IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v194y2012i1p399-41210.1007-s10479-010-0709-y.html
   My bibliography  Save this article

Strong bounds with cut and column generation for class-teacher timetabling

Author

Listed:
  • Haroldo Santos
  • Eduardo Uchoa
  • Luiz Ochi
  • Nelson Maculan

Abstract

This work presents an integer programming formulation for a variant of the Class-Teacher Timetabling problem, which considers the satisfaction of teacher preferences and also the proper distribution of lessons throughout the week. The formulation contains a very large number of variables and is enhanced by cuts. Therefore, a cut and column generation algorithm to solve its linear relaxation is provided. The lower bounds obtained are very good, allowing us to prove the optimality of previously known solutions in three formerly open instances. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • Haroldo Santos & Eduardo Uchoa & Luiz Ochi & Nelson Maculan, 2012. "Strong bounds with cut and column generation for class-teacher timetabling," Annals of Operations Research, Springer, vol. 194(1), pages 399-412, April.
    • Handle: RePEc:spr:annopr:v:194:y:2012:i:1:p:399-412:10.1007/s10479-010-0709-y
    DOI: 10.1007/s10479-010-0709-y
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-010-0709-y
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-010-0709-y?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. Hertz, A., 1991. "Tabu search for large scale timetabling problems," European Journal of Operational Research, Elsevier, vol. 54(1), pages 39-47, September.
    2. Costa, Daniel, 1994. "A tabu search algorithm for computing an operational timetable," European Journal of Operational Research, Elsevier, vol. 76(1), pages 98-110, July.
    3. WOLSEY, Laurence A., 1975. "Faces for a linear inequality in 0-1 variables," LIDAM Reprints CORE 218, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. D. Abramson, 1991. "Constructing School Timetables Using Simulated Annealing: Sequential and Parallel Algorithms," Management Science, INFORMS, vol. 37(1), pages 98-113, January.
    5. Cynthia Barnhart & Ellis L. Johnson & George L. Nemhauser & Martin W. P. Savelsbergh & Pamela H. Vance, 1998. "Branch-and-Price: Column Generation for Solving Huge Integer Programs," Operations Research, INFORMS, vol. 46(3), pages 316-329, June.
    6. K Papoutsis & C Valouxis & E Housos, 2003. "A column generation approach for the timetabling problem of Greek high schools," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(3), pages 230-238, March.
    7. George B. Dantzig & Philip Wolfe, 1960. "Decomposition Principle for Linear Programs," Operations Research, INFORMS, vol. 8(1), pages 101-111, February.
    8. Drexl, Andreas & Salewski, Frank, 1997. "Distribution requirements and compactness constraints in school timetabling," European Journal of Operational Research, Elsevier, vol. 102(1), pages 193-214, October.
    9. Daskalaki, S. & Birbas, T. & Housos, E., 2004. "An integer programming formulation for a case study in university timetabling," European Journal of Operational Research, Elsevier, vol. 153(1), pages 117-135, February.
    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. Lemos, Alexandre & Melo, Francisco S. & Monteiro, Pedro T. & Lynce, Inês, 2019. "Room usage optimization in timetabling: A case study at Universidade de Lisboa," Operations Research Perspectives, Elsevier, vol. 6(C).
    2. Dorneles, Árton P. & de Araújo, Olinto C.B. & Buriol, Luciana S., 2017. "A column generation approach to high school timetabling modeled as a multicommodity flow problem," European Journal of Operational Research, Elsevier, vol. 256(3), pages 685-695.
    3. P. Solano Cutillas & D. Pérez-Perales & M. M. E. Alemany Díaz, 2022. "A mathematical programming tool for an efficient decision-making on teaching assignment under non-regular time schedules," Operational Research, Springer, vol. 22(3), pages 2899-2942, July.
    4. Saviniec, Landir & Santos, Maristela O. & Costa, Alysson M., 2018. "Parallel local search algorithms for high school timetabling problems," European Journal of Operational Research, Elsevier, vol. 265(1), pages 81-98.
    5. 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.
    6. Johnes, Jill, 2015. "Operational Research in education," European Journal of Operational Research, Elsevier, vol. 243(3), pages 683-696.
    7. George Henrique Godim Fonseca & Haroldo Gambini Santos & Túlio Ângelo Machado Toffolo & Samuel Souza Brito & Marcone Jamilson Freitas Souza, 2016. "GOAL solver: a hybrid local search based solver for high school timetabling," Annals of Operations Research, Springer, vol. 239(1), pages 77-97, April.
    8. Fonseca, George H.G. & Santos, Haroldo G. & Carrano, Eduardo G. & Stidsen, Thomas J.R., 2017. "Integer programming techniques for educational timetabling," European Journal of Operational Research, Elsevier, vol. 262(1), pages 28-39.
    9. George H. G. Fonseca & Haroldo G. Santos & Eduardo G. Carrano, 2016. "Late acceptance hill-climbing for high school timetabling," Journal of Scheduling, Springer, vol. 19(4), pages 453-465, August.
    10. Emir Demirović & Nysret Musliu, 2017. "Modeling high school timetabling with bitvectors," Annals of Operations Research, Springer, vol. 252(2), pages 215-238, May.
    11. R. A. Oude Vrielink & E. A. Jansen & E. W. Hans & J. Hillegersberg, 2019. "Practices in timetabling in higher education institutions: a systematic review," Annals of Operations Research, Springer, vol. 275(1), pages 145-160, April.

    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. Salem Al-Yakoob & Hanif Sherali, 2015. "A column generation mathematical programming approach for a class-faculty assignment problem with preferences," Computational Management Science, Springer, vol. 12(2), pages 297-318, April.
    2. Johnes, Jill, 2015. "Operational Research in education," European Journal of Operational Research, Elsevier, vol. 243(3), pages 683-696.
    3. K Papoutsis & C Valouxis & E Housos, 2003. "A column generation approach for the timetabling problem of Greek high schools," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(3), pages 230-238, March.
    4. Dimopoulou, M. & Miliotis, P., 2001. "Implementation of a university course and examination timetabling system," European Journal of Operational Research, Elsevier, vol. 130(1), pages 202-213, April.
    5. Kristiansen, Simon & Sørensen, Matias & Stidsen, Thomas R., 2011. "Elective course planning," European Journal of Operational Research, Elsevier, vol. 215(3), pages 713-720, December.
    6. Daskalaki, S. & Birbas, T., 2005. "Efficient solutions for a university timetabling problem through integer programming," European Journal of Operational Research, Elsevier, vol. 160(1), pages 106-120, January.
    7. Zhang, Defu & Liu, Yongkai & M'Hallah, Rym & Leung, Stephen C.H., 2010. "A simulated annealing with a new neighborhood structure based algorithm for high school timetabling problems," European Journal of Operational Research, Elsevier, vol. 203(3), pages 550-558, June.
    8. Nelishia Pillay, 2014. "A survey of school timetabling research," Annals of Operations Research, Springer, vol. 218(1), pages 261-293, July.
    9. Pongcharoen, P. & Promtet, W. & Yenradee, P. & Hicks, C., 2008. "Stochastic Optimisation Timetabling Tool for university course scheduling," International Journal of Production Economics, Elsevier, vol. 112(2), pages 903-918, April.
    10. Schirmer, Andreas & Potzhar, Kathrin, 2001. "Professional course scheduling in airline transport pilot training: A case from Lufthansa flight training," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 539, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    11. Omid Shahvari & Rasaratnam Logendran & Madjid Tavana, 2022. "An efficient model-based branch-and-price algorithm for unrelated-parallel machine batching and scheduling problems," Journal of Scheduling, Springer, vol. 25(5), pages 589-621, October.
    12. Barry C. Smith & Ellis L. Johnson, 2006. "Robust Airline Fleet Assignment: Imposing Station Purity Using Station Decomposition," Transportation Science, INFORMS, vol. 40(4), pages 497-516, November.
    13. Bani, Abderrahman & El Hallaoui, Issmail & Corréa, Ayoub Insa & Tahir, Adil, 2023. "Solving a real-world multi-depot multi-period petrol replenishment problem with complex loading constraints," European Journal of Operational Research, Elsevier, vol. 311(1), pages 154-172.
    14. 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.
    15. De Causmaecker, Patrick & Demeester, Peter & Vanden Berghe, Greet, 2009. "A decomposed metaheuristic approach for a real-world university timetabling problem," European Journal of Operational Research, Elsevier, vol. 195(1), pages 307-318, May.
    16. 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.
    17. H. Fei & C. Chu & N. Meskens, 2009. "Solving a tactical operating room planning problem by a column-generation-based heuristic procedure with four criteria," Annals of Operations Research, Springer, vol. 166(1), pages 91-108, February.
    18. Klose, Andreas & Gortz, Simon, 2007. "A branch-and-price algorithm for the capacitated facility location problem," European Journal of Operational Research, Elsevier, vol. 179(3), pages 1109-1125, June.
    19. Lin, Zhiyuan & Kwan, Raymond S.K., 2016. "A branch-and-price approach for solving the train unit scheduling problem," Transportation Research Part B: Methodological, Elsevier, vol. 94(C), pages 97-120.
    20. Cangalovic, Mirjana & Kovacevic-Vujcic, Vera & Ivanovic, Lav & Drazic, Milan, 1998. "Modeling and solving a real-life assignment problem at universities," European Journal of Operational Research, Elsevier, vol. 110(2), pages 223-233, 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:spr:annopr:v:194:y:2012:i:1:p:399-412:10.1007/s10479-010-0709-y. 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.