Penalising Patterns in Timetables: Novel Integer Programming Formulations

  • Edmund K. Burke
  • Jakub Mareček
  • Andrew J. Parkes
  • Hana Rudová
Part of the Operations Research Proceedings book series (ORP, volume 2007)

Abstract

Many complex timetabling problems have an underpinning bounded graph colouring component, a pattern penalisation component and a number of side constraints. The bounded graph colouring component corresponds to hard constraints such as “students are in at most one place at one time” and “there is a limited number of rooms” [3]. Despite the hardness of graph colouring, it is often easy to generate feasible colourings. However, real-world timetabling systems [5] have to cope with much more challenging requirements, such as “students should not have gaps in their individual daily timetables”, which often make the problem over-constrained. The key to tackling this challenge is a suitable formulation of “soft” constraints, which count and minimise penalties incurred by matches of various patterns. Several integer programming formulations are presented and discussed in this paper.

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References

  1. 1.
    T. Achterberg. Constraint Integer Programming. PhD thesis, Berlin, 2007.Google Scholar
  2. 2.
    P. Avella and I. Vasil’ev. A computational study of a cutting plane algorithm for university course timetabling. J. Scheduling, 8(6):497–514, 2005.CrossRefGoogle Scholar
  3. 3.
    E. K. Burke, D. de Werra, and J. H. Kingston. Applications to timetabling. In Handbook of Graph Theory, pages 445–474. CRC, London, UK, 2004.Google Scholar
  4. 4.
    E. K. Burke, J. Mareček, A. J. Parkes, and H. Rudová. On a clique-based integer programming formulation of vertex colouring with applications in course timetabling. Technical report, 2007. at http://arxiv.org/abs/0710.3603.Google Scholar
  5. 5.
    E. K. Burke and S. Petrovic. Recent research directions in automated timetabling. European J. Oper. Res., 140(2):266–280, 2002.CrossRefGoogle Scholar
  6. 6.
    L. D. Gaspero and A. Schaerf. Multi neighborhood local search with application to the course timetabling problem. In Practice and Theory of Automated Timetabling, PATAT 2002, pages 262–275, Berlin, 2003. Springer.Google Scholar
  7. 7.
    L. D. Gaspero and A. Schaerf. Neighborhood portfolio approach for local search applied to timetabling problems. J. Math. Model. Algorithms, 5(1):65–89, 2006.CrossRefGoogle Scholar
  8. 8.
    T. Koch. Rapid Mathematical Programming. PhD thesis, Berlin, 2004.Google Scholar
  9. 9.
    I. Méndez-Díaz and P. Zabala. A cutting plane algorithm for graph coloring. Discrete App. Math., 2008. In press.Google Scholar
  10. 10.
    H. Rudová and K. Murray. University course timetabling with soft constraints. In Practice and Theory of Automated Timetabling, PATAT 2002, pages 310–328, Berlin, 2003. Springer.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Edmund K. Burke
    • 1
  • Jakub Mareček
    • 1
  • Andrew J. Parkes
    • 1
  • Hana Rudová
    • 2
  1. 1.Automated Scheduling, Optimisation and Planning GroupThe University of Nottingham School of Computer Science and ITNottinghamUK
  2. 2.Masaryk University Faculty of InformaticsBrnoThe Czech Republic

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