Scheduling asynchronous round-robin tournaments

We study the problem of scheduling asynchronous round-robin tournaments. We consider three measures of a schedule that concern the quality and fairness of a tournament. We show that the schedule generated by the well-known “circle design” performs well with respect to all three measures when the number of teams is even, but not when the number of teams is odd. We propose a different schedule that performs optimally with respect to all measures when the number of teams is odd.