A New Lower Bound to the Traveling Tournament Problem

Optimization in sports is a field of increasing interest. The traveling tournament problem abstracts certain characteristics of sports scheduling problems. We propose a new method for determining a lower bound to this problem. The new bound improves upon the previously best known lower bound. Numerical results on benchmark instances showed reductions as large as 38.6% in the gaps between lower and upper bounds.

[1]  C. Ribeiro,et al.  OR APPLICATIONS IN SPORTS SCHEDULING AND MANAGEMENT , 2003 .

[2]  George L. Nemhauser,et al.  Solving the Travelling Tournament Problem: A Combined Integer Programming and Constraint Programming Approach , 2002, PATAT.

[3]  Joseph Y.-T. Leung,et al.  Handbook of Scheduling: Algorithms, Models, and Performance Analysis , 2004 .

[4]  Pascal Van Hentenryck,et al.  A simulated annealing approach to the traveling tournament problem , 2006, J. Sched..

[5]  Michael A. Trick,et al.  A Benders approach for the constrained minimum break problem , 2007, Eur. J. Oper. Res..

[6]  Alexandre R. Duarte,et al.  Referee Assignment in Sports Tournaments , 2006 .

[7]  Celso C. Ribeiro,et al.  Heuristics for the mirrored traveling tournament problem , 2007, Eur. J. Oper. Res..

[8]  George L. Nemhauser,et al.  The Traveling Tournament Problem Description and Benchmarks , 2001, CP.

[9]  Celso C. Ribeiro,et al.  An application of integer programming to playoff elimination in football championships , 2005, Int. Trans. Oper. Res..

[10]  Celso C. Ribeiro,et al.  Maximizing breaks and bounding solutions to the mirrored traveling tournament problem , 2006, Discret. Appl. Math..

[11]  Michael A. Trick,et al.  Round robin scheduling - a survey , 2008, Eur. J. Oper. Res..

[12]  George L. Nemhauser,et al.  Sports Scheduling , 2004, Handbook of Scheduling.

[13]  Tomomi Matsui,et al.  Constructive Algorithms for the Constant Distance Traveling Tournament Problem , 2006, PATAT.

[14]  P. Harker,et al.  Scheduling a Major College Basketball Conference , 1998 .