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A graph-based MIP formulation of the International Timetabling Competition 2019

Author

Listed:
  • Dennis S. Holm

    (Technical University of Denmark)

  • Rasmus Ø. Mikkelsen

    (Technical University of Denmark)

  • Matias Sørensen
  • Thomas J. R. Stidsen

    (Technical University of Denmark)

Abstract

The International Timetabling Competition 2019 (ITC 2019) posed a university timetabling problem involving assigning classes to times and rooms for an entire semester while assigning students to required classes. We propose a new mixed integer programming (MIP) formulation of the problem. The MIP formulation takes advantage of different graph structures in conflict graphs to construct a strong formulation of the constraints. In addition, we introduce a reduction algorithm that removes redundancies from the input data. We show that the reduction algorithm, combined with the graph-based MIP formulation, outperforms the MIP formulated by Holm et al. (A MIP formulation of the International Timetabling Competition 2019 problem, 2020) and thus becomes the new state-of-the-art MIP formulation for the ITC 2019. This paper reports the graph-based MIP formulation, which we used during the ITC 2019, and discusses additional approaches that one can use to strengthen the MIP.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jsched:v:25:y:2022:i:4:d:10.1007_s10951-022-00724-y
    DOI: 10.1007/s10951-022-00724-y
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    References listed on IDEAS

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    1. Barry McCollum & Andrea Schaerf & Ben Paechter & Paul McMullan & Rhyd Lewis & Andrew J. Parkes & Luca Di Gaspero & Rong Qu & Edmund K. Burke, 2010. "Setting the Research Agenda in Automated Timetabling: The Second International Timetabling Competition," INFORMS Journal on Computing, INFORMS, vol. 22(1), pages 120-130, February.
    2. 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.
    3. Gerhard Post & Luca Gaspero & Jeffrey H. Kingston & Barry McCollum & Andrea Schaerf, 2016. "The Third International Timetabling Competition," Annals of Operations Research, Springer, vol. 239(1), pages 69-75, April.
    4. Edmund Burke & Jakub Mareček & Andrew Parkes & Hana Rudová, 2010. "A supernodal formulation of vertex colouring with applications in course timetabling," Annals of Operations Research, Springer, vol. 179(1), pages 105-130, September.
    5. 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.
    6. Edmund Burke & Jakub Mareček & Andrew Parkes & Hana Rudová, 2012. "A branch-and-cut procedure for the Udine Course Timetabling problem," Annals of Operations Research, Springer, vol. 194(1), pages 71-87, April.
    7. 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.
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    Cited by:

    1. 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.
    2. 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.

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