# On the Design of a Decision Support System for Robotic Equipment Adoption in Construction Processes
## 3 Development of the Prototype
### Knowledgebase
#### 3.2.2 Quantitative Part  
The elicitation of the quantitative part of the decision model involves the definition of the conditional probabilities, the utility function, and utilities in collaboration with the domain experts. We propose to elicit the conditional probability tables by mapping verbal statements of probability from \"impossible\" to \"certain\" to probabilities from 0 to 1 [31, 39, 40]. We defined the conditional probabilities for our use case scenario in collaboration with domain experts by performing educated guesses based on the expected performance of the collaborative robot in comparison to the conventional manual process. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**KPI**} & \multirow{2}{*}{**Variable**} & \multirow{2}{*}{**Relevance**} & \multicolumn{6}{c}{**UC**} & \multirow{2}{*}{**Supporting Literature**} & \multirow{2}{*}{**Description**} \\ \cline{3-3} \cline{5-10}  & & & **1** & **2** & **3** & **4** & **5** & & **Literature** & & \\ \hline \multirow{2}{*}{-} & Project size & \multirow{2}{*}{
\begin{tabular}{c} Project information \\ \end{tabular} } & \multirow{2}{*}{x} & \multirow{2}{*}{x} & \multirow{2}{*}{x} & \multirow{2}{*}{x} & \multirow{2}{*}{x} & \multirow{2}{*}{x} & [28, 37]} & The project size can impact the decision of & & & whether adopting a robot or not \\ \cline{5-10}  & & & & & & & & & The use of a BIM model is necessary for the & \\ \cline{5-10}  & & & & & & & & & & & deployment of the collaborative robot that \\ \cline{5-10}  & & & & & & & & & & & is developed within the research project \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._  
Figure 2: Simplified decision model for UC4—marking and spraying. Each variable has been studied singularly to associate a mutually agreed verbal statement of probability. In Table 4 we present one of the conditional probability tables of our use case scenario as an example. In particular, we see the conditional probabilities P(M | Q.D) of the variable material (M), given quality (Q), and decision (D). Utility assessment or preference elicitation concerns the definition of the utility function, necessary for the construction of the decision-theoretic expert system [32]. We define a utility function that allows one to capture the preferences of the users for our use case. Our utility function is chosen as:  
\[\text{U}=\text{p}\times\text{uP}+\text{q}\times\text{uQ}+\text{s}\times\text {uS} \tag{1}\]  
The parameters p, q, and s sum to one and represent the coefficients that allow the user to weight the utilities according to his preferences. uP, uQ, and uS represent the subjective utilities as defined in Table 5. Subjective utilities are assigned by ordering outcomes from worst to best [31]. We assigned utility 0 to the worst possible outcome, and utility 100 to the best possible outcome. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Quality (Q)**} & \multirow{2}{*}{**Decision (D)**} & \multicolumn{4}{c}{**Material (M)**} \\ \cline{3-5}  & & **Reduced** & **Unaltered** & **Increased** \\ \hline \multirow{2}{*}{Increased} & Conventional method & 0.05 & 0.90 & 0.05 \\  & Collaborative robot & 0.90 & 0.05 & 0.05 \\ \hline \multirow{2}{*}{Unaltered} & Conventional method & 0.10 & 0.80 & 0.10 \\  & Collaborative robot & 0.80 & 0.10 & 0.10 \\ \hline \multirow{2}{*}{Reduced} & Conventional method & 0.00 & 0.50 & 0.50 \\  & Collaborative robot & 0.00 & 0.50 & 0.50 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Conditional probability table of coordination time P(M | Q.D).