**5. Conclusions**

A factorial ecological-extended physical input-output model (FE-PIOM) was developed for enhancing urban solid waste system (USWS) performance, which integrated techniques of physical input-output model (PIOM), ecological network analysis (ENA), and fractional factorial analysis (FFA). The FE-PIOM could effectively assess urban solid waste productions and embodied flow path, quantify single and joint effects of multiple factors, as well as provide sound urban solid waste reduction path. The developed FE-PIOM was employed to a real case study of Fujian, an important economic development province in China, for supporting the tradeoff between economic development and environmental protection.

The main findings are summarized as: (i) the amount of indirect waste production was higher than the direct waste production, with the indirect production occupying more than 60 to 70% of the total production (i.e., the sum of direct and indirect productions); (ii) the indirect waste flows were more complicated than those of direct flows; (iii) solid waste mainly was produced by primary manufacturing (PM) and advanced manufacturing (AM), accounting for 30% and 38% of the total production, respectively; (iv) AM was the biggest sector which controlled the other producers, while its control weight was too high (35 to 50% of the total weight); (v) the USWS was mutualistic due to *SI* > 0 and *MI* > 1; (vi) AM\_a (i.e., direct consumption coefficient of AM) and PM\_a (i.e., direct consumption coefficient of PM) were the most important factors which had negative effects on USWS solid waste production intensity (SPI), contributing 50–60% and 22–37% to standard effects; (vii) the interactions between CON\_e\*OTH\_e (i.e., solid waste production of CON\*solid waste production of OTH) and TRA\_e\*OTH\_e were obvious; (viii) for enhancing USWS performance, reducing the commodity consumption of AM and PM from other sectors by 20% (e.g., improve material usage efficiency and develop advanced material), as well as decreasing economic activities of CON, TRA, and OTH by 20%, would be useful.

This is the first attempt to apply the FE-PIOM to a real-world case, and results can support decision makers to adjust related economic activity strategies for reducing urban solid waste production, improving ecological hierarchy structure and promoting ecological pairwise relationships. More efforts can be made in future work. This research used the input-output tables of 2012 and 2017 due to data limitation; meanwhile, the production structure of Fujian had little changes in previous years. Predicting future input-output tables (e.g., for the periods of 2021–2025, 2026–2030, and 2031–2035) using the RAS method could help plan an optimal urban solid waste reduction path. It is essential to integrate fuzzy/stochastic analysis methods into the FE-PIOM to cope with the inherent uncertainties existing in economic growth, industrial structure transition and solid waste reduction.

**Author Contributions:** Conceptualization, methodology, writing—original draft, writing-review & editing, J.L.; conceptualization, funding acquisition, supervision, writing—review & editing, Y.L.; conceptualization, resources, G.H.; software, data duration, Y.Y.; methodology, X.W. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Key Research & Development Program of China (2016YFC0502803) and the Education Department of Fujian Province (JT180453).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Acknowledgments:** This research was supported by the National Key Research and Development Program of China (2016YFC0502803) and the Education Department of Fujian Province (JT180453). The authors are grateful to the editors and the anonymous reviewers for their insightful comments and suggestions.

**Conflicts of Interest:** The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
