HMFA with steel stock of a building in Taiwan. Abbreviations: MD, the total amount of newly added material (t); MS, material stock (t); SR, stock ratio; AL, allocation factor; i, object; j, material; k, object type; l, a single object; t, year

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The process of HMFA is demonstrated by evaluating the inflow of steel stock (j) of a single building (l) with SS (k) in Taiwan for the year 2011 (t). The building (i) is categorized in the construction sector in IOTs. Information on the total amount of steel used for building construction in the construction sector (MDi,j,t) is collected from the annual report of the Taiwan Steel & Iron Industries Association (TSIIA) (Shih, 2016). Then the steel stock MSi,j,t is calculated by multiplying the MDi,j,t by the stock ratio SRi,t derived from FCFi,t and TSi,t of the construction sector in IOTs. Finally, the MSi,j,t is converted to the amount of steel stock of a single building (MSi,j,k,l,t) according to the ratio of steel content 𝜌j,k in the SS buildings and the total gross floor area Pk,l,t (m2). This example is illustrated in Figure 1.