Minimization of rest mismatches in round robin tournaments

In sports tournaments, an occurrence of a difference in the rest periods of opponent teams in a game, which we refer to as a rest mismatch, will disadvantage the less rested team. Thus, it is only fair to expect opposing teams to have rested equally before their game. In this work, we introduce and study the Rest Mismatch Problem where the goal is to minimize the number of rest mismatches in a round robin tournament. Two integer linear formulations and a constraint programming formulation are provided, and their computational performances are compared for several problem instances. Moreover, a heuristic algorithm is developed which finds a single round robin schedule with zero mismatches when the number of teams in the tournament is a multiple of 8, and four mismatches when it is a multiple of 4 but not 8.