  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 & 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.
