The waste input-output approach to materials flow analysis: Concepts and application to base metals

Shinichiro Nakamura*, Kenichi Nakajima, Yasushi Kondo, Tetsuya Nagasaka

*Corresponding author for this work

Research output: Contribution to journalReview articlepeer-review

142 Citations (Scopus)


A general analytical model of materials flow analysis (MFA) incorporating physical waste input-output is proposed that is fully consistent with the mass balance principle. Exploiting the triangular nature of the matrix of input coefficients, which is obtained by rearranging the ordering of sectors according to degrees of fabrication, the material composition matrix is derived, which gives the material composition of products. A formal mathematical definition of materials (or the objects, the flow of which is to be accounted for by MFA) is also introduced, which excludes the occurrence of double accounting in economy-wide MFAs involving diverse inputs. By using the model, monetary input-output (IO) tables can easily be converted into a physical material flow account (or physical input-output tables [PIOT]) of an arbitrary number of materials, and the material composition of a product can be decomposed into its input origin. The first point represents substantial saving in the otherwise prohibitive cost that is associated with independent compilation of PIOT. The proposed methodology is applied to Japanese IO data for the flow of 11 base metals and their scrap (available as e-supplement on the JIE Web site).

Original languageEnglish
Pages (from-to)50-63
Number of pages14
JournalJournal of Industrial Ecology
Issue number4
Publication statusPublished - 2007 Sept


  • Double counting
  • Industrial ecology
  • Input-output analysis
  • Material composition
  • Physical input-output tables (PIOT)
  • Triangularity

ASJC Scopus subject areas

  • Environmental Science(all)
  • Social Sciences(all)


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