Fair sports timetabling : balancing timetabling inconveniences in time-relaxed sports timetabling

Since a time-relaxed round-robin timetable contains many more time slots than games per team, it is crucial to fairly distribute rest times between teams’ consecutive games. We generate equitably-efficient timetables which are Pareto efficient, i.e. we cannot improve a team’s timetable without deteriorating it for at least one other team, and which comply with the Pigou-Dalton principle of fairness, i.e. we cannot shift a penalty from a worse-off to a better-off team without increasing the total penalty. In order to generate these timetables, we propose an integer programming model and a multi-objective evolutionary algorithm