How to schedule the Volleyball Nations League

Abstract

The Volleyball Nations League is the elite annual international competition within volleyball, with the sixteen best nations per gender contesting the trophy in a tournament that spans over 6 weeks. The first five weeks contain a single round robin tournament, where matches are played in different venues across the globe. As a consequence, each team follows an intensive travel plan, where it happens quite often that there is a large discrepancy between travel burdens of opposing teams. This is considered a disadvantage for the team that travelled more. We analyse this problem, and find that it is closely related to the well-known Social Golfer Problem: we name the resulting problem the Traveling Social Golfer Problem (TSGP). We propose a decomposition approach for the TSGP, leading to the so-called Venue Assignment Problem and the Nation Assignment Problem. We prove that a solution to the Venue Assignment problem determines the amount of unfairness, and we also prove that any solution of the Venue Assignment problem can be extended to a solution to the Nation Assignment problem satisfying the so-called home-venue property. Using integer programming methods, we find, for real-life instances, the fairest schedules with respect to the difference in travel distance.