Input-Output and Hybrid LCA (Subject Editor: Sangwon Suh)

The International Journal of Life Cycle Assessment

, Volume 12, Issue 6, pp 381-390

First online:

Power series expansion and structural analysis for life cycle assessment

  • Sangwon SuhAffiliated withDepartment of Bio-based Products, College of Natural Resources, University of MinnesotaInstitute of Environmental Sciences (CML), Leiden University Email author 
  • , Reinout HeijungsAffiliated withInstitute of Environmental Sciences (CML), Leiden University

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Goal, Scope and Background

The usefulness of power series expansion for an LCA system has often been doubted, as those systems may not possess the unique properties that enable power series expansion and analyses based on the power series. This paper surveys the existing literature on power series expansion of monetary input-output system and discusses how the power series expansion can be utilized for more general systems including the LCA model.


The inherent properties of matrices that are capable of producing power series forms for their inverse and, further, can utilize structural path analysis are analyzed. Using these analyses, the way how a matrix that is not eligible for structural analyses is converted into an eligible form is investigated. A numerical example is presented to demonstrate the findings.


The necessary and sufficient condition for an indecomposable, real square technology matrix can be expressed using power series was identified. Two additional conditions for a technology matrix to be utilized for structural analyses using power series expansion are discussed as well. It was also shown that an LCA system that fulfills the Hawkins-Simon condition can be easily converted into the form that is eligible for structural analysis by rescaling the columns and rows.


As a numerical example, an application of accumulative structural path analysis for an LCA system is shown. The implications of the results are discussed in a more plain language as well.


The survey presented in this paper provides not only the conditions under which a linear system is expressed using a power series form but also the way to appropriately convert a system to utilize the rich analytical tools using power series expansion for structural analyses.

Recommendations and Perspectives

Widely used LCA databases and software tools have employed the linear systems approach as the basis. Much of these developments in the domain of LCA have been made, however, in isolation of the rich findings of IOA. There will be much to benefit LCA through an active dialogue between the two disciplines.

There are rich analytical tools available through the use of power series expansion. The current survey will help software developers and LCA practitioners to apply such tools in LCA.


Input-output analysis IOA LCA practitioners LCA software developers monetary input-output system power series expansion structural path analysis