School bus routing by maximizing trip compatibility

TL;DR

This paper introduces a new school bus routing model that maximizes trip compatibility and minimizes travel time, leading to fewer buses needed compared to traditional models.

Contribution

It presents a novel formulation that integrates trip compatibility into routing, improving overall bus utilization and reducing fleet size.

Findings

Up to 13% fewer buses needed with the new model

Generated trips are more compatible for scheduling

Model outperforms traditional routing approaches

Abstract

School bus planning is usually divided into routing and scheduling due to the complexity of solving them concurrently. However, the separation between these two steps may lead to worse solutions with higher overall costs than that from solving them together. When finding the minimal number of trips in the routing problem, neglecting the importance of trip compatibility may increase the number of buses actually needed in the scheduling problem. This paper proposes a new formulation for the multi-school homogeneous fleet routing problem that maximizes trip compatibility while minimizing total travel time. This incorporates the trip compatibility for the scheduling problem in the routing problem. Since the problem is inherently just a routing problem, finding a good solution is not cumbersome. To compare the performance of the model with traditional routing problems, we generate eight mid-size data sets. Through importing the generated trips of the routing problems into the bus scheduling (blocking) problem, it is shown that the proposed model uses up to 13% fewer buses than the common traditional routing models.