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Penalising Patterns in Timetables: Novel Integer Programming Formulations

In: Operations Research Proceedings 2007

Author

Listed:
  • Edmund K. Burke

    (The University of Nottingham School of Computer Science and IT)

  • Jakub Mareček

    (The University of Nottingham School of Computer Science and IT)

  • Andrew J. Parkes

    (The University of Nottingham School of Computer Science and IT)

  • Hana Rudová

    (Masaryk University Faculty of Informatics)

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.

Suggested Citation

  • Edmund K. Burke & Jakub Mareček & Andrew J. Parkes & Hana Rudová, 2008. "Penalising Patterns in Timetables: Novel Integer Programming Formulations," Operations Research Proceedings, in: Jörg Kalcsics & Stefan Nickel (ed.), Operations Research Proceedings 2007, pages 409-414, Springer.
    • Handle: RePEc:spr:oprchp:978-3-540-77903-2_63
    DOI: 10.1007/978-3-540-77903-2_63
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    Cited by:

    1. Arnaud Coster & Nysret Musliu & Andrea Schaerf & Johannes Schoisswohl & Kate Smith-Miles, 2022. "Algorithm selection and instance space analysis for curriculum-based course timetabling," Journal of Scheduling, Springer, vol. 25(1), pages 35-58, February.
    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. Dennis S. Holm & Rasmus Ø. Mikkelsen & Matias Sørensen & Thomas J. R. Stidsen, 2022. "A graph-based MIP formulation of the International Timetabling Competition 2019," Journal of Scheduling, Springer, vol. 25(4), pages 405-428, August.

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