### Previous Research on Criteria-Based Method Comparison  
To define the comparison criteria, we extensively evaluated previous studies that include criteria for method comparison. These studies provide approaches for classifying and comparing some of the existing methods to analyze their feasibility. Some method comparisons rest upon specific criteria, such as the usability, maturity, and theoretical soundness of the methods [12; 13; 14; 15]. Table 1 outlines the methods and criteria covered by previous studies. The investigated methods are physical input-output table (PIOT), substance flow analysis (SFA), material flow analysis (MFA), energy analysis, ecological network analysis (ENA), life cycle inventory (LCI), LCA, carbon footprint, water footprint, ecological footprint, material-input per service unit (MIPS), _energy_ analysis, and exergy analysis. The table only includes the studies that, on the one hand, focus on environmental assessment methods and, on the other hand, that also use comparison criteria. Besides these studies, some investigations compare methods without this kind of criteria, and some other studies use criteria but compare other methods not concerning environmental assessment. Based on specific criteria, some studies classify methods for decision-making, either on a business or political level. This usually requires all three dimensions of sustainability: environmental, economic, and social, to be considered. [PERSON] et al. [14] categorize 32 sustainability assessment tools, which partly overlap, and illustrate them in different categories. They distinguish between indicators, product-related assessment, and integrated assessment. [PERSON] et al. [20] introduce seven criteria for comparing 18 assessment tools and distinguish between integrated and sustainability assessments. The latter is described as being more comprehensive. [PERSON] et al. [21] provide an overview of 41 sustainability indices regarding the number of sub-indicators, scaling, weighting, and aggregation. Sustainability assessment methods extend beyond a purely physical and scientific assessment due to their rather qualitative evaluation. Moreover, [PERSON] and [PERSON] [16] as well as [PERSON] and [PERSON] [22] apply five criteria represented by three questions to assess 13 methods. This research focuses on environmental aspects. [PERSON] and [PERSON] [23] categorize environmental indicators distinguishing between drivers, pressures, state, impact, and response called the DPSIR framework. For the comparison of environmental impact assessments, previous studies also provide some criteria. The International Association for Impact Assessment defines 24 principles to follow. Assessments should be purposive, rigorous, practical, relevant, efficient, adaptive, participative, interdisciplinary, credible, integrated, transparent, systematic, etc. [24]. However, these criteria are vague and partly opposite to one another. [PERSON] and [PERSON] [17], [PERSON] et al. [13], [PERSON] et al. [12], and others (cf. Table 1) propose more precise criteria that can be rated more clearly. For example, the criterion 'life cycle thinking' can be fulfilled clearly for different standard methods.