article
An exact approach for the balanced k-way partitioning problem with weight constraints and its application to sports team realignment
Autor
Recalde, Diego
Severín, Daniel Esteban
Torres, Ramiro
Vaca, Polo
Institución
Resumen
In this work a balanced k-way partitioning problem with weight constraints is defined to model the sports team realignment. Sports teams must be partitioned into a fixed number of groups according to some regulations, where the total distance of the road trips that all teams must travel to play a double round robin tournament in each group is minimized. Two integer programming formulations for this problem are introduced, and the validity of three families of inequalities associated to the polytope of these formulations is proved. The performance of a tabu search procedure and a branch and cut algorithm, which uses the valid inequalities as cuts, is evaluated over simulated and real-world instances. In particular, an optimal solution for the realignment of the Ecuadorian football league is reported and the methodology can be suitable adapted for the realignment of other sports leagues. Fil: Recalde, Diego. Escuela Politécnica Nacional. Departamento de Matemática. Quito; Ecuador Fil: Severín, Daniel. Universidad Nacional de Rosario. FCEIA. CONICET. Rosario; Argentina Fil: Torres, Ramiro. Escuela Politécnica Nacional. Departamento de Matemática. Quito; Ecuador Fil: Vaca, Polo. Escuela Politécnica Nacional. Departamento de Matemática. Quito; Ecuador