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A mixed-integer programming approach for solving university course timetabling problems

Author

Listed:
  • Efstratios Rappos

    (University of Applied Sciences of Western Switzerland (HES-SO))

  • Eric Thiémard

    (University of Applied Sciences of Western Switzerland (HES-SO))

  • Stephan Robert

    (University of Applied Sciences of Western Switzerland (HES-SO))

  • Jean-François Hêche

    (University of Applied Sciences of Western Switzerland (HES-SO))

Abstract

This article presents a mixed-integer programming model for solving the university timetabling problem which considers the allocation of students to classes and the assignment of rooms and time periods to each class. The model was developed as part of our participation in the International Timetabling Competition 2019 and produced a ranking of second place at the competition. Modeling a timetabling problem as a mixed-integer program is not new. Our contribution rests on a number of innovative features adapted to this problem which allow for a reduction in the number of variables and constraints of the mixed-integer program to manageable levels achieving a reasonable computational performance. The proposed algorithm consists of a first-stage method to obtain an initial feasible solution and a second-stage local search procedure to iteratively improve the solution value, both of which involve the optimization of mixed-integer programming problems.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jsched:v:25:y:2022:i:4:d:10.1007_s10951-021-00715-5
    DOI: 10.1007/s10951-021-00715-5
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    References listed on IDEAS

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    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
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    Cited by:

    1. Sunil B. Bhoi & Jayesh M. Dhodiya, 2024. "Multi-objective faculty course assignment problem based on the double parametric form of fuzzy preferences," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 34(2), pages 1-16.
    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.
    3. 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.

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