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Improved bounds for the traveling umpire problem: A stronger formulation and a relax-and-fix heuristic

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  • de Oliveira, Lucas
  • de Souza, Cid C.
  • Yunes, Tallys

Abstract

Given a double round-robin tournament, the traveling umpire problem (TUP) consists of determining which games will be handled by each one of several umpire crews during the tournament. The objective is to minimize the total distance traveled by the umpires, while respecting constraints that include visiting every team at home, and not seeing a team or venue too often. We strengthen a known integer programming formulation for the TUP and use it to implement a relax-and-fix heuristic that improves the quality of 24 out of 25 best-known feasible solutions to instances in the TUP benchmark. We also improve all best-known lower bounds for those instances and, for the first time, provide lower bounds for instances with more than 16 teams.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:236:y:2014:i:2:p:592-600
    DOI: 10.1016/j.ejor.2013.12.019
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    References listed on IDEAS

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    1. A.T. Ernst & H. Jiang & M. Krishnamoorthy & B. Owens & D. Sier, 2004. "An Annotated Bibliography of Personnel Scheduling and Rostering," Annals of Operations Research, Springer, vol. 127(1), pages 21-144, March.
    2. Michael A. Trick & Hakan Yildiz & Tallys Yunes, 2012. "Scheduling Major League Baseball Umpires and the Traveling Umpire Problem," Interfaces, INFORMS, vol. 42(3), pages 232-244, June.
    3. James R. Evans, 1988. "A Microcomputer-Based Decision Support System for Scheduling Umpires in the American Baseball League," Interfaces, INFORMS, vol. 18(6), pages 42-51, December.
    4. 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.
    5. Adam Farmer & Jeffrey S. Smith & Luke T. Miller, 2007. "Scheduling Umpire Crews for Professional Tennis Tournaments," Interfaces, INFORMS, vol. 37(2), pages 187-196, April.
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    Cited by:

    1. Xue, Li & Luo, Zhixing & Lim, Andrew, 2015. "Two exact algorithms for the traveling umpire problem," European Journal of Operational Research, Elsevier, vol. 243(3), pages 932-943.
    2. Özlü, Oğuzhan & Sokol, Joel, 2016. "An optimization approach to designing a baseball scout network," European Journal of Operational Research, Elsevier, vol. 255(3), pages 948-960.
    3. Toffolo, Túlio A.M. & Wauters, Tony & Van Malderen, Sam & Vanden Berghe, Greet, 2016. "Branch-and-bound with decomposition-based lower bounds for the Traveling Umpire Problem," European Journal of Operational Research, Elsevier, vol. 250(3), pages 737-744.
    4. 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.
    5. 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.

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