NDLI: Toward a solution of allocation in life cycle inventories: the use of least-squares techniques

Content Provider	Springer Nature Link
Author	Marvuglia, Antoni Cellura, Maurizio Heijungs, Reiut
Copyright Year	2010
Abstract	The matrix method for the solution of the so-called inventory problem in LCA generally determines the inventory vector related to a specific system of processes by solving a system of linear equations. The paper proposes a new approach to deal with systems characterized by a rectangular (and thus non-invertible) coefficients matrix. The approach, based on the application of regression techniques, allows solving the system without using computational expedients such as the allocation procedure.The regression techniques used in the paper are (besides the ordinary least squares, OLS) total least squares (TLS) and data least squares (DLS). In this paper, the authors present the application of TLS and DLS to a case study related to the production of bricks, showing the differences between the results accomplished by the traditional matrix approach and those obtained with these techniques. The system boundaries were chosen such that the resulting technology matrix was not too big and thus easy to display, but at the same time complex enough to provide a valid demonstrative example for analyzing the results of the application of the above-described techniques.The results obtained for the case study taken into consideration showed an obvious but not overwhelming difference between the inventory vectors obtained by using the least-squares techniques and those obtained with the solutions based upon allocation. The inventory vectors obtained with the DLS and TLS techniques are closer to those obtained with the physical rather than with the economic allocation. However, this finding most probably cannot be generalized to every inventory problem.Since the solution of the inventory problem in life cycle inventory (LCI) is not a standard forecasting problem because the real solution (the real inventory vector related to the investigated functional unit) is unknown, we are not able to compute a proper performance indicator for the implemented algorithms. However, considering that the obtained least squares solutions are unique and their differences from the traditional solutions are not overwhelming, this methodology is worthy of further investigation.In order to make TLS and DLS techniques a valuable alternative to the traditional allocation procedures, there is a need to optimize them for the very particular systems that commonly occur in LCI, i.e., systems with sparse coefficients matrices and a vector of constants whose entries are almost always all null but one. This optimization is crucial for their applicability in the LCI context.
Starting Page	1020
Ending Page	1040
Page Count	21
File Format	PDF
ISSN	09483349
Journal	The International Journal of Life Cycle Assessment
Volume Number	15
Issue Number	9
e-ISSN	16147502
Language	English
Publisher	Springer-Verlag
Publisher Date	2010-07-08
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Allocation Discrepancy vector Least squares Multi-functional process Orthogonal regression Over-determined system Environmental Economics Environment
Content Type	Text
Resource Type	Article
Subject	Environmental Science

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