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

  • UNCERTAINTIES IN LCA
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Abstract

Purpose

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.

Methods

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.

Results and discussion

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.

Conclusions

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.

Recommendations

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.

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Acknowledgment

This work has been carried out with support from (1) the GENIUS LOCI project titled “The role of the building sector on climate change”, funded by the Italian Ministries of Economy; Education; University and Research, Environment and Territory protection, Agricultural and Forestry policies; (2) the Teaching Staff mobility funds in the framework of the LLP/Erasmus program, under the Erasmus Bilateral Agreement in force between the University of Palermo and the University of Leiden.

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Authors and Affiliations

  1. Cork Constraint Computation Centre (4C), University College Cork, Western Gateway Building, Cork, Ireland

    Antonino Marvuglia

  2. Dipartimento di Ricerche Energetiche ed Ambientali (DREAM), Università degli Studi di Palermo, Viale delle Scienze, 90128, Palermo, Italy

    Maurizio Cellura

  3. Institute of Environmental Sciences, Leiden University, P.O. Box 9518, 2300, RA, Leiden, The Netherlands

    Reinout Heijungs

Authors
  1. Antonino Marvuglia
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  2. Maurizio Cellura
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  3. Reinout Heijungs
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Correspondence to Antonino Marvuglia.

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Responsible editor: Andreas Ciroth

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Marvuglia, A., Cellura, M. & Heijungs, R. Toward a solution of allocation in life cycle inventories: the use of least-squares techniques. Int J Life Cycle Assess 15, 1020–1040 (2010). https://doi.org/10.1007/s11367-010-0214-1

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