1749. Fair Schedules for Single Round Robin Tournaments with Ranked Participants
Invited abstract in session WC-40: Sports timetabling, stream Sports and Entertainment.
Wednesday, 12:30-14:00Room: Newlyn LG.02
Authors (first author is the speaker)
| 1. | Sten Wessel
|
| Mathematics and Computer Science, Eindhoven University of Technology | |
| 2. | Cor Hurkens
|
| mathematics, Eindhoven University of Technology | |
| 3. | Frits Spieksma
|
| Mathematics and Computer Science, Eindhoven University of Technology |
Abstract
We consider schedules for single round-robin (SRR) tournaments on an even number of players, where each of the players plays every other player exactly once, either at home or away. We assume that the players are sorted on a predetermined ranking, where the first player is the strongest, and the last player is the weakest player of the competition. With only one match between any pair of opponents, one team will have the asymmetric advantage of playing home, which we consider as having positive effect on the match outcome for that player.
To prevent distortion of the outcome of an SRR tournament as well as to guarantee equal treatment of the participants, we argue that each participant should face its opponents when ranked by strength in an alternating fashion with respect to the home/away advantage. For example, we consider it unfair for a player to play many home matches against top-ranked opponents, or to play many home matches against low-ranked opponents. We refer to this as ranking fairness.
We provide an explicit construction proving that so-called single-break, ranking-fair schedules exist when the number of participants is a multiple of 4. Further, we give an integer programming formulation that outputs single-break ranking-fair schedules when they exist. Finally, we show that the circle method, the most popular method to come to a schedule for an SRR tournament, does not allow ranking-fair schedules when the number of teams exceeds 8.
Keywords
- OR in Sports
- Scheduling
- Combinatorial Optimization
Status: accepted
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