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When Is the Classroom Assignment Problem Hard?

Author

Listed:
  • Michael W. Carter

    (University of Toronto, Toronto, Ontario, Canada)

  • Craig A. Tovey

    (Georgia Institute of Technology, Atlanta, Georgia)

Abstract

The classroom assignment (or hotel room or interval scheduling) problem is to assign classes, which meet at different time intervals, to rooms. Two classes may not meet simultaneously in the same room, nor may a class meet in two different rooms. Thousands of colleges and secondary schools face this problem every semester. There has been some confusion as to how hard this problem is. Many colleges claim that it is easy, while others complain that it is next to impossible. In the literature, some authors claim or conjecture polynomial time algorithms, while others develop heuristic approaches. The goal of this paper is to resolve the confusion by identifying cases where the problem will be easy and others where it will be hard. We focus on the kinds of cases that schedulers are apt to encounter in practice.

Suggested Citation

  • Michael W. Carter & Craig A. Tovey, 1992. "When Is the Classroom Assignment Problem Hard?," Operations Research, INFORMS, vol. 40(1-supplem), pages 28-39, February.
    • Handle: RePEc:inm:oropre:v:40:y:1992:i:1-supplement-1:p:s28-s39
    DOI: 10.1287/opre.40.1.S28
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    Citations

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    Cited by:

    1. Ciamac C. Moallemi & Utkarsh Patange, 2024. "Hybrid Scheduling with Mixed-Integer Programming at Columbia Business School," Interfaces, INFORMS, vol. 54(3), pages 222-240, May.
    2. Antoon W.J. Kolen & Jan Karel Lenstra & Christos H. Papadimitriou & Frits C.R. Spieksma, 2007. "Interval scheduling: A survey," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(5), pages 530-543, August.
    3. C Beyrouthy & E K Burke & D Landa-Silva & B McCollum & P McMullan & A J Parkes, 2009. "Towards improving the utilization of university teaching space," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(1), pages 130-143, January.
    4. Mausser, Helmut E. & Magazine, Michael J., 1996. "Comparison of neural and heuristic methods for a timetabling problem," European Journal of Operational Research, Elsevier, vol. 93(2), pages 271-287, September.
    5. Craig A. Tovey, 2002. "Tutorial on Computational Complexity," Interfaces, INFORMS, vol. 32(3), pages 30-61, June.
    6. Jeffrey Kingston, 2012. "Resource assignment in high school timetabling," Annals of Operations Research, Springer, vol. 194(1), pages 241-254, April.
    7. Jason J. Sauppe & David R. Morrison & Sheldon H. Jacobson, 2015. "Assigning Panels to Meeting Rooms at the National Science Foundation," Interfaces, INFORMS, vol. 45(6), pages 529-542, December.
    8. Johnes, Jill, 2015. "Operational Research in education," European Journal of Operational Research, Elsevier, vol. 243(3), pages 683-696.
    9. Dienstknecht, Michael & Briskorn, Dirk, 2024. "Sharing in construction projects — On determining optimal container assignments for the on-site accommodation of trades," European Journal of Operational Research, Elsevier, vol. 315(1), pages 324-337.
    10. Clarence H. Martin, 2004. "Ohio University's College of Business Uses Integer Programming to Schedule Classes," Interfaces, INFORMS, vol. 34(6), pages 460-465, December.
    11. Raphael Medeiros Alves & Francisco Cunha & Anand Subramanian & Alisson V. Brito, 2022. "Minimizing energy consumption in a real-life classroom assignment problem," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(4), pages 1149-1175, December.
    12. Nelishia Pillay, 2014. "A survey of school timetabling research," Annals of Operations Research, Springer, vol. 218(1), pages 261-293, July.
    13. Yim, Seho & Hong, Sung-Pil & Park, Myoung-Ju & Chung, Yerim, 2022. "Inverse interval scheduling via reduction on a single machine," European Journal of Operational Research, Elsevier, vol. 303(2), pages 541-549.
    14. Kovalyov, Mikhail Y. & Ng, C.T. & Cheng, T.C. Edwin, 2007. "Fixed interval scheduling: Models, applications, computational complexity and algorithms," European Journal of Operational Research, Elsevier, vol. 178(2), pages 331-342, April.
    15. Oliver Czibula & Hanyu Gu & Aaron Russell & Yakov Zinder, 2017. "A multi-stage IP-based heuristic for class timetabling and trainer rostering," Annals of Operations Research, Springer, vol. 252(2), pages 305-333, May.
    16. Zhang, Xiandong & (Yale) Gong, Yeming & Zhou, Shuyu & de Koster, René & van de Velde, Steef, 2016. "Increasing the revenue of self-storage warehouses by optimizing order scheduling," European Journal of Operational Research, Elsevier, vol. 252(1), pages 69-78.

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