The Multi-Round Balanced Traveling Tournament Problem

• Published in: Proceedings of the International Conference on Automated Planning and Scheduling Vol. 21; pp. 106 - 113
• Main Authors: Hoshino, Richard, Kawarabayashi, Ken-ichi
• Format: Journal Article
• Language: English
• Published: 22.03.2011
• ISSN: 2334-0835; 2334-0843; 2334-0843
• DOI: 10.1609/icaps.v21i1.13443

Given an n-team sports league, the Traveling Tournament Problem (TTP) seeks to determine an optimal double round-robin schedule minimizing the sum total of distances traveled by the n teams as they move from city to city. In the TTP, the number of "rounds" is fixed at r = 2. In this paper, we propose the Multi-Round Balanced Traveling Tournament Problem (mb-TTP), inspired by the actual league structure of Japanese professional baseball, where n = 6 teams play 120 intra-league games over r = 8 rounds, subject to various constraints that ensure competitive balance. These additional balancing constraints enable us to reformulate the 2k-round mb-TTP as a shortest path problem on a directed graph, for all k >= 1. We apply our theoretical algorithm to the 6-team Nippon (Japanese) Professional Baseball Central League, creating a distance-optimal schedule with 57836 kilometres of total travel, a 26.8% reduction compared to the 79067 kilometres traveled by these six teams during the 2010 regular season.