IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v280y2019i1d10.1007_s10479-018-3096-4.html
   My bibliography  Save this article

Flow formulations for curriculum-based course timetabling

Author

Listed:
  • Niels-Christian F. Bagger

    (MaCom A/S
    Technical University of Denmark)

  • Simon Kristiansen

    (RHA Software Group)

  • Matias Sørensen

    (MaCom A/S
    Technical University of Denmark)

  • Thomas R. Stidsen

    (Technical University of Denmark)

Abstract

In this paper we present two mixed-integer programming formulations for the curriculum based course timetabling problem (CTT). We show that the formulations contain underlying network structures by dividing the CTT into two separate models and then connect the two models using flow formulation techniques. The first mixed-integer programming formulation is based on an underlying minimum cost flow problem, which decreases the number of integer variables significantly and improves the performance compared to an intuitive mixed-integer programming formulation. The second formulation is based on a multi-commodity flow problem which in general is NP-hard, however, we prove that it suffices to solve the linear programming relaxation of the model. The formulations show competitiveness with other approaches based on mixed-integer programming from the literature and improve the currently best known lower bound on one data instance in the benchmark data set from the second international timetabling competition. Regarding upper bounds, the formulation based on the minimum cost flow problem performs better on average than other mixed integer programming approaches for the CTT.

Suggested Citation

  • Niels-Christian F. Bagger & Simon Kristiansen & Matias Sørensen & Thomas R. Stidsen, 2019. "Flow formulations for curriculum-based course timetabling," Annals of Operations Research, Springer, vol. 280(1), pages 121-150, September.
    • Handle: RePEc:spr:annopr:v:280:y:2019:i:1:d:10.1007_s10479-018-3096-4
    DOI: 10.1007/s10479-018-3096-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-018-3096-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10479-018-3096-4?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. Hao, Jin-Kao & Benlic, Una, 2011. "Lower bounds for the ITC-2007 curriculum-based course timetabling problem," European Journal of Operational Research, Elsevier, vol. 212(3), pages 464-472, August.
    2. Barry McCollum & Andrea Schaerf & Ben Paechter & Paul McMullan & Rhyd Lewis & Andrew J. Parkes & Luca Di Gaspero & Rong Qu & Edmund K. Burke, 2010. "Setting the Research Agenda in Automated Timetabling: The Second International Timetabling Competition," INFORMS Journal on Computing, INFORMS, vol. 22(1), pages 120-130, February.
    3. Andrea Bettinelli & Valentina Cacchiani & Roberto Roberti & Paolo Toth, 2015. "An overview of curriculum-based course timetabling," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 313-349, July.
    4. Gerald Lach & Marco Lübbecke, 2012. "Curriculum based course timetabling: new solutions to Udine benchmark instances," Annals of Operations Research, Springer, vol. 194(1), pages 255-272, April.
    5. Andrea Bettinelli & Valentina Cacchiani & Roberto Roberti & Paolo Toth, 2015. "Rejoinder on: an overview of curriculum-based course timetabling," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 366-368, July.
    6. Alex Bonutti & Fabio Cesco & Luca Gaspero & Andrea Schaerf, 2012. "Benchmarking curriculum-based course timetabling: formulations, data formats, instances, validation, visualization, and results," Annals of Operations Research, Springer, vol. 194(1), pages 59-70, April.
    7. Edmund Burke & Jakub Mareček & Andrew Parkes & Hana Rudová, 2012. "A branch-and-cut procedure for the Udine Course Timetabling problem," Annals of Operations Research, Springer, vol. 194(1), pages 71-87, April.
    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. Dennis S. Holm & Rasmus Ø. Mikkelsen & Matias Sørensen & Thomas J. R. Stidsen, 2022. "A graph-based MIP formulation of the International Timetabling Competition 2019," Journal of Scheduling, Springer, vol. 25(4), pages 405-428, August.

