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)


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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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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