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).

SummaryAlloying elements in steel add a wide range of valuable properties to steel materials that are indispensable for the global economy. However, they are likely to be effectively irretrievably blended into the steel when recycled because of (among other issues) the lack of information about the composition of the scrap. This results in the alloying elements dissipating in slag during steelmaking and/or becoming contaminants in secondary steel. We used the waste input-output material flow analysis model to quantify the unintentional flows of alloying elements (i.e., chromium, nickel, and molybdenum) that occur in steel materials and that result from mixing during end-of-life (EOL) processes. The model can be used to predict in detail the flows of ferrous materials in various phases, including the recycling phase by extending steel, alloying element source, and iron and steel scrap sectors. Application of the model to Japanese data indicates the critical importance of the recycling of EOL vehicles (ELVs) in Japan because passenger cars are the final destination of the largest share of these alloying elements. However, the contents of alloying elements are rarely considered in current ELV recycling. Consequently, the present study demonstrates that considerable amounts of alloying elements, which correspond to 7% to 8% of the annual consumption in electric arc furnace (EAF) steelmaking, are unintentionally introduced into EAFs. This result suggests the importance of quality-based scrap recycling for efficient management of alloying elements.

Steel is not elemental iron but rather a group of iron-based alloys containing many elements, especially chromium, nickel, and molybdenum. Steel recycling is expected to promote efficient resource use. However, open-loop recycling of steel could result in quality loss of nickel and molybdenum and/or material loss of chromium. Knowledge about alloying element substance flow is needed to avoid such losses. Material flow analyses (MFAs) indicate the importance of steel recycling to recovery of alloying elements. Flows of nickel, chromium, and molybdenum are interconnected, but MFAs have paid little attention to the interconnected flow of materials/substances in supply chains. This study combined a waste input-output material flow model and physical unit input-output analysis to perform a simultaneous MFA for nickel, chromium, and molybdenum in the Japanese economy in 2000. Results indicated the importance of recovery of these elements in recycling policies for end-of-life (EoL) vehicles and constructions. Improvement in EoL sorting technologies and implementation of designs for recycling/disassembly at the manufacturing phase are needed. Possible solutions include development of sorting processes for steel scrap and introduction of easier methods for identifying the composition of secondary resources. Recovery of steel scrap with a high alloy content will reduce primary inputs of alloying elements and contribute to more efficient resource use.

This paper uses firm‐level data to examine how supply chain networks affected the recovery of firms from the Great East Japan Earthquake. Extensive supply chains can negatively affect recovery through higher vulnerability to network disruption and positively through support from trading partners, easier search for new partners, and general benefits of agglomeration. Our results indicate that networks with firms outside of the impacted area contributed to the earlier resumption of production, whereas networks within the region contributed to sales recovery in the medium term. The results suggest that the positive effects of supply chains typically exceed the negative effects.

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