v, can be obtained
using Eq. (8.5) where 1 is a vector consisting of all ones.

A p,scaled ¼ A p diag s p (8.3)

A m,scaled ¼ diag αðÞA p,scaled (8.4)
T
v ¼ A m,scaled Þ 1 (8.5)
ð
The life-cycle cost is then equivalent to vector v. To illustrate this
approach, we use the following example from Heijungs et al. (2013) and
the subsequent reinterpretation by Moreau and Weidema (2015) which
considers the life cycle of a chair. The system is shown in Fig. 8.1, the tech-
nology matrix (A p ) is given in Table 8.1, while the associated market price

Electricity Wood
generation production

Electricity Wood

Production
of chair

Chair

Use of chair

Broken
chair

Disposal of
chair
Fig. 8.1 Process flow diagram for chair life cycle. (Modified from Heijungs, R., Settanni, E.,
Guin ee, J., 2013. Toward a computational structure for life cycle sustainability analysis:
unifying LCA and LCC. Int. J. Life Cycle Assess. 18, 1722–1733. doi:10.1007/s11367-012-
0461-4.)