Skip to main content
SpringerLink
Log in

Curriculum based course timetabling: new solutions to Udine benchmark instances

  • Published:
Annals of Operations Research Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Achterberg, T. (2009). SCIP: solving constraint integer programs. Mathematical Programming Computation, 1, 1–41.

    Article  Google Scholar 

  • Burke, E. K., & Petrovic, S. (2002). Recent research directions in automated timetabling. European Journal of Operational Research, 140(2), 266–280.

    Article  Google Scholar 

  • Burke, E. K., Mareček, J., Parkes, A. J., & Rudová, H. (2007). On a clique-based integer programming formulation of vertex colouring with applications in course timetabling. Technical Report NOTTCS-TR-2007-10, The University of Nottingham. arXiv:0710.3603v2.

  • Burke, E. K., Mareček, J., Parkes, A. J., & Rudová, H. (2008a). A branch-and-cut procedure for the Udine course timetabling problem. In E.K. Burke & M. Gendreau (Eds.), Proceedings of the 7th international conference on the practice and theory of automated timetabling, PATAT 2008, Montréal, CA.

  • Burke, E. K., Mareček, J., Parkes, A. J., & Rudová, H. (2008b). Penalising patterns in timetables: Strengthened integer programming formulations. In J. Kalcsics & S. Nickel (Eds.) Operations research proceedings 2007 (pp. 409–414). Berlin: Springer.

    Chapter  Google Scholar 

  • Burke, E. K., Mareček, J., Parkes, A. J., & Rudová, H. (2008). Uses and abuses of MIP in course timetabling. Poster at the workshop on mixed integer programming, MIP2007, Montréal, 2008. Available online at http://cs.nott.ac.uk/jxm/timetabling/mip2007-poster.pdf.

  • Carter, M. W. (2001). A comprehensive course timetabling and student scheduling system at the University of Waterloo. In E. Burke & W. Erben (Eds.) Lect. Notes Comp. Science : Vol. 2079. Proceedings of the 3th international conference on the practice and theory of automated timetabling, PATAT 2000 (pp. 64–82). Berlin: Springer.

    Google Scholar 

  • Daskalaki, S., & Birbas, T. (2005). Efficient solutions for a university timetabling problem through integer programming. European Journal of Operational Research, 127(1), 106–120.

    Article  Google Scholar 

  • Daskalaki, S., Birbas, T., & Housos, E. (2004). An integer programming formulation for a case study in university timetabling. European Journal of Operational Research, 153, 117–135.

    Article  Google Scholar 

  • De Cesco, F., Di Gaspero, L., & Schaerf, A. (2008). Benchmarking curriculum-based course timetabling: Formulations, data formats, instances, validation, and results. In E.K. Burke & M. Gendreau (Eds.), Proceedings of the 7th international conference on the practice and theory of automated timetabling, PATAT 2008, Montréal, CA.

  • Di Gaspero, L., & Schaerf, A. (2003). Multi neighborhood local search with application to the course timetabling problem. In E. Burke & P. De Causmaecker (Eds.) Lect. Notes Comp. Science : Vol. 2740. Proceedings of the 4th international conference on the practice and theory of automated timetabling, PATAT 2002 (pp. 262–275). Berlin: Springer.

    Chapter  Google Scholar 

  • Di Gaspero, L., & Schaerf, A. (2006). Neighborhood portfolio approach for local search applied to timetabling problems. Journal of Mathematical Modelling and Algorithms, 5, 65–89.

    Article  Google Scholar 

  • Di Gaspero, L., McCollum, B., & Schaerf, A. (2007). The second international timetabling competition (ITC-2007): Curriculum-based course timetabling (track 3). Technical Report QUB/IEEE/Tech/ITC2007/CurriculumCTT/v1.0, Queen’s University, Belfast, United Kingdom, August 2007.

  • Lach, G., & Lübbecke, M. E. (2008). Optimal university course timetables and the partial transversal polytope. In C. C. McGeoch (Ed.) Lect. Notes Comput. Sci. : Vol. 5038. Proceedings of the 7th workshop on experimental algorithms (WEA) (pp. 235–248). Berlin: Springer.

    Google Scholar 

  • Lovász, L., & Plummer, M. D. (1986). Matching theory. Amsterdam: North-Holland.

    Google Scholar 

  • McCollum, B., McMullan, P., Paechter, B., Lewis, R., Schaerf, A., Di Gaspero, L., Parkes, A. J., Qu, R., & Burke, E. (2009, in press). Setting the research agenda in automated timetabling: The second international timetabling competition. INFORMS Journal on Computing.

  • Müller, T. (2008). ITC2007 solver description: A hybrid approach. In Proceedings of the 7th international conference on the practice and theory of automated timetabling, PATAT 2008, Montréal, CA.

  • Qualizza, A., & Serafini, P. (2005). A column generation scheme for faculty timetabling. In E. K. Burke, & M. A. Trick (Eds.) Lect. Notes Comp. Science : Vol. 3616. Proceedings of the 5th international conference on the practice and theory of automated timetabling, PATAT 2004 (pp. 161–173). Berlin: Springer.

    Chapter  Google Scholar 

  • Schaerf, A. (1999). A survey of automated timetabling. Artificial Intelligence Review, 13(2), 87–127.

    Article  Google Scholar 

  • Schimmelpfeng, K., & Helber, S. (2007). Application of a real-world university-course timetabling model solved by integer programming. OR Spectrum, 29, 783–803.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Mathematik, Technische Universität Berlin, MA 7-2, Straße des 17. Juni 136, 10623, Berlin, Germany

    Gerald Lach

  2. Fachbereich Mathematik, AG Optimierung, Technische Universität Darmstadt, Dolivostr. 15, 64293, Darmstadt, Germany

    Marco E. Lübbecke

Authors
  1. Gerald Lach
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Marco E. Lübbecke
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gerald Lach.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lach, G., Lübbecke, M.E. Curriculum based course timetabling: new solutions to Udine benchmark instances. Ann Oper Res 194, 255–272 (2012). https://doi.org/10.1007/s10479-010-0700-7

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-010-0700-7

Keywords

Search

Navigation