A Two-Stage Algorithm for School Bus Stop Location and Routing Problem With Walking Accessibility and Mixed Load

This paper proposes a School Bus Stop location and Routing Problem with Walking Accessibility and Mixed Load (SBSLRP-WA-ML), where the individual difference of walking accessibilities among students and the possibility of serving students attending different schools with the same bus simultaneously are considered. We first develop a mixed integer programming model for SBSLRP-WA-ML with the objective of minimizing the total commuting time, including walking time from the residence to school, in-vehicle travel time, and service time at stops. A two-stage solution method is then developed. In stage 1, an iterative clustering method based on k-means and Density-Based Spatial Clustering of Applications with Noise (DBSCAN) is used to locate bus stops aiming at minimizing the number of stops subject to various walking accessibilities. In stage 2, an improved ant colony optimization algorithm (IACO) integrating two local search operators is devised, which is used to generate bus routes with minimal total commuting time. A number of instances of different sizes are generated to verify the solution approach, and the influential factors with respect to total commuting time are analyzed. The model is also compared to the door-to-door school bus services. Comparison to similar methods and sensitivity analysis of parameters are also conducted to analyze the performance and robustness of the proposed approach.