Round‑robin scheduling with regard to rest diferences

Tasbih Tufaha ^[1] ; Burak Çavdaroğlu ^[1] ; Tankut Atan ^[2]
1. [1] Kadir Has University
  
  Kadir Has University
  
  Turquía
2. [2] Bahçeşehir University
  
  Bahçeşehir University
  
  Turquía
Localización: Top, ISSN-e 1863-8279, ISSN 1134-5764, Vol. 31, Nº. 2, 2023, págs. 269-301
Idioma: inglés
Enlaces
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Resumen
- Fairness is a key consideration in designing sports 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 diference between the rest durations of opposing teams in each game of a round-robin tournament. The rest diference problem proposed here constructs a timetable that determines both the round and the matchday of each game such that the total rest diference throughout the tournament is minimized. We provide a mixed-integer programming formulation and a matheuristic algorithm that tackle the rest diference problem. Moreover, we develop a polynomial-time exact algorithm for some special cases of the problem.
  
  This algorithm fnds optimal schedules with zero total rest diference 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 presented.