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The timetable constrained distance minimization problem

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  • Rasmus Rasmussen
  • Michael Trick

Abstract

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. Copyright Springer Science+Business Media, LLC 2009

Suggested Citation

  • Rasmus Rasmussen & Michael Trick, 2009. "The timetable constrained distance minimization problem," Annals of Operations Research, Springer, vol. 171(1), pages 45-59, October.
    • Handle: RePEc:spr:annopr:v:171:y:2009:i:1:p:45-59:10.1007/s10479-008-0384-4
    DOI: 10.1007/s10479-008-0384-4
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    References listed on IDEAS

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    1. Cynthia Barnhart & Ellis L. Johnson & George L. Nemhauser & Martin W. P. Savelsbergh & Pamela H. Vance, 1998. "Branch-and-Price: Column Generation for Solving Huge Integer Programs," Operations Research, INFORMS, vol. 46(3), pages 316-329, June.
    2. Henz, Martin & Muller, Tobias & Thiel, Sven, 2004. "Global constraints for round robin tournament scheduling," European Journal of Operational Research, Elsevier, vol. 153(1), pages 92-101, February.
    3. Rasmussen, Rasmus V. & Trick, Michael A., 2007. "A Benders approach for the constrained minimum break problem," European Journal of Operational Research, Elsevier, vol. 177(1), pages 198-213, February.
    4. Lim, A. & Rodrigues, B. & Zhang, X., 2006. "A simulated annealing and hill-climbing algorithm for the traveling tournament problem," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1459-1478, November.
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