A mixed-integer linear programming approach to constructing sporting fixtures with minimal inequity

Ideally, sporting fixtures should be equitable to all teams. This typically means each team plays all other opponents an equal number of times, and other inherent inequities such as a home-field advantage are shared equally across the fixture. However, in some instances this is not possible. Time constraints may prevent teams from playing all other teams an equal number of times, while venue constraints may only permit a subset of the teams to play in each round. Challenges such as these are considered, and a mixed-integer linear programming formulation which takes such issues into account is proposed. Two examples are given which demonstrate that the proposed formulation can be solved to provable optimality in tractable time on modern machines, while heuristic approaches could be used to rapidly obtain high-quality solutions if needed.