Sustainability 2022 , 14 , 2619
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to be compared were system expansion, physical partitioning and economic partitioning. Nine potential features of allocation methods were identified in a review of scientific papers on allocation issues. These features referred to the consideration of market mechanisms (e.g., reference products, geographical context, changes in prices) [6,13,16,19,33]; considera- tions of the physical properties of coproducts [6,13,15,16,32]; method resistance towards changes, such as price fluctuations and changing reference products [6,13,19,22,56]; ease of applying the method [13,22]; ease of understanding and interpreting the allocation results (transparency) [13,57]; amount of data required [38,57]; ability to take small quantities of byproducts into consideration [22]; ability to handle diverse physical properties of the coproducts [6,16,58]; and ability to reflect on socioeconomic factors and/or driving forces for the production process [19,22]. Accordingly, the following criteria were defined to establish a hierarchy that could be applied to choose an appropriate allocation method: physical system [6,13,15,16,32], economic system [6,13,16,22,32,33,58], stability [6,13,19,22,56], calculability and interpre- tation [13,22,38,57] and flexibility [6,16,22,58]. The subcriteria ability to bear and market environment were then added to the economic criterion (hierarchy illustrated in Figure 3). 3.2. Pairwise Comparison of the Alternatives with Respect to (Sub-)Criteria Referring to the selected scientific literature and the judgment scale given in Table 1, the three alternatives (economic partitioning, system expansion and physical partitioning) were compared pairwise with regard to the (sub-)criteria physical system, ability to bear, market environment, system stability, calculability and interpretation and flexibility. The resulting relative weights of the alternatives (allocation methods) with respect to the (sub-)criteria are illustrated in Figure 4 (consistency ratios: physical system, 0.0000; ability to bear, 0.0692; market environment, 0.1797; system stability, 0.0000; calculability and interpretation, 0.0000; flexibility, 0.0000).
Figure4. Relative weights of the alternatives (allocation methods) with respect to the (sub-)criteria. 3.3. Pairwise Comparison of the Criteria with Respect to the Goal The execution of the pairwise comparisons by the biorefineries’ representatives re- sulted in 26 responses, five of which were excluded due to inconsistencies (i.e., C.R. ≥ 0.2). The different criteria weightings assigned by the practitioners were compared to investigate their preferences, and the results were grouped to identify potential influencing factors (impact type, type of byproduct and the respective professional background). Regarding the overall results ( n = 21), the respective relative weights of the five criteria are fairly balanced, with the criterion flexibility lagging slightly behind (using geometric means: sys- tem stability, 25.82%; economic, 21.07%; calculability and interpretation, 20.85%; physical system, 19.27%; flexibility, 12.98%; C.R.: 0.0046). Only minor differences were observed in the weightings regarding the allocation type (cost allocation and environmental impact allocation) and the byproducts (lignin and fines); aggregated results (using geometric means) are given in Table 3 (Figure S1 on the respective
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