Model for Optimization of Locations of Schools and Student Transportation in Rural Areas

Low population densities make it difficult to design efficient networks of schools in rural areas. The most common solution is to operate small schools with children in multiple grades in each classroom, even though this solution may not be the least expensive. School consolidation proposals are difficult to implement because communities may have emotional bonds with their local schools and the impacts on secondary services, such as student transportation, are difficult to evaluate. In rural areas, particularly in Brazil, reductions in the costs associated with school operations and student transportation could allow boards of education to allocate more resources to improve educational practices and teaching materials. This paper presents a methodology for optimizing the location of schools and student transportation in rural areas. This methodology is based on two mixed-integer programming models, which are used sequentially. The first one deals with the school location and sizing problem, and the second one deals with the school bus routing and shift programming problem. The methodology was applied with data from Barao de Grajaú, which is in the northeast region of Brazil, and provided savings in operating costs of 10% to 17%.