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

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  • 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
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    References listed on IDEAS

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    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. 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.
    4. Johnes, Jill, 2015. "Operational Research in education," European Journal of Operational Research, Elsevier, vol. 243(3), pages 683-696.
    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. 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.
    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.

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