Models and solution approaches for integrated student to school assignment and school bus routing problem focusing on special needs students

Abstract

This dissertation addresses the integrated problem of assigning students to schools and generating school bus routes particularly focusing on the special needs students is addressed. Special needs students generally require supplementary accommodations and must be picked up from and dropped off at their home addresses. This will increase the number of nodes in the network and therefore introduces additional complexities to the problems of assignment and routing for students. An integrated single objective mathematical model is first developed that simultaneously assigns the students to schools based on their needs and generates efficient bus routes to deliver the students to their designated schools, while incorporating multi-loads and heterogeneous bus fleet features as well. This problem is known to be NP-hard, meaning that it is most likely not solvable using exact methods especially when the size of the network increases. A two-phase heuristic solution approach that can generate high quality solutions is proposed based on the capacitated clustering problem. Several random instances are generated to evaluate the performance of the model and the proposed solution approach. A real-world case study from Fort Smith Public School in Arkansas is also used to evaluate and compare the performance of the integrated model and the proposed solution approach with the literature. The case study results determine that the proposed heuristic approach improves the quality of the solution (total miles driven) by 35% on average when compared with the previously developed heuristic solution approaches in the literature. Additionally, goal programming is adopted to convert the integrated model to a multi-objective assignment and routing model in which the number of buses and maximum ride distance are minimized along with the total travel distance. The goal programming model improves the ride distances by 21% on average when compared with the post process analysis on ride distances using the optimum solution from the single objective model.