Capacitated School Bus Routing Problem with Time Windows, Heterogeneous Fleets and Travel Assistants

The School Bus Routing Problem (SBRP) is a well-known example of an optimization problem in which, given a variety of feasible solutions to the problem of transporting pupils to school, we seek out an optimal solution. With over 1.3 million students in England having special education needs and a growing demand for inclusion in the educational community, creating optimal and inclusive school bus routes is essential to promoting this inclusion. The standard SBRP is a highly constrained problem. When considering the needs of pupils with Special Educational Needs and Disabilities (SEND), the problem becomes even more complex and constrained. In this study, we describe an SBRP formulation capturing SEND specific requirements, catering for heterogeneous fleets, mixed riding, time windows and the use of travel assistants for pupils with special needs. We then present preliminary results investigating the performance of a meta-heuristic and an exact approach, in the context of a real-life case study. Our findings show that when the number of instances increases, exact solvers very rapidly become unworkable. This motivates the development of metaheuristic approaches to this problem. Our results encourage additional research into optimizing school bus routing algorithms to benefit from both precise and heuristic solvers.