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Integer programming techniques for educational timetabling

Author

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  • 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
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    References listed on IDEAS

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    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.
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    Cited by:

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    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.

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