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Room usage optimization in timetabling: A case study at Universidade de Lisboa

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  • Lemos, Alexandre
  • Melo, Francisco S.
  • Monteiro, Pedro T.
  • Lynce, Inês

Abstract

This paper discusses the problem of room usage optimization for university timetables: given a timetable, we want to optimize the room occupation by determining the events allocated to each room, while ensuring that the rooms have enough capacity to “seat” all people participating in those events. This paper contributes with two approaches to the problem of optimizing the timetable scheduled for each room. The first approach consists of a two-stage Integer Linear Programming (ILP) which applies a lexicographic optimization wherein the goal of the first stage is to maximize the number of students seated and that of the second stage is to optimize the room occupation. This is provably optimal, in both optimization criteria. However, it is computationally demanding, requiring significant computation time for large problems. To address this issue, we propose a second approach, consisting of a greedy algorithm. The algorithm assigns lectures to rooms greedily, according to a specific cost function that seeks to maximize the number of students seated. We show that the proposed cost function guarantees that the greedy algorithm performs within 63% of the total number of students. We apply both algorithms in a case study involving real data from Instituto Superior Técnico (IST), the engineering school from Universidade de Lisboa. Our results confirm that the greedy algorithm is two orders of magnitude faster than ILP when considering large data sets. Comparing the performance of the two methods we observe that the performance of the greedy algorithm, when compared to the ILP-based approach, is within 2% for the number of seated students and 34% for the room occupation. The GRASP algorithm is a good extension of the greedy algorithm, which is able to improve in 12% the quality of the solution (in terms of compactness) without adding significant CPU time. Overall, the two proposed approaches provide significant gains for both optimization criteria when compared to the current hand-made solutions.

Suggested Citation

  • Lemos, Alexandre & Melo, Francisco S. & Monteiro, Pedro T. & Lynce, Inês, 2019. "Room usage optimization in timetabling: A case study at Universidade de Lisboa," Operations Research Perspectives, Elsevier, vol. 6(C).
    • Handle: RePEc:eee:oprepe:v:6:y:2019:i:c:s2214716018301696
    DOI: 10.1016/j.orp.2018.100092
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    1. Vermuyten, Hendrik & Lemmens, Stef & Marques, Inês & Beliën, Jeroen, 2016. "Developing compact course timetables with optimized student flows," European Journal of Operational Research, Elsevier, vol. 251(2), pages 651-661.
    2. 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.
    3. Haroldo Santos & Eduardo Uchoa & Luiz Ochi & Nelson Maculan, 2012. "Strong bounds with cut and column generation for class-teacher timetabling," Annals of Operations Research, Springer, vol. 194(1), pages 399-412, April.
    4. Lindahl, Michael & Mason, Andrew J. & Stidsen, Thomas & Sørensen, Matias, 2018. "A strategic view of University timetabling," European Journal of Operational Research, Elsevier, vol. 266(1), pages 35-45.
    5. Arnaldo Vieira Moura & Rafael Augusto Scaraficci, 2010. "A GRASP strategy for a more constrained School Timetabling Problem," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 7(2), pages 152-170.
    6. Christos Gogos & Panayiotis Alefragis & Efthymios Housos, 2012. "An improved multi-staged algorithmic process for the solution of the examination timetabling problem," Annals of Operations Research, Springer, vol. 194(1), pages 203-221, April.
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    Cited by:

    1. Alexandre Lemos & Pedro T. Monteiro & Inês Lynce, 2021. "Disruptions in timetables: a case study at Universidade de Lisboa," Journal of Scheduling, Springer, vol. 24(1), pages 35-48, February.
    2. Alexandre Lemos & Pedro T. Monteiro & Inês Lynce, 2022. "Introducing UniCorT: an iterative university course timetabling tool with MaxSAT," Journal of Scheduling, Springer, vol. 25(4), pages 371-390, August.
    3. 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.
    4. Akin Ozkan & Aydin Ulucan & Ceren Dirik & Kazim Baris Atici, 2025. "University course timetabling with multi-section courses, room stability and lecturer preferences: an application in a business school," Computational Management Science, Springer, vol. 22(1), pages 1-22, June.
    5. 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.

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