# Optimal Integrated Single-Framework Algorithm for the Multi-Level School Bus Network Problem
## 8 Conclusions  
This study developed an integrated optimization algorithm for multi-level school bus routing, aiming to enhance efficiency by combining trips for high schools, middle schools, and elementary schools. The research compared cost savings between identical routings for morning and afternoon versus distinct routings for each time window, highlighting the economic and planning benefits of tailored routings. The results of this study clearly showed that the integrated framework appears to be more efficient in terms of the balance between total student travel time, bus travel distance, and operating costs, resulting in a lower total cost. This indicates that, despite any potential complexities of integrating routes for morning and afternoon, the cost savings are significant. The separated framework consistently incurs higher total costs across all school levels (HS, MS, and ES) and time windows (M and A) compared to the integrated framework. This suggests that operating separate routes for the morning and afternoon is less cost-effective than integrating them.  
In practical cases and for the implementation of this integrated algorithm, there are some issues that should be considered, such as flexibility in routing. Constraints and/or objectives that allow for dynamic routing in case of unforeseen circumstances like road closures, traffic, or emergencies might be modified. Real-time or historical traffic data to more accurately estimate travel times and avoid traffic congestion should be incorporated. In order to ensure service quality, objectives related to the quality of service, such as minimizing the number of stops each student must endure or ensuring that no student is on the bus for an excessively long duration, can be included. Lastly, equity considerations such as ensuring that the routing algorithm provides equitable service across different neighborhoods and avoiding bias toward certain areas are crucial.  
Future studies can consider more aspects of the SBRP, including mixed loads of students, heterogeneous fleets, special-education students (both mixed and not mixed load), students' walking distance, road network structure, load balancing, and the ability to relocate buses among schools [51].  
Conceptualization, Y.-J.L.; methodology, Y.-J.L. and A.N.; software, A.N.; validation, A.N. and Y.-J.L.; formal analysis, A.N.; investigation, A.N. and Y.-J.L.; resources, A.N.; data curation, A.N.; writing--original draft preparation, A.N.; writing--review and editing, Y.-J.L.; visualization, A.N.; supervision, Y.-J.L.; project administration, Y.-J.L.; funding acquisition, Y.-J.L. All authors have read and agreed to the published version of the manuscript.  
This research was funded by Urban Mobility and Equity Center at Morgan State University, which is an University Transpotation Center funded by the Department of Transportation, USA. The APC was waived by the Algorithms.  
The data can be available upon request.  
This research was supported by the Urban Mobility & Equity Center at Morgan State University and the University Transportation Center(s) Program of the U.S. Department of Transportation. Views and results expressed in this paper represent the opinion of the authors and do not necessarily reflect the official policy of the institutions with which the authors are affiliated.  
The authors declare no conflict of interest.