**2. Methodology**

Figure 1 summarizes the three main steps followed in this literature review. First, the literature search was performed. Second, a critical review was conducted to identify the main issues and bottlenecks in the LCA literature when implementing the ISO allocation procedures. The critical review was combined with a text-mining process to quantitatively assess the current practices in the LCA literature (focusing on all the LCA case studies selected by the query). Third, a bibliometric analysis was performed based on citation network analysis (CNA).

**Figure 1.** The three steps followed in the literature review.

The literature search was based on data collected from the Scopus database in February 2019. The searched publication fields were: title, abstract, and keywords. The search string was characterized by the terms: "Life Cycle Assessment", "LCA", "multifunctionality", "allocation" and "multi-output". Since allocation approaches are also used in other fields (e.g., in business management), the query was first limited to environmental assessment or engineering-related fields. Because of this, the documents were reduced from 1310 documents to 1152. This allowed us to exclude 145 documents belonging to business management, 6 related to veterinary science and 7 others. Our analysis was further refined by considering articles only from the category of Scopus "journals". By applying this last adjustment, the articles resulting from the search became 930. Since only research articles were analyzed, some relevant books or conference proceedings may have been excluded from the analysis. Nevertheless, books often resume the contributions previously published as articles, and some excluded documents might have been considered by some of the reviewed reviews. Figure 2 shows the number of publications per year, highlighting the growing interest in the topic.

The corpus of documents on which the analyses were performed included the 930 articles retrieved from Scopus and the main LCA guides and standards, i.e., ISO technical reports and standards (also withdrawn ones like ISO 14041:1998) [23–26], the International Reference Life Cycle Data System (ILCD) handbook [27], the Product Environmental Footprint (PEF) guide [28] and the Product Environmental Footprint Category Rules (PEFCR) guidance [29]. Out of the 930 documents, 307 studies were identified through their title and abstract as "methodological articles" (of which 117 were review articles focusing on a specific sector where LCA is applied). These methodological articles focused either on the general methodological debate about multifunctionality procedures, or discussed a specific method, or introduced a new model to solve multifunctionality. The most relevant articles in this group were critically reviewed to understand the main issues when solving multifunctionality in LCA while

claiming compliance with ISO. This critical review focused mainly on the articles cited more than 20 times ("most cited ones") and the articles published after 2015 ("recent ones").

**Figure 2.** The time distribution of the articles on multifunctionality in LCA published in scientific journals per year retrieved from Scopus.

The critical review was combined with a text-mining process whose aim was to quantify the current practices when solving multifunctionality issues. The text-mining process was manually performed on the remaining 532 case studies. These 532 case studies resulted from a further refinement which excluded 91 articles that either did not apply full LCA or were not environmental LCA studies. Concerning the multifunctional case studies retrieved from the literature, we observed that specific parts of the bioeconomy namely agriculture (63 case studies), bioenergy (185), bio-based materials (52) and anaerobic digestion (21), were the ones most affected by the issue of multifunctionality together with related sectors namely aquaculture (14), dairy and meat products (79), fossil counterparts (34) and waste management (50). These sectors together represented 94% of the 532 case studies identified by the query.

Text-mining software can detect relevant terms or keywords in the corpus of literature with less time and cost than a person [30]. However, when the keywords represent technical concepts, dedicated software typically achieves low to medium efficiencies (e.g., 25%–65%) [30]. For instance, software could not understand when the concept "system expansion" was used as an alternative expression for substitution or for system enlargement. To increase the efficiency of the text-mining method, the quantitative estimation was performed directly by the analyst. When the terms representing the concepts of interest (e.g., "allocation") were encountered, the context of their use was assessed by reading the surrounding text.

In the third step, i.e., the bibliometric review, the 930 articles were investigated by CNA. The CNA was performed using Pajek software [31]. Documents are considered "nodes" and the citations are the "links" between these documents. The type of nodes is defined therefore based on the type of document. The "sources" are the documents that are cited but cite no other documents and therefore represent the origins of the knowledge. The "sinks" are the documents that cite other documents but are not cited and therefore could represent the "current stage" of the knowledge stream. Intermediate documents cite other previous documents and are also cited by more recent documents [21]. Our CNA aimed at identifying the main path of research. This path represents the main knowledge flow in a specific topic, i.e., the major contributions that have influenced the development of the research, which does not mean directly the most cited ones overall [32,33]. The main path was obtained by using an algorithm that computed what citations between articles had been more significant. In particular, such a significance

was calculated through the key-route method [34]. This method identifies the main chain of articles by considering the highest transversal count [33,34]. The transversal counts measure the significance of a citation link, i.e., by counting the times a citation link is traversed [34]. The transversal count adopted was the search path count (SPC). The SPC assigns as value to each link the number of paths traversing the link among all possible paths connecting all the sources to all the sinks [21,22].
