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A combined approximation for the traveling tournament problem and the traveling umpire problem

Author

Listed:
  • Bender Marco
  • Westphal Stephan

    (Clausthal University of Technology – Institute for Applied Stochastics and Operations Research, Germany)

Abstract

We consider the traveling tournament problem (TTP) and the traveling umpire problem (TUP). In TTP, the task is to design a double round-robin schedule, where no two teams play against each other in two consecutive rounds, and the total travel distance is minimized. In TUP, the task is to find an assignment of umpires for a given tournament such that every umpire handles at least one game at every team’s home venue and an umpire neither visits a venue nor sees a team (home or away) too often. The task is to minimize the total distance traveled by the umpires. We present a combined approximation for this problem, when the number of umpires is odd. We therefore first design an approximation algorithm for TTP and then show how to define an umpire assignment for this tournament such that a constant-factor approximation for TUP is guaranteed.

Suggested Citation

  • Bender Marco & Westphal Stephan, 2016. "A combined approximation for the traveling tournament problem and the traveling umpire problem," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 12(3), pages 139-149, September.
    • Handle: RePEc:bpj:jqsprt:v:12:y:2016:i:3:p:139-149:n:2
    DOI: 10.1515/jqas-2015-0111
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    References listed on IDEAS

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    1. 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.
    2. Wauters, Tony & Van Malderen, Sam & Vanden Berghe, Greet, 2014. "Decomposition and local search based methods for the traveling umpire problem," European Journal of Operational Research, Elsevier, vol. 238(3), pages 886-898.
    3. Trick, Michael A. & Yildiz, Hakan, 2012. "Locally Optimized Crossover for the Traveling Umpire Problem," European Journal of Operational Research, Elsevier, vol. 216(2), pages 286-292.
    4. de Oliveira, Lucas & de Souza, Cid C. & Yunes, Tallys, 2014. "Improved bounds for the traveling umpire problem: A stronger formulation and a relax-and-fix heuristic," European Journal of Operational Research, Elsevier, vol. 236(2), pages 592-600.
    5. Ryuhei Miyashiro & Tomomi Matsui & Shinji Imahori, 2012. "An approximation algorithm for the traveling tournament problem," Annals of Operations Research, Springer, vol. 194(1), pages 317-324, April.
    6. Clemens Thielen & Stephan Westphal, 2012. "Approximation algorithms for TTP(2)," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 76(1), pages 1-20, August.
    7. Ribeiro, Celso C. & Urrutia, Sebastian, 2007. "Heuristics for the mirrored traveling tournament problem," European Journal of Operational Research, Elsevier, vol. 179(3), pages 775-787, June.
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    1. Guillermo Durán & Mario Guajardo & Facundo Gutiérrez, 2022. "Efficient referee assignment in Argentinean professional basketball leagues using operations research methods," Annals of Operations Research, Springer, vol. 316(2), pages 1121-1139, September.

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