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these, the respective individual judgments were used as the main basis for the analysis. In addition, aggregations of the judgments were also performed (with regard to the allocation type, byproduct and practitioners’ professional backgrounds) using the geometric mean, as described and recommended by Saaty and Shang [52] and as performed by several authors regarding different topics [53]. This approach enabled us to attain quite low consistency ratios for the aggregated criteria rankings (the highest C.R. was 0.0308, described in detail in the Results section). Microsoft Excel (Excel version 2108, Microsoft Office LTSC Professional Plus 2021, Microsoft Corporation, Redmond, WA, USA) was used to perform all AHP calculations, and R (R version 4.1.2, R Foundation for Statistical Computing, Vienna, Austria; RStudio version 2021.09.2, RStudio Inc., Boston, MA, USA; packages: base 4.1.2 and tidyverse 1.3.1) as well as Microsoft PowerPoint (PowerPoint version 2108, Microsoft Office LTSC Professional Plus 2021, Microsoft Corporation, Redmond, WA, USA) were used for the illustrations. 2.4.3. The Specific Cases of Lignin and Fiber Fines, and Involvement of Experts The AHP was carried out on two different potential biorefinery (by-)products from the wood pulping process that are expected to have practical relevance: lignin and fiber fines. In addition to these two wood biorefinery byproducts, two subjects for allocations were investigated: the allocation of costs and the allocation of the environmental impacts to the byproducts. Experts were identified and asked to perform pairwise comparisons of the criteria with respect to the goal (four pairwise comparisons per interviewed person: cost and environmental allocation for lignin and fines) and pairwise comparisons of the two subcri- teria with respect to the economic criterium (also resulting in four pairwise comparisons per interviewee). Representatives were contacted from three different Austrian pulp and paper companies that were familiar with both lignin and fines due to their participation in related research project activities [54]. Within each company, people with three differ- ent professional backgrounds were taken into consideration (research and development, production, finance and controlling). Additional requirements for the selection of experts were: a profound knowledge level in their respective professional field (ideally, employees in management positions), familiarity with both lignin and fiber fines, and their availability and willingness to invest time to complete the whole survey consistently, which might be considered by some as burdensome [55]. Seven interviewees (three from R&D, two from production, two from finance and controlling) participated in the survey, which resulted in the collection of 26 responses, 21 of which were valid (the response composition appears in Table 2). The approach and survey were explained to the participants beforehand and conducted using the online survey web application tool LimeSurvey; if needed, additional calls were made by telephone to clarify the subject and procedure. The survey can be found in the Appendix: therewith, the criteria and corresponding subcriteria were compared pairwise to identify the respective preferences of the stakeholders. These ratings were then used to derive the matrices, and the AHP procedure was carried out [50].
Table2. Composition of the sample (altogether, 21 valid matrices were derived from the answers of seven (7) participants who conducted pairwise comparisons of the criteria and subcriteria).
By-Product
Impact Category
Professional Background
Lignin ( n =10)
Costs ( n =10)
R&D( n =7)
Environmental impact ( n =11)
Production ( n =8) Finance and controlling ( n =6)
Fiber fines ( n =11)
3. Results 3.1. Development of the Hierarchy: Identification of Alternatives, Criteria, and Sub-Criteria The structure of the hierarchy, including the overall goal, criteria, subcriteria and alter- natives, is explained and illustrated in Figure 3. The allocation approaches (alternatives)
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