*Result*: Mathematical model and matheuristic algorithm for the multi-period school bus routing problem.
*Further Information*
*This article addresses a new variant of the School Bus Routing Problem named the Multi-Period School Bus Routing Problem. In this problem, routes are created to pick up students at the selected bus stops considering a set of periods, ensuring that students are consistently allocated to the same stop along the subset of periods in which they require transportation. The objective is to minimize the total distance traveled by the fleet in all the considered periods, considering vehicle capacity and maximum walking constraints. To solve the problem, a mathematical model, based on Mixed Integer Linear Programming, and a matheuristic algorithm, based on Iterated Local Search and Variable Neighborhood Descent, are proposed. Moreover, two new strategies to address the student allocation sub-problem are presented. Instances from previous literature are extended to consider the student period-dependent demands, resulting in 448 new instances, which are used to evaluate the algorithms by means of computational experiments. The results obtained show that the proposed algorithm is capable of solving large instances with a low computational effort, obtaining optimal solutions or small percentage gaps. Furthermore, it also highlights the positive impact of the multi-period approach on the total distance traveled compared to the single-period approach. [ABSTRACT FROM AUTHOR]*
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