A column generation approach for a school bus routing problem with resource constraints

The Multiple Vehicle Traveling Purchaser Problem describes a school bus routing problem that combines bus stop selection and bus route generation. This problem aims at selecting a set of bus stops from among a group of potential locations to pick up students, and for designing bus routes to visit the selected stops and to carry the students to their school. We address a variation of this problem that considers certain constraints on each bus route, such as bounds on the distances traveled by the students, bounds on the number of visited bus stops, and bounds on the minimum number of students that a vehicle has to pick up.Since column generation methods can easily deal with constraints on the consumption of resources related to each column, such as the constraints on routes mentioned above, and these methods are an alternative to other approaches based on three index variable formulations which suffer from the drawback of symmetry, we propose a branch-and-price algorithm based on a set partitioning formulation for this problem.We also study, using an extensive computational experience, the impact of enriching our proposal with additional inequalities in a branch-and-cut-and-price algorithm, which has revealed the importance of supplementing our column generation algorithm with cuts to improve its performance.