The timetable constrained distance minimization problem

We define the timetable constrained distance minimization problem (TCDMP) which is a sports scheduling problem applicable for tournaments where the total travel distance must be minimized. The problem consists of finding an optimal home-away assignment when the opponents of each team in each time slot are given. We present an integer programming, a constraint programming formulation and describe two alternative solution methods: a hybrid integer programming/constraint programming approach and a branch and price algorithm. We test all four solution methods on benchmark problems and compare the performance. Furthermore, we present a new heuristic solution method called the circular traveling salesman approach (CTSA) for solving the traveling tournament problem. The solution method is able to obtain high quality solutions almost instantaneously, and by applying the TCDMP, we show how the solutions can be further improved.

[1]  G. Nemhauser,et al.  BRANCH-AND-PRICE: GENERATION FOR SOLVING HUGE INTEGER PROGRAMS , 1998 .

[2]  Jean-Charles Régin,et al.  A Filtering Algorithm for Global Sequencing Constraints , 1997, CP.

[3]  Gilles Pesant,et al.  Revisiting the Sequence Constraint , 2006, CP.

[4]  Danny De Schreye.  Constraint-based Round Robin Tournament Planning , 1999 .

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

[6]  Martin W. P. Savelsbergh,et al.  Branch-and-Price: Column Generation for Solving Huge Integer Programs , 1998, Oper. Res..

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

[8]  Federico Della Croce,et al.  Scheduling the Italian Football League: an ILP-based approach , 2006, Comput. Oper. Res..

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

[10]  Martin Henz,et al.  Global constraints for round robin tournament scheduling , 2004, Eur. J. Oper. Res..

[11]  T. Benoist,et al.  Lagrange Relaxation and Constraint Programming Collaborative schemes for Traveling Tournament Problems , 2001 .

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

[13]  Michael Jünger,et al.  Minimizing breaks by maximizing cuts , 2003, Oper. Res. Lett..

[14]  Andrea Schaerf,et al.  Scheduling Sport Tournaments using Constraint Logic Programming , 1999, Constraints.

[15]  Tomomi Matsui,et al.  Semidefinite programming based approaches to the break minimization problem , 2006, Comput. Oper. Res..

[16]  George L. Nemhauser,et al.  Scheduling A Major College Basketball Conference , 1998, Oper. Res..

[17]  X. Zhang,et al.  A simulated annealing and hill-climbing algorithm for the traveling tournament problem , 2006, Eur. J. Oper. Res..

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

[19]  Jean-Charles Régin.  Minimization of the number of breaks in sports scheduling problems using constraint programming , 1998, Constraint Programming and Large Scale Discrete Optimization.

[20]  Pascal Van Hentenryck,et al.  Traveling Tournament Scheduling: A Systematic Evaluation of Simulated Annealling , 2006, CPAIOR.

[21]  Martin Henz,et al.  Scheduling a Major College Basketball Conference - Revisited , 2001, Oper. Res..

[22]  Michael A. Trick.  A Schedule-Then-Break Approach to Sports Timetabling , 2000, PATAT.

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