    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. Bagger, Niels-Christian F. & Sørensen, Matias & Stidsen, Thomas R., 2019. "Dantzig–Wolfe decomposition of the daily course pattern formulation for curriculum-based course timetabling," European Journal of Operational Research, Elsevier, vol. 272(2), pages 430-446.
    2. Niels-Christian Fink Bagger & Guy Desaulniers & Jacques Desrosiers, 2019. "Daily course pattern formulation and valid inequalities for the curriculum-based course timetabling problem," Journal of Scheduling, Springer, vol. 22(2), pages 155-172, April.
    3. Mutsunori Banbara & Katsumi Inoue & Benjamin Kaufmann & Tenda Okimoto & Torsten Schaub & Takehide Soh & Naoyuki Tamura & Philipp Wanko, 2019. "$${\varvec{teaspoon}}$$ teaspoon : solving the curriculum-based course timetabling problems with answer set programming," Annals of Operations Research, Springer, vol. 275(1), pages 3-37, April.
    4. Rasmus Ø. Mikkelsen & Dennis S. Holm, 2022. "A parallelized matheuristic for the International Timetabling Competition 2019," Journal of Scheduling, Springer, vol. 25(4), pages 429-452, August.
    5. Alexander Kiefer & Richard F. Hartl & Alexander Schnell, 2017. "Adaptive large neighborhood search for the curriculum-based course timetabling problem," Annals of Operations Research, Springer, vol. 252(2), pages 255-282, May.
    6. Michael Lindahl & Matias Sørensen & Thomas R. Stidsen, 2018. "A fix-and-optimize matheuristic for university timetabling," Journal of Heuristics, Springer, vol. 24(4), pages 645-665, August.
    7. Andrea Bettinelli & Valentina Cacchiani & Roberto Roberti & Paolo Toth, 2015. "An overview of curriculum-based course timetabling," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 313-349, July.
    8. Massimiliano Caramia & Stefano Giordani, 2020. "Curriculum-Based Course Timetabling with Student Flow, Soft Constraints, and Smoothing Objectives: an Application to a Real Case Study," SN Operations Research Forum, Springer, vol. 1(2), pages 1-21, June.
    9. Ceschia, Sara & Di Gaspero, Luca & Schaerf, Andrea, 2023. "Educational timetabling: Problems, benchmarks, and state-of-the-art results," European Journal of Operational Research, Elsevier, vol. 308(1), pages 1-18.
    10. Fabian Dunke & Stefan Nickel, 2023. "A matheuristic for customized multi-level multi-criteria university timetabling," Annals of Operations Research, Springer, vol. 328(2), pages 1313-1348, September.
    11. Lindahl, Michael & Stidsen, Thomas & Sørensen, Matias, 2019. "Quality recovering of university timetables," European Journal of Operational Research, Elsevier, vol. 276(2), pages 422-435.
    12. Efstratios Rappos & Eric Thiémard & Stephan Robert & Jean-François Hêche, 2022. "A mixed-integer programming approach for solving university course timetabling problems," Journal of Scheduling, Springer, vol. 25(4), pages 391-404, August.
    13. Esmaeilbeigi, Rasul & Mak-Hau, Vicky & Yearwood, John & Nguyen, Vivian, 2022. "The multiphase course timetabling problem," European Journal of Operational Research, Elsevier, vol. 300(3), pages 1098-1119.
    14. Seizinger, Markus & Brunner, Jens O., 2023. "Optimized planning of nursing curricula in dual vocational schools focusing on the German health care system," European Journal of Operational Research, Elsevier, vol. 304(3), pages 1223-1241.
    15. Lindahl, Michael & Mason, Andrew J. & Stidsen, Thomas & Sørensen, Matias, 2018. "A strategic view of University timetabling," European Journal of Operational Research, Elsevier, vol. 266(1), pages 35-45.
    16. Cristian D. Palma & Patrick Bornhardt, 2020. "Considering Section Balance in an Integer Optimization Model for the Curriculum-Based Course Timetabling Problem," Mathematics, MDPI, vol. 8(10), pages 1-12, October.
    17. Mats Carlsson & Sara Ceschia & Luca Gaspero & Rasmus Ørnstrup Mikkelsen & Andrea Schaerf & Thomas Jacob Riis Stidsen, 2023. "Exact and metaheuristic methods for a real-world examination timetabling problem," Journal of Scheduling, Springer, vol. 26(4), pages 353-367, August.
    18. Vermuyten, Hendrik & Lemmens, Stef & Marques, Inês & Beliën, Jeroen, 2016. "Developing compact course timetables with optimized student flows," European Journal of Operational Research, Elsevier, vol. 251(2), pages 651-661.
    19. Alexandre Lemos & Pedro T. Monteiro & Inês Lynce, 2021. "Disruptions in timetables: a case study at Universidade de Lisboa," Journal of Scheduling, Springer, vol. 24(1), pages 35-48, February.
    20. Dennis S. Holm & Rasmus Ø. Mikkelsen & Matias Sørensen & Thomas J. R. Stidsen, 2022. "A graph-based MIP formulation of the International Timetabling Competition 2019," Journal of Scheduling, Springer, vol. 25(4), pages 405-428, August.

    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:spr:annopr:v:280:y:2019:i:1:d:10.1007_s10479-018-3096-4. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.