The Traveling Social Golfer Problem: The Case of the Volleyball Nations League

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 result of this setup, there is a large discrepancy between the travel burdens of meeting teams, which is a disadvantage for the teams that have to travel a lot. We analyse this problem, and find that it is related to the well-known Social Golfer Problem. We propose a decomposition approach for the resulting optimization problem, leading to the so-called Venue Assignment Problem. Using integer programming methods, we find, for real-life instances, the fairest schedules with respect to the difference in travel distance.