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The multiphase course timetabling problem

Author

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  • Esmaeilbeigi, Rasul
  • Mak-Hau, Vicky
  • Yearwood, John
  • Nguyen, Vivian

Abstract

This paper introduces the multiphase course timetabling problem and presents mathematical formulations and effective solution algorithms to solve it in a real case study. Consider a pool of lessons and a number of students who are required to take a subset of these lessons to graduate. Each lesson consists of a predetermined and consecutive sequence of phases with possibly different resource requirements and duration. Students who take a lesson must be present in certain phases of the lesson. Similarly, resources that are allocated to the lesson must be present in certain phases of the lesson depending on their roles. The objective is to maximize the weighted sum of student-lesson allocations subject to some capacity, availability and prerequisite constraints. The problem is formulated as an integer linear program called the session-index formulation. The formulation is then extended by introducing various side constraints that capture business requirements of a pilot training program. An enhanced branch-and-check algorithm is proposed to solve the problem more efficiently. Large instances of the problem are solved by utilizing an effective fix-and-optimize matheuristic. Results of a computational study on a set of real-world instances of the problem demonstrate the efficacy of the proposed exact and matheuristic algorithms. Due to the novelty and complexity of the problem, the efficacy of the proposed methodology to solve its real-world instances, and the implementation and realization of these contributions within a decision support system, this work was recognized as a semi-finalist of INFORMS Franz Edelman Award (2021).

Suggested Citation

  • Esmaeilbeigi, Rasul & Mak-Hau, Vicky & Yearwood, John & Nguyen, Vivian, 2022. "The multiphase course timetabling problem," European Journal of Operational Research, Elsevier, vol. 300(3), pages 1098-1119.
    • Handle: RePEc:eee:ejores:v:300:y:2022:i:3:p:1098-1119
    DOI: 10.1016/j.ejor.2021.10.014
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    References listed on IDEAS

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    1. Nelishia Pillay, 2016. "A review of hyper-heuristics for educational timetabling," Annals of Operations Research, Springer, vol. 239(1), pages 3-38, April.
    2. Nelishia Pillay, 2014. "A survey of school timetabling research," Annals of Operations Research, Springer, vol. 218(1), pages 261-293, July.
    3. Burke, Edmund Kieran & Petrovic, Sanja, 2002. "Recent research directions in automated timetabling," European Journal of Operational Research, Elsevier, vol. 140(2), pages 266-280, July.
    4. A.T. Ernst & H. Jiang & M. Krishnamoorthy & B. Owens & D. Sier, 2004. "An Annotated Bibliography of Personnel Scheduling and Rostering," Annals of Operations Research, Springer, vol. 127(1), pages 21-144, March.
    5. Archetti, Claudia & Bianchessi, Nicola & Speranza, M. Grazia, 2014. "Branch-and-cut algorithms for the split delivery vehicle routing problem," European Journal of Operational Research, Elsevier, vol. 238(3), pages 685-698.
    6. Ernst, A. T. & Jiang, H. & Krishnamoorthy, M. & Sier, D., 2004. "Staff scheduling and rostering: A review of applications, methods and models," European Journal of Operational Research, Elsevier, vol. 153(1), pages 3-27, February.
    7. Esmaeilbeigi, Rasul & Charkhgard, Parisa & Charkhgard, Hadi, 2016. "Order acceptance and scheduling problems in two-machine flow shops: New mixed integer programming formulations," European Journal of Operational Research, Elsevier, vol. 251(2), pages 419-431.
    8. Saviniec, Landir & Santos, Maristela O. & Costa, Alysson M. & Santos, Lana M.R. dos, 2020. "Pattern-based models and a cooperative parallel metaheuristic for high school timetabling problems," European Journal of Operational Research, Elsevier, vol. 280(3), pages 1064-1081.
    9. Roshanaei, Vahid & Naderi, Bahman, 2021. "Solving integrated operating room planning and scheduling: Logic-based Benders decomposition versus Branch-Price-and-Cut," European Journal of Operational Research, Elsevier, vol. 293(1), pages 65-78.
    10. Gschwind, Timo & Bianchessi, Nicola & Irnich, Stefan, 2019. "Stabilized branch-price-and-cut for the commodity-constrained split delivery vehicle routing problem," European Journal of Operational Research, Elsevier, vol. 278(1), pages 91-104.
    11. Michael Lindahl & Matias Sørensen & Thomas R. Stidsen, 2018. "A fix-and-optimize matheuristic for university timetabling," Journal of Heuristics, Springer, vol. 24(4), pages 645-665, August.
    12. 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.
    13. 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.
    14. Bagger, Niels-Christian F. & Sørensen, Matias & Stidsen, Thomas R., 2019. "Dantzig–Wolfe decomposition of the daily course pattern formulation for curriculum-based course timetabling," European Journal of Operational Research, Elsevier, vol. 272(2), pages 430-446.
    15. 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.
    16. 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.
    17. Gerardo Gonzalez & Christopher Richards & Alexandra Newman, 2018. "Optimal Course Scheduling for United States Air Force Academy Cadets," Interfaces, INFORMS, vol. 48(3), pages 217-234, June.
    18. Nicola Bianchessi & Michael Drexl & Stefan Irnich, 2019. "The Split Delivery Vehicle Routing Problem with Time Windows and Customer Inconvenience Constraints," Transportation Science, INFORMS, vol. 53(4), pages 1067-1084, March.
    19. Luciano Costa & Claudio Contardo & Guy Desaulniers, 2019. "Exact Branch-Price-and-Cut Algorithms for Vehicle Routing," Transportation Science, INFORMS, vol. 53(4), pages 946-985, July.
    20. Nicola Bianchessi & Stefan Irnich, 2019. "Branch-and-Cut for the Split Delivery Vehicle Routing Problem with Time Windows," Transportation Science, INFORMS, vol. 53(2), pages 442-462, March.
    21. Hanif D. Sherali & J. Cole Smith, 2001. "Improving Discrete Model Representations via Symmetry Considerations," Management Science, INFORMS, vol. 47(10), pages 1396-1407, October.
    22. Fonseca, George H.G. & Santos, Haroldo G. & Carrano, Eduardo G. & Stidsen, Thomas J.R., 2017. "Integer programming techniques for educational timetabling," European Journal of Operational Research, Elsevier, vol. 262(1), pages 28-39.
    23. Rahmaniani, Ragheb & Crