A Branch-and-Cut Algorithm for Scheduling the Highly-Constrained Chilean Soccer Tournament

The qualifying phase of the Chilean soccer championship follows the structure of a compact single round robin tournament. Good schedules are of major importance for the success of the tournament, making them more balanced, profitable, and attractive. The schedules were prepared by ad hoc procedures until 2004, when a rough integer programming strategy was proposed. In this work, we improve the original integer programming formulation. We derive valid inequalities for improving the linear relaxation bound and we propose a new branchand-cut strategy for the problem. Computational results on a real-life instance illustrate the effectiveness of the approach and the improvement in solution quality.