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Curriculum based course timetabling: new solutions to Udine benchmark instances

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  • Gerald Lach
  • Marco Lübbecke

Abstract

We present an integer programming approach to the university course timetabling problem, in which weekly lectures have to be scheduled and assigned to rooms. Students’ curricula impose restrictions as to which courses may not be scheduled in parallel. Besides some hard constraints (no two courses in the same room at the same time, etc.), there are several soft constraints in practice which give a convenient structure to timetables; these should be met as well as possible. We report on solving benchmark instances from the literature and the 2nd International Timetabling Competition which are based on real data from the university of Udine. The first set is solved to proven optimality; for the second set we give solutions which on average compete well with or beat the previously best known solutions. Our algorithm is not an overall winner, but it is very robust in the sense that it deterministically gives satisfactory lower and upper bounds in reasonable computation time without particular tuning. For slightly larger instances from the literature our approach shows significant potential as it considerably beats previous benchmarks. We further present solutions of proven quality to a few much larger instances with more elaborate hard constraints. Copyright Springer Science+Business Media, LLC 2012

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  • Gerald Lach & Marco Lübbecke, 2012. "Curriculum based course timetabling: new solutions to Udine benchmark instances," Annals of Operations Research, Springer, vol. 194(1), pages 255-272, April.
    • Handle: RePEc:spr:annopr:v:194:y:2012:i:1:p:255-272:10.1007/s10479-010-0700-7
    DOI: 10.1007/s10479-010-0700-7
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    1. Burke, Edmund Kieran & Petrovic, Sanja, 2002. "Recent research directions in automated timetabling," European Journal of Operational Research, Elsevier, vol. 140(2), pages 266-280, July.
    2. 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.
    3. 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.
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    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. Biniyam Asmare Kassa, 2015. "Implementing a Class-Scheduling System at the College of Business and Economics of Bahir Dar University, Ethiopia," Interfaces, INFORMS, vol. 45(3), pages 203-215, June.
    3. Mats Carlsson & Sara Ceschia & Luca Gaspero & Rasmus Ørnstrup Mikkelsen & Andrea Schaerf & Thomas Jacob Riis Stidsen, 2023. "Exact and metaheuristic methods for a real-world examination timetabling problem," Journal of Scheduling, Springer, vol. 26(4), pages 353-367, August.
    4. 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.
    5. Lindahl, Michael & Mason, Andrew J. & Stidsen, Thomas & Sørensen, Matias, 2018. "A strategic view of University timetabling," European Journal of Operational Research, Elsevier, vol. 266(1), pages 35-45.
    6. Britta Herres & Heinz Schmitz, 2021. "Decomposition of university course timetabling," Annals of Operations Research, Springer, vol. 302(2), pages 405-423, July.
    7. Massimiliano Caramia & Stefano Giordani, 2020. "Curriculum-Based Course Timetabling with Student Flow, Soft Constraints, and Smoothing Objectives: an Application to a Real Case Study," SN Operations Research Forum, Springer, vol. 1(2), pages 1-21, June.
    8. Mutsunori Banbara & Katsumi Inoue & Benjamin Kaufmann & Tenda Okimoto & Torsten Schaub & Takehide Soh & Naoyuki Tamura & Philipp Wanko, 2019. "$${\varvec{teaspoon}}$$ teaspoon : solving the curriculum-based course timetabling problems with answer set programming," Annals of Operations Research, Springer, vol. 275(1), pages 3-37, April.
    9. Rasmus Ø. Mikkelsen & Dennis S. Holm, 2022. "A parallelized matheuristic for the International Timetabling Competition 2019," Journal of Scheduling, Springer, vol. 25(4), pages 429-452, August.
    10. Cristian D. Palma & Patrick Bornhardt, 2020. "Considering Section Balance in an Integer Optimization Model for the Curriculum-Based Course Timetabling Problem," Mathematics, MDPI, vol. 8(10), pages 1-12, October.
    11. 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.
    12. Bagger, Niels-Christian F. & Sørensen, Matias & Stidsen, Thomas R., 2019. "Dantzig–Wolfe decomposition of the daily course pattern formulation for curriculum-based course timetabling," European Journal of Operational Research, Elsevier, vol. 272(2), pages 430-446.
    13. 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.
    14. Niels-Christian Fink Bagger & Guy Desaulniers & Jacques Desrosiers, 2019. "Daily course pattern formulation and valid inequalities for the curriculum-based course timetabling problem," Journal of Scheduling, Springer, vol. 22(2), pages 155-172, April.
    15. 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.
    16. Alejandro Cataldo & Juan-Carlos Ferrer & Jaime Miranda & Pablo A. Rey & Antoine Sauré, 2017. "An integer programming approach to curriculum-based examination timetabling," Annals of Operations Research, Springer, vol. 258(2), pages 369-393, November.
    17. Thepphakorn, Thatchai & Pongcharoen, Pupong & Hicks, Chris, 2014. "An ant colony based timetabling tool," International Journal of Production Economics, Elsevier, vol. 149(C), pages 131-144.
    18. Niels-Christian F. Bagger & Simon Kristiansen & Matias Sørensen & Thomas R. Stidsen, 2019. "Flow formulations for curriculum-based course timetabling," Annals of Operations Research, Springer, vol. 280(1), pages 121-150, September.
    19. Marco Lübbecke, 2015. "Comments 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 359-361, July.

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