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Considering Section Balance in an Integer Optimization Model for the Curriculum-Based Course Timetabling Problem

Author

Listed:
  • Cristian D. Palma

    (Facultad de Ingeniería, Universidad del Desarrollo, Concepción 4040418, Chile)

  • Patrick Bornhardt

    (Facultad de Ingeniería, Universidad del Desarrollo, Concepción 4040418, Chile)

Abstract

University course timetabling is a complex and time-consuming duty that every educational institution faces regularly. It consists of scheduling a set of lectures in predefined time slots so as to avoid student conflicts, meet teacher and room availability, and manage several institution-specific operational rules. In this paper, we schedule courses based on a curriculum, that is, before the students’ registration. Unlike other curriculum-based models, the proposed model considers two practical aspects when managing the conflicts between lectures: (i) it schedules sections of subjects so that each section is evenly likely to be registered by the students, and (ii) it considers the failure rates and periodicity a subject is taught. We present a multi-objective integer programming model that maximizes the use of specific time slots, the symmetry in which the lectures of a course are scheduled during a week, and the flexibility for straggler students to take courses. The model is solved using commercial software, and it is applied to a real course-timetabling problem. We show the advantages of its use by comparing the model’s solution with the actual solution obtained by the manual scheduling.

Suggested Citation

  • Cristian D. Palma & Patrick Bornhardt, 2020. "Considering Section Balance in an Integer Optimization Model for the Curriculum-Based Course Timetabling Problem," Mathematics, MDPI, vol. 8(10), pages 1-12, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1763-:d:427435
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    References listed on IDEAS

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    1. Jaime Miranda, 2010. "eClasSkeduler: A Course Scheduling System for the Executive Education Unit at the Universidad de Chile," Interfaces, INFORMS, vol. 40(3), pages 196-207, June.
    2. Nelishia Pillay, 2014. "A survey of school timetabling research," Annals of Operations Research, Springer, vol. 218(1), pages 261-293, July.
    3. Andrea Bettinelli & Valentina Cacchiani & Roberto Roberti & Paolo Toth, 2015. "An overview of curriculum-based course timetabling," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 313-349, July.
    4. Dimopoulou, M. & Miliotis, P., 2001. "Implementation of a university course and examination timetabling system," European Journal of Operational Research, Elsevier, vol. 130(1), pages 202-213, April.
    5. Gerald Lach & Marco Lübbecke, 2012. "Curriculum based course timetabling: new solutions to Udine benchmark instances," Annals of Operations Research, Springer, vol. 194(1), pages 255-272, April.
    6. Andrea Bettinelli & Valentina Cacchiani & Roberto Roberti & Paolo Toth, 2015. "Rejoinder on: an overview of curriculum-based course timetabling," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 366-368, July.
    7. Badri, Masood A., 1996. "A two-stage multiobjective scheduling model for [faculty-course-time] assignments," European Journal of Operational Research, Elsevier, vol. 94(1), pages 16-28, October.
    8. van den Broek, John & Hurkens, Cor & Woeginger, Gerhard, 2009. "Timetabling problems at the TU Eindhoven," European Journal of Operational Research, Elsevier, vol. 196(3), pages 877-885, August.
    9. Salem Al-Yakoob & Hanif Sherali & Mona Al-Jazzaf, 2010. "A mixed-integer mathematical modeling approach to exam timetabling," Computational Management Science, Springer, vol. 7(1), pages 19-46, January.
    10. Daskalaki, S. & Birbas, T. & Housos, E., 2004. "An integer programming formulation for a case study in university timetabling," European Journal of Operational Research, Elsevier, vol. 153(1), pages 117-135, February.
    11. Ünal, Yusuf Ziya & Uysal, Özgür, 2014. "A new mixed integer programming model for curriculum balancing: Application to a Turkish university," European Journal of Operational Research, Elsevier, vol. 238(1), pages 339-347.
    12. Alvarez-Valdes, Ramon & Crespo, Enric & Tamarit, Jose M., 2002. "Design and implementation of a course scheduling system using Tabu Search," European Journal of Operational Research, Elsevier, vol. 137(3), pages 512-523, March.
    13. Jan Stallaert, 1997. "Automated Timetabling Improves Course Scheduling at UCLA," Interfaces, INFORMS, vol. 27(4), pages 67-81, August.
    14. Timothy R. Hinkin & Gary M. Thompson, 2002. "SchedulExpert: Scheduling Courses in the Cornell University School of Hotel Administration," Interfaces, INFORMS, vol. 32(6), pages 45-57, December.
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