The school bus routing problem with student choice: a bilevel approach and a simple and effective metaheuristic

Abstract

AbstractThe school bus routing problem (SBRP) involves interrelated decisions such as selecting the bus stops, allocating the students to the selected bus stops, and designing the routes for transporting the students to the school taking into account the bus capacity constraint, with the objective of minimizing the cost of the routes. This paper addresses the SBRP when the reaction of students to the selection of bus stops is taken into account, that is, when students are allowed to choose the selected bus stop that best suits them. A bilevel optimization model with multiple followers is formulated, and its transformation into a single‐level mixed integer linear programming (MILP) model is proposed. A simple and effective metaheuristic algorithm is also developed to solve the problem. This algorithm involves solving four MILP problems at the beginning, which can be used to obtain tight upper bounds of the optimal solution. Extensive computational experiments on SBRP benchmark instances from the literature show the effectiveness of the proposed algorithm in terms of both the quality of the solution found and the required computing time.