Schedules for sports tournaments on a single court minimizing waiting times

S. Knust: Scheduling sports tournaments on a single court minimizing waiting times Operations Research Letters 36 (2008), 471-476

The considered single round robin tournament may be formulated as follows. Given is an odd number n=2k+1 of teams, where each team has to play against each other team exactly once. These kn matches have to be scheduled in k rounds r=1,...,k=(n-1)/2 on a single court such that

• in each round exactly n matches are consecutively played on the court in n slots one after the other, and
• in each round each team plays exactly two matches.

Furthermore, depending on the sports discipline, zero waiting times (i.e. no resting time between two matches of the same team) may be allowed or not. The objective is to find a schedule which minimizes the waiting times for the teams (avoid long waiting times and minimize total waiting time).

For two variants (zero waiting times allowed or not) schedules for any odd number of teams are constructed minimizing the number of long waiting times and the total waiting time simultaneously. Here the corresponding optimal schedules for n < 20 can be found:

• Optimal schedules for the problem with zero waiting times not allowed
• Optimal schedules for the problem with zero waiting times allowed
• Construction of schedules for the problem with zero waiting times not allowed
• Construction of schedules for the problem with zero waiting times allowed