IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v272y2019i2p430-446.html
   My bibliography  Save this article

Dantzig–Wolfe decomposition of the daily course pattern formulation for curriculum-based course timetabling

Author

Listed:
  • Bagger, Niels-Christian F.
  • Sørensen, Matias
  • Stidsen, Thomas R.

Abstract

In this paper, we considered the problem of Curriculum-Based Course Timetabling, i.e., assigning weekly lectures to a time schedule and rooms. We developed a Column Generation algorithm based on a pattern formulation of the time scheduling part of the problem by Bagger et al. (2016). The pattern formulation is an enumeration of all schedules by which each course can be assigned on each day; it is a lower bounding model. Pattern enumeration has also been considered in Burke (2008), where the authors enumerated all schedules to which each curriculum can be assigned on each day. We applied the Dantzig–Wolfe reformulation, so each column corresponded to a schedule for an entire day.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:272:y:2019:i:2:p:430-446
    DOI: 10.1016/j.ejor.2018.06.042
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221718305794
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2018.06.042?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. Roberto Asín Achá & Robert Nieuwenhuis, 2014. "Curriculum-based course timetabling with SAT and MaxSAT," Annals of Operations Research, Springer, vol. 218(1), pages 71-91, July.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Edmund Burke & Jakub Mareček & Andrew Parkes & Hana Rudová, 2010. "A supernodal formulation of vertex colouring with applications in course timetabling," Annals of Operations Research, Springer, vol. 179(1), pages 105-130, September.
    8. 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.
    9. 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. 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.
    2. 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.

    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    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. Lindahl, Michael & Stidsen, Thomas & Sørensen, Matias, 2019. "Quality recovering of university timetables," European Journal of Operational Research, Elsevier, vol. 276(2), pages 422-435.
    11. 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.
    12. Andrea Schaerf, 2015. "Comments 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 362-365, July.
    13. 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.
    14. 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.
    15. 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.
    16. Arnaud Coster & Nysret Musliu & Andrea Schaerf & Johannes Schoisswohl & Kate Smith-Miles, 2022. "Algorithm selection and instance space analysis for curriculum-based course timetabling," Journal of Scheduling, Springer, vol. 25(1), pages 35-58, February.
    17. 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.
    18. 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.
    19. 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.
    20. 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.

    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:272:y:2019:i:2:p:430-446. 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.