IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v236y2014i2p592-600.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221713010035
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2013.12.019?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    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. 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.
    5. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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.
    4. 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.
    5. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Mancini Simona & Isabello Andrea, 2014. "Fair referee assignment for the Italian soccer serieA," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 10(2), pages 153-160, June.
    3. Guillermo Durán, 2021. "Sports scheduling and other topics in sports analytics: a survey with special reference to Latin America," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 125-155, April.
    4. 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.
    5. Yun-Chia Liang & Yen-Yu Lin & Angela Hsiang-Ling Chen & Wei-Sheng Chen, 2021. "Variable Neighborhood Search for Major League Baseball Scheduling Problem," Sustainability, MDPI, vol. 13(7), pages 1-18, April.
    6. Alan T. Murray & Antonio Ortiz & Seonga Cho, 2022. "Enhancing strategic defensive positioning and performance in the outfield," Journal of Geographical Systems, Springer, vol. 24(2), pages 223-240, April.
    7. 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.
    8. 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.
    9. Lamghari, Amina & Ferland, Jacques A., 2011. "Assigning judges to competitions of several rounds using Tabu search," European Journal of Operational Research, Elsevier, vol. 210(3), pages 694-705, May.
    10. 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.
    11. 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.
    12. Marjorie Cone Saur & Kaleigh Starr & Mark Husted & Alexandra M. Newman, 2012. "Scheduling Softball Series in the Rocky Mountain Athletic Conference," Interfaces, INFORMS, vol. 42(3), pages 296-309, June.
    13. Michael A. Trick & Hakan Yildiz, 2011. "Benders' cuts guided large neighborhood search for the traveling umpire problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(8), pages 771-781, December.
    14. David Rea & Craig Froehle & Suzanne Masterson & Brian Stettler & Gregory Fermann & Arthur Pancioli, 2021. "Unequal but Fair: Incorporating Distributive Justice in Operational Allocation Models," Production and Operations Management, Production and Operations Management Society, vol. 30(7), pages 2304-2320, July.
    15. Michael R. Miller & Robert J. Alexander & Vincent A. Arbige & Robert F. Dell & Steven R. Kremer & Brian P. McClune & Jane E. Oppenlander & Joshua P. Tomlin, 2017. "Optimal Allocation of Students to Naval Nuclear-Power Training Units," Interfaces, INFORMS, vol. 47(4), pages 320-335, August.
    16. Mehran Hojati, 2010. "Near-optimal solution to an employee assignment problem with seniority," Annals of Operations Research, Springer, vol. 181(1), pages 539-557, December.
    17. Elina Rönnberg & Torbjörn Larsson, 2010. "Automating the self-scheduling process of nurses in Swedish healthcare: a pilot study," Health Care Management Science, Springer, vol. 13(1), pages 35-53, March.
    18. Borgonjon, Tessa & Maenhout, Broos, 2022. "An exact approach for the personnel task rescheduling problem with task retiming," European Journal of Operational Research, Elsevier, vol. 296(2), pages 465-484.
    19. Young-Chae Hong & Amy Cohn & Stephen Gorga & Edmond O’Brien & William Pozehl & Jennifer Zank, 2019. "Using Optimization Techniques and Multidisciplinary Collaboration to Solve a Challenging Real-World Residency Scheduling Problem," Interfaces, INFORMS, vol. 49(3), pages 201-212, May.
    20. Masoud Yaghini & Mohammad Karimi & Mohadeseh Rahbar, 2015. "A set covering approach for multi-depot train driver scheduling," Journal of Combinatorial Optimization, Springer, vol. 29(3), pages 636-654, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:236:y:2014:i:2:p:592-600. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.