This paper proposes an optimal combinatorial method for finding groups of industries with relatively large CO2 emissions through industrial relations. Using an economic input-output table, we estimated a non-symmetric matrix describing how much CO2 is emitted in producing the commodity of industry i, which was purchased to produce commodity of industry j, to meet the final demand for a specific commodity. A symmetric strength of relations matrix describing the CO2 emissions associated with the industrial relations was further estimated using the non-symmetric matrix. The strength of relations matrix can be viewed as a representation of the supply-chain network of the final commodity. In this study, we estimated the strength of relations matrix associated with the final demand for automobiles and applied the multiway cut approach using nonnegative matrix factorization to the matrix in order to find environmentally important industry clusters in the Japanese automobile supply chain. According to our empirical results, the optimal number of industry clusters is 19, and 4 industry clusters are playing a key role in CO2 emission reduction.
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