Integrated student to school assignment and school bus routing problem for special needs students

In this paper, we address the combined problem of assigning students to schools and generating school bus routes for special needs students. Special needs students typically require additional accommodations, both in terms of the services available at school and during pick-ups and drop-offs. This introduces additional complexities to the problems of assignment and routing for students. We develop a mathematical model that jointly addresses these problems, and incorporate multi-loads and heterogeneous bus fleet features. The model simultaneously assigns special needs students to schools based on their level of need and the availability of resources, and generates efficient routes to transport them to their designated schools. We propose a two-phase heuristic approach using the capacitated clustering problem, which is capable of generating high-quality solutions. We evaluate our proposed methodology using several randomly generated instances, and a real-world case study in Fort Smith, Arkansas. The results from the case study demonstrate that the proposed methodology can reduce the total miles traveled by buses by over 35% on average, when compared to previously developed heuristics in the literature for the same case study.