A Bigram Based ILP Formulation for Break Minimization in Sports Scheduling Problems

Constructing a suitable schedule for sports competitions is a crucial issue in sports scheduling. The round-robin tournament is a competition adopted in many professional sports. For most round-robin tournaments, it is considered undesirable that a team plays consecutive away or home matches; such an occurrence is called a break. Accordingly, it is preferable to reduce the number of breaks in a tournament. A common approach is to first construct a schedule and then determine a home-away assignment based on the given schedule to minimize the number of breaks (first-schedule-then-break). In this study, we concentrate on the problem that arises at the second stage of the first-schedule-then-break approach, namely, the break minimization problem (BMP). We propose a novel integer linear programming formulation called the “bigram based formulation.” The computational experiments show its effectiveness over the well-known integer linear programming formulation. We also investigate its valid inequalities, which further enhances the computational performance.