## 6 Conclusions  
The effective design of predictive approaches that anticipate supplier delivery risks represents a fundamental step to building a more resilient supply chain.  
This paper's main contribution is thus twofold. First, a new deep-learning approach to solving the problem of predicting supplier delivery risks in a regression manner by simultaneously considering autocorrelation in data and macroeconomic indicators as additional input was proposed for the first time. Then, an empirical investigation of the predictive capability of the proposed approach and a comparison against several benchmarks of its main building block was conducted in a real automotive case study.  
In particular, which predictive accuracy the new proposed approach was able to reach was first investigated. The results highlight the overall capability of the proposed approach to provide good predictions of delivery delays with errors that, for 50% of the considered components, span from 25% to 88% in terms of _SMAPE_ and from 2.8 days to 6.9 days in terms of _MAE_.  
Then, the predictive accuracy advantages that the proposed deep-learning approach can obtain compared to traditional statistical models like ARIMA have been explored. The results report that the proposed approach outperformed the other benchmarks in 41% to 62% of instances, depending on the considered metrics.  
Lastly, the predictive accuracy advantages that the integration of macroeconomic indicators could bring compared to models built without considering these variables have been analyzed. The experiments highlighted the fact that macroeconomic variables were found to affect the overall predictive performance seriously and have an impact of up to 85% on the final result.  
However, the results reported in the study must be considered subject to some limitations. In particular, the case-based research methodology adopted cannot be easily extended to other sectors. Furthermore, the results cannot be extended to components for which less than 30 historical data points can be collected.  
Future research can thus be directed at testing the proposed approach on multiple case studies that can also consider more components. Furthermore, investigating hybrid approaches that combine local models built independently for each component with global models built for different groups of components could be another interesting research direction when a different amount of historical data is available for each component. Lastly, integrating delivery delay predictions in typical SC risk-management problems such as supplier selection and order allocations, inventory management, or SC network design, and understanding how predictions' short- and long-term accuracy impacts these decisions can be promising research areas.  
Conceptualization, M.G. and M.B.; methodology, M.G. and F.C.; software, M.G. and L.C.; formal analysis, M.G., F.C. and L.C; investigation, M.G., F.C. and L.C.; resources, M.G., F.C. and L.C.; data curation, M.G., F.C. and L.C.; writing--original draft preparation, M.G., F.C. and L.C.; writing--review and editing, M.G., F.C., L.C. and M.B.; visualization, M.G., F.C. and L.C.; supervision M.B.; project administration, M.B.; funding acquisition, M.B. All authors have read and agreed to the published version of the manuscript.  
This study was carried out within the MICS (Made in Italy--Circular and Sustainable) Extended Partnership and received funding from the European Union Next-Generation EU (PIANO NAZIONALE DI RIPRESA E RESILENZA (PNRR)--MISSIONe 4 COMPONENTE 2, INVESTI-MENTO 1.3--D.D. 1551.11-10-2022, PE00000004). This manuscript reflects only the authors' views and opinions; neither the European Union nor the European Commission can be considered responsible for them.  
Not applicable.  
The data presented in this study are available on request from the corresponding author due to privacy issues.  
The authors declare no conflicts of interest.