Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A Branch-and-Cut Algorithm for the Undirected Traveling Purchaser Problem
Operations Research
The Capacitated m-Ring-Star Problem
Operations Research
A column generation approach for a school bus routing problem with resource constraints
Computers and Operations Research
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School bus routing problems, combining bus stop selection and bus route generation, look simultaneously for a set of bus stops to pick up students from among a group of potential locations, and for bus routes to visit the selected stops and carry the students to their school. These problems, classified as Location-Routing problems, are of interest in densely populated urban areas. This article introduces a generalization of the vehicle routing problem called the multi-vehicle traveling purchaser problem, modeling a family of routing problems combining stop selection and bus route generation. It discusses a Mixed Integer Programming formulation extending previous studies on the classical single vehicle traveling purchaser problem. The proposed model is based on a single commodity flow formulation combining continuous variables with binary variables by means of coupling constraints. Additional valid inequalities are proposed with the purpose of strengthening its Linear Programming relaxation. These valid inequalities are obtained by projecting out the flow variables. We develop a branch-and-cut algorithm that makes use of the proposed model and valid inequalities. This cutting plane algorithm is implemented and tested on a large family of symmetric and asymmetric instances derived from randomly generated problems, showing the usefulness of the proposed valid inequalities.