Optimal Integrated Single-Framework Algorithm for the Multi-Level School Bus Network Problem

In many states in the United States, school bus fleets are assigned to serve students sequentially at three levels-high school, middle school, and elementary school; however, in past studies, each of these stages in the problem was considered separately. This study introduces a novel integrated school bus problem that considers the sequential operation of fleets for all three levels in a unified framework. An example of a hypothetical network was developed and tested to demonstrate the developed algorithm. The algorithm successfully handled the integration of school buses' optimal route generation while meeting all constraints. The results showed that the routings with the integrated single-framework algorithm can reduce the total costs by 4.5% to 12.4% compared to the routings with the separated level algorithm. Also, it showed that the total costs of the integrated routing framework for different morning and afternoon time windows are 8.28% less than the same routings (identically reversed) for the morning and afternoon time windows.