The Rest Difference Problem in Round-Robin Tournaments

Abstract

Fairness is a key consideration in designing tournament schedules. When two teams play against each other, it is only fair to let them rest the same amount of time before their game. In this study, we aim to reduce, if not eliminate, the difference between the rest durations of opposing teams in each game of a round-robin tournament. The rest difference problem proposed in this study constructs a timetable that determines both the round and the matchday of each game such that the total rest difference throughout the tournament is minimized. We provide a mixed-integer programming formulation and a matheuristic algorithm that solve the problem. Moreover, we de velop a polynomial-time exact algorithm for some special cases of the problem. This algorithm finds optimal schedules with zero total rest difference when the number of teams is a positive-integer power of 2 and the number of games in each day is even. Some theoretical results regarding tournaments with one-game matchdays are also provided.