U12 Basketball League Scheduling Problem Based on Minimizing the Total Traveling Distance and the Number of Breaks

Sports scheduling is one of the widely investigated application problems in artificial intelligence and operations research. This problem can be represented as a combinatorial optimization problem, in which the date and the venue of each game must be determined, subject to a given set of constraints. In 2018, Japan Basketball Association (JBA) has started to implement the league games in the prefectures, and regarding U12 (under 12 years old), league games are currently being held in most prefectures. In this paper, the main focus is laid on the U12 Basketball League Scheduling Problem. First, a formal framework for the U12 Basketball League Scheduling based on minimizing the total traveling distance (U12-BLSdist) is defined. A novel solution criterion called an egalitarian solution for U12-BLSdist is also provided. Next, a formal framework for the U12 Basketball league scheduling problem based on minimizing the number of breaks (U12-BLSbreak) is defined. Furthermore, the frameworks U12-BLSdist and U12-BLSbreak are formalized as 0-1 integer programming problems. In the experiments, we use the real data of U12 basketball league games played in Hyogo prefecture in 2018 and solve the U12-BLSdist and U12-BLSbreak problems. An optimal league scheduling and an egalitarian league scheduling for the U12-BLSdist, and the minimal number of breaks for the U12-BLSbreak are reported by comparing with the league scheduling actually used in 2018.