Integrated break and carryover effect minimization

A fair schedule helps in improving the competitiveness and attractiveness of sports tournaments and in turn contributes positively to the sports economy. Break minimization and carryover effects minimization are considered to be two important criteria of fairness in scheduling of compact round-robin tournaments, and most related research looks at these problems separately. Various studies have sought to minimize the carryover effects in tournaments so that the number of breaks per team does not exceed a specific level. This study, however, is the first effort to define an integrated problem that aims to minimize the carryover effects and the number of breaks simultaneously for round-robin tournaments. We first introduce the mathematical formulation for the problem, whose objective measures how well a schedule simultaneously performs with respect to the number of breaks and the carryover effects. We then develop a heuristic method for this computationally hard problem. Comparing our results with the previous literature and the current practices of some European leagues, we show that our method provides schedules with better objective function values.