IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v262y2017i1p28-39.html
   My bibliography  Save this article

Integer programming techniques for educational timetabling

Author

Listed:
  • Fonseca, George H.G.
  • Santos, Haroldo G.
  • Carrano, Eduardo G.
  • Stidsen, Thomas J.R.

Abstract

Educational timetabling problems require the assignment of times and resources to events, while sets of required and desirable constraints must be considered. The XHSTT format was adopted in this work because it models the main features of educational timetabling and it is the most used format in recent studies in the field. This work presents new cuts and reformulations for the existing integer programming model for XHSTT. The proposed cuts improved hugely the linear relaxation of the formulation, leading to an average gap reduction of 32%. Applied to XHSTT-2014 instance set, the alternative formulation provided four new best known lower bounds and, used in a matheuristic framework, improved eleven best known solutions. The computational experiments also show that the resulting integer programming models from the proposed formulation are more effectively solved for most of the instances.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:262:y:2017:i:1:p:28-39
    DOI: 10.1016/j.ejor.2017.03.020
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221717302242
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2017.03.020?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. Gerhard Post & Jeffrey Kingston & Samad Ahmadi & Sophia Daskalaki & Christos Gogos & Jari Kyngas & Cimmo Nurmi & Nysret Musliu & Nelishia Pillay & Haroldo Santos & Andrea Schaerf, 2014. "XHSTT: an XML archive for high school timetabling problems in different countries," Annals of Operations Research, Springer, vol. 218(1), pages 295-301, July.
    2. Burke, E.K. & Eckersley, A.J. & McCollum, B. & Petrovic, S. & Qu, R., 2010. "Hybrid variable neighbourhood approaches to university exam timetabling," European Journal of Operational Research, Elsevier, vol. 206(1), pages 46-53, October.
    3. Tomáš Müller, 2009. "ITC2007 solver description: a hybrid approach," Annals of Operations Research, Springer, vol. 172(1), pages 429-446, November.
    4. 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.
    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. 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.
    7. Arnaldo Vieira Moura & Rafael Augusto Scaraficci, 2010. "A GRASP strategy for a more constrained School Timetabling Problem," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 7(2), pages 152-170.
    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. Karol Kowalewski, 2018. "Uwarunkowania rozwoju startupów – perspektywa północno-wschodniej Polski," Nowoczesne Systemy Zarządzania. Modern Management Systems, Military University of Technology, Faculty of Security, Logistics and Management, Institute of Organization and Management, issue 3, pages 245-257.
    3. 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.
    4. Felipe Rosa-Rivera & Jose I. Nunez-Varela & Cesar A. Puente-Montejano & Sandra E. Nava-Muñoz, 2021. "Measuring the complexity of university timetabling instances," Journal of Scheduling, Springer, vol. 24(1), pages 103-121, February.
    5. 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.
    6. Lobo, Mariana F & Azzone, Vanessa & Lopes, Fernando & Freitas, Alberto & Costa-Pereira, Altamiro & Normand, Sharon-Lise & Teixeira-Pinto, Armando, 2020. "Understanding the large heterogeneity in hospital readmissions and mortality for acute myocardial infarction," Health Policy, Elsevier, vol. 124(7), pages 684-694.
    7. Aslan, Ayse & Bakir, Ilke & Vis, Iris F.A., 2020. "A dynamic thompson sampling hyper-heuristic framework for learning activity planning in personalized learning," European Journal of Operational Research, Elsevier, vol. 286(2), pages 673-688.

    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. 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.
    2. Johnes, Jill, 2015. "Operational Research in education," European Journal of Operational Research, Elsevier, vol. 243(3), pages 683-696.
    3. 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.
    4. Emir Demirović & Nysret Musliu, 2017. "Modeling high school timetabling with bitvectors," Annals of Operations Research, Springer, vol. 252(2), pages 215-238, May.
    5. 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.
    6. 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.
    7. 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.
    8. De Boeck, Liesje & Beliën, Jeroen & Creemers, Stefan, 2016. "A column generation approach for solving the examination-timetabling problemAuthor-Name: Woumans, Gert," European Journal of Operational Research, Elsevier, vol. 253(1), pages 178-194.
    9. 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).
    10. 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.
    11. 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.
    12. Maenhout, Broos & Vanhoucke, Mario, 2010. "A hybrid scatter search heuristic for personalized crew rostering in the airline industry," European Journal of Operational Research, Elsevier, vol. 206(1), pages 155-167, October.
    13. Hoogervorst, R. & Dollevoet, T.A.B. & Maróti, G. & Huisman, D., 2018. "Reducing Passenger Delays by Rolling Stock Rescheduling," Econometric Institute Research Papers EI2018-29, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    14. Arpan Rijal & Marco Bijvank & Asvin Goel & René de Koster, 2021. "Workforce Scheduling with Order-Picking Assignments in Distribution Facilities," Transportation Science, INFORMS, vol. 55(3), pages 725-746, May.
    15. Isabel Martins & Filipe Alvelos & Miguel Constantino, 2012. "A branch-and-price approach for harvest scheduling subject to maximum area restrictions," Computational Optimization and Applications, Springer, vol. 51(1), pages 363-385, January.
    16. Shan Lan & John-Paul Clarke & Cynthia Barnhart, 2006. "Planning for Robust Airline Operations: Optimizing Aircraft Routings and Flight Departure Times to Minimize Passenger Disruptions," Transportation Science, INFORMS, vol. 40(1), pages 15-28, February.
    17. Wu, Weitiao & Lin, Yue & Liu, Ronghui & Jin, Wenzhou, 2022. "The multi-depot electric vehicle scheduling problem with power grid characteristics," Transportation Research Part B: Methodological, Elsevier, vol. 155(C), pages 322-347.
    18. Anuj Mehrotra & Joseph Shantz & Michael A. Trick, 2005. "Determining newspaper marketing zones using contiguous clustering," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(1), pages 82-92, February.
    19. Lentink, R.M. & Fioole, P-J. & Kroon, L.G. & van 't Woudt, C., 2003. "Applying Operations Research techniques to planning of train shunting," ERIM Report Series Research in Management ERS-2003-094-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    20. 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.

    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:262:y:2017:i:1:p:28-39. 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.