## 3 Literature Overview and Indicator Selection
### Criteria  
To each by-product is associated a value, according to the assessment of 5 criteria [18]:  
1. Legislation, for both inbound and outbound by-products;
2. Class of by-product, for both inbound and outbound by-products;
3. Use of by-product, for inbound by-products;
4. Destination of by-product, for outbound by-products;
5. Problems/risks, for both inbound and outbound by-products.  
The legislation criteria consider the requirements needed for each by-product, when recovered, recycled, and re-used, mainly according to the EU Construction and Demolition waste protocol [21]. The class of by-products is evaluated in line with the D.M. 27/09/2010 that implements the EU Waste Framework Directive [22], regulating hazardous and non-hazardous inert and non-inert waste; values are assigned accordingly. Criteria use and destination of by-products are determined according to the characteristics of each material and the potential practical applications, taking into account the need for pretreatment operations. The use criterion is evaluated according to the following options: (i) by-product is treated by both the donor and recipient company; (ii) by-product is treated by the recipient company; and (iii) by-product treatment is not required by either of the companies. The destination criterion considers (i) the industrial landfill; (ii) the need for pretreatment; and (iii) the absence of pretreatment [35]. Finally, the problem/risk category takes into account the frequency of occurrence of potential barriers or difficulties related to waste management and business operation deriving from drastic changes in industry and society [36; 37].  
The evaluation assumes three discrete values: one, three, or five. The analytical hierarchy process (AHP) supported the evaluation of weights for criteria following the methodology proposed by [PERSON] [37]. AHP allows the assigning of a priority to a series of decision-making alternatives, or comparative evaluation of criteria which is both qualitative and quantitative, and therefore not directly comparable, by combining multidimensional scales into a single priority scale. To assure a consistent outcome, AHP requires calculation of the consistent ratio CR--namely, the probability that the final result comes from a rational, consistent process that respects transitivity among criteria. Proponents of AHP state that a CR higher than 10% does not assure sufficient transitivity [38]; if a final CR does not reach such a threshold, inconsistencies must be identified and the judgment reviewed. A consistent review may achieve a CR of around 1% [39]. Our evaluation process achieved a CR = 1.3%, which is widely satisfactory. The procedure proposed by [PERSON] [37] also informs confidence intervals (95%) for the evaluation.  
Five representative stakeholders have been asked to give their judgment on the selected criteria: the managers of two of the companies involved in the IS (Company 2 and Company 6), two scholars, and a legislator. Table 2 shows the outcomes of the judgment as well as the evaluation criteria.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Criteria**} & \multicolumn{2}{c}{**Weight/**} & \multirow{2}{*}{**Evaluation**} & \multirow{2}{*}{**Value**} \\  & **Confidence Intervals** & & \\ \hline \multirow{2}{*}{Legislation} & 17.4\% & Good practices & 1 \\  & (\(\pm\)3.0 pp) & General requirement & 3 \\  & (\(\pm\)3.0 pp) & Specific legal requirement & 5 \\ \hline \multirow{2}{*}{Class of by-product} & 19.8\% & Non-hazardous—inert & 1 \\  & (\(\pm\)3.0 pp) & Non-hazardous—non-inert & 3 \\  & (\(\pm\)3.0 pp) & Hazardous & 5 \\ \hline \multirow{2}{*}{Use of by-product} & \multirow{2}{*}{18.6\% (\(\pm\)4.4 pp)} & Treatment by both the giving and & \multirow{2}{*}{1} \\  & & receiving company & \\ \end{tabular}
\end{table}
Table 2: Weight, evaluation, and values of the selected criteria.