Sailing League Problems
Robert Schüler, Achill Schürmann
TL;DR
The paper studies the sailing league scheduling problem, formalizing a pairing list with $N_{\text{teams}}$, $N_{\text{flights}}$, $N_{\text{inrace}}$ and the pairings $\lambda(t,t')$, aiming to minimize the spread $\lambda_{\max}-\lambda_{\min}$. It links this problem to combinatorial design theory, particularly resolvable block designs, and proposes optimization models: a boolean quadratic program and several integer linear programs, plus relaxations. The authors apply these methods to three real-world leagues (the Asian Pacific Champions League, the German Sailing Leagues, and the European Sailing Champions League) and obtain optimal or near-optimal schedules; in two cases they prove optimality or near-optimal bounds, while the European case remains open. The work highlights the practical impact of combining design theory with OR techniques to improve fairness in multi-race sailing events and outlines directions for further research.
Abstract
We describe a class of combinatorial design problems which typically occur in professional sailing league competitions. We discuss connections to resolvable block designs and equitable coverings and to scheduling problems in operations research. We in particular give suitable boolean quadratic and integer linear optimization problem formulations, as well as further heuristics and restrictions, that can be used to solve sailing league problems in practice. We apply those techniques to three case studies obtained from real sailing leagues and compare the results with previously used tournament plans.