*1.2. Literature Review*

The physical input-output model (PIOM) proposed by Leontief [9] is effective for assessing the direct/indirect solid waste embodied in the flow of goods [10]. In the PIOM, a conventional economic system is transformed into an urban solid waste system (USWS). It can facilitate managers to account the solid waste flows in a USWS based on the material balance principle. Liang and Zhang [11] employed a PIOM to investigate the impacts of four categories of solid waste recycling on urban solid waste metabolism to support sustainable development. Wang et al. [12] used the PIOM for estimating the whole regional energy and environmental benefits of solid waste utilization for energy recovery, where power generation from energy recovery (e.g., waste incineration) and total mitigation potentials for air pollutant emissions were predicted. Meyer et al. [13] utilized the PIOM to model three streams of solid waste generated from commercial economic sectors in the United States; the model ranked all economic sectors based on solid waste production and pointed out potential areas to continue to pursue innovations in material use. Huang et al. [14] employed a PIOM to quantify different types of solid waste production recycling over the period 2005–2017 in China. The results revealed that China experienced an increment in the recycling of five types of solid waste.

The USWS contains various sectors, diversified flows, and compounded interactions [14]. Diagnosing the metabolism of the USWS by analyzing sector metabolic relationships and figuring out hierarchical structure is helpful [15]. The PIOM can be extended to handle these problems through introducing ecological network analysis (ENA). Zhang et al. [16] integrated a PIOM with ENA to analyze the directions, locations and drivers of carbon flows resulting from global trade, where large CO<sup>2</sup> transfers were recognized and adjustments of the national mitigation targets were proposed. Wang et al. [17] coupled a PIOM with ENA to evaluate water-related impacts of energy-related decisions, where sectoral embodied consumption of water and energy, and their intersector flows, were mapped. Wang [18] incorporated a PIOM with ENA to comprehensively estimate the metabolic status of an energy system in China, in which the system properties, indicators of sectors (e.g., the out-degree, betweenness, and closeness centrality degree), and betweenness-based energy consumption were calculated. Zheng et al. [19] combined ENA with a PIOM to investigate integral carbon emissions at the city scale; the complex structures and relationships of carbon emission flows in 2010 due to inter-sector trade were assessed.

In fact, a USWS has complexities related to different production technologies, industry scales, and pollution intensities. Valuable information is often hidden under the interrelationships between these factors and the consequent effects [20,21]. For example, variations in metal productive capability can affect the amount of solid waste delivered to the electrical equipment manufacture sector, as well as the amount of solid waste received from

the metal ore mining sector. Finding crucial impact factors is beneficial to develop more specific solid waste reduction strategies. Factorial analysis (FA) has the ability to quantify the sensitivity of model response to significant factors and their interactions [22]. One concern is that traditional full factorial analysis may be unfeasible when many factors are taken into account (due to a large number of calculations). Fractional factorial analysis (FFA) is effective for quantifying the significance of factors by carrying out a small number of computed cases, which decreases the calculation cost and ensures result accuracy [23]. FFA has been successfully used in experimental designs for detecting response sensitivity [24–26].

Previous studies proved the feasibility and practicability of PIOM, ENA, and FFA (a summary of previous literature is presented in Table A1); however, there are some research gaps to be filled. First, a PIOM can assess physical direct and indirect solid waste production flows of USWS but has difficulty in analyzing ecological relationships between various sectors. Secondly, ENA can effectively reveal the metabolic condition including ecological control and utility relationships but cannot screen the key factors and evaluate their interactions. Third, FFA can help decision-makers accurately adjust key factors to improve system performance, with few studies applied FFA to USWS. Fourth, no previous study has been reported on the integration of PIOM, ENA and FFA for urban solid waste reduction in USWS.
