Integrating tours in double round robin tournaments: Models, heuristics and a case study

Abstract

During the last decades, the use of advanced optimization algorithms to generate sports timetables has caught the attention of both academics and practitioners. From a managerial standpoint, the competition’s structure and the design of the league’s schedule represent key strategic decisions with a direct impact in terms of revenue and other important indicators. Argentina’s National Basketball League (LNB) has undergone a major transformation since 2014, implementing a tour-based schedule design to reduce the total distance traveled by teams by tackling a variant of the well-known Traveling Tournament Problem (TTP). Using the LNB as a laboratory, in this work, we consider a double round robin tournament where, in some rounds, known in advance, tours of a given length can be defined in order to reduce the overall travel distance. In this fashion, the schedule follows a more structured format while still capturing the benefits in terms of distance reduction generated by the tours. To our knowledge, this problem has not been considered previously in the related sports timetabling literature. Methodologically, we formulate an Integer Linear Programming model to construct the schedule. In order to scale to real-world instances, we further propose a matheuristic that decomposes the problem into different stages. Throughout extensive computational experiments, In addition, we evaluate the behavior of the algorithms on synthetic instances derived from benchmark from related sport scheduling problems from the related literature and provide a detailed analysis over six LNB seasons. Overall, the results show that our framework reduces the traveled distance in most of the instances and that it translates into higher revenue under moderate stadium attendance assumptions, with increments reaching up to 40 percent.