## 4 Case Study
### Experimentation  
To test the DSS prototype, a real-world case scenario was built with 500 pharmacies to be served daily in a metropolitan area in Rome (Italy), delimited by a latitude between 41.8538 and 41.8814, and a longitude between 12.4397 and 12.5070. A preliminary analysis allowed 325 potential parking slots and one van depot to be identified (see Figure 5).  
The value of the new approach can be measured with respect to several aspects, including (a) accuracy, (b) consistency and stability, (c) time saved and reduction in the cognitive effort of the decision makers, and (d) perception of flexibility experienced by end users. We conducted a test in a simulated environment, in which we were able to evaluate only (a) and (b), leaving an assessment of (c) and (d) to a future on-the-field study with real end users.  
To verify whether the LLM correctly captures the DMs' qualitative preferences and integrates them into the optimization algorithm effectively (criterion (a)), we generated (based on the logistics experience of the authors) ten fictitious stakeholder requests for eight of the most common categories of preferences listed in Section 4.1, which resulted into eighty statements. Specifically, we formulated a range of requests commonly raised by various stakeholders--such as drivers, citizens, and customers--when deploying decision support systems in city logistics design projects. The preferences were expressed in Italian and articulated with the utmost clarity and linguistic precision.  
Figure 4: Architecture of the DSS.  
To assess the consistency and stability of the DSS (criterion (b)), an LLM (other than the one used in the prototype) was used to randomly modify each request 5 times with decreasing levels of clarity and coherence (the last incorporating dialectal elements). The success rate was then evaluated subjectively by the authors of the study and is reported in Table 1. The results show that, with perfectly articulated requests (degradation level 0) and slightly less clear ones (degradation level 1), accuracy is at its peak (98.8%). As the degradation level increases, accuracy declines slightly but steadily. When informal phrasing and regional vocabulary are introduced (degradation level 5), accuracy falls more sharply to 91.3%. As a conclusion, the DSS performs very well under optimal and near-optimal conditions but experiences noticeable difficulty as the quality of input degrades, particularly at the highest degradation level.  
As a side note, in the phase of analyzing the solution of problems \(\mathcal{P}^{(h)}\), the LLM presented to the decision maker a report including graphical summaries like those reported in Figure 6 (describing the spatial distribution of customers and parking slots) and Figure 7 (describing parking slot densities and parking slot average distances from customers). Based on this information, the users decided whether to accept the current solution \(\mathbf{x}^{(h)}\) or request the inclusion of additional preferences into the optimization model.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Degradation Levels** & **Accuracy (\%)** \\ \hline
0 (perfectly articulated requests) & 98.8 \\ \hline
1 & 98.8 \\ \hline
2 & 97.5 \\ \hline
3 & 96.3 \\ \hline
4 & 95.0 \\ \hline
5 (informal phrasing, regional vocabulary) & 91.3 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Accuracy across different degradation levels of requests.  
Figure 5: Spatial distribution of customers and parking slots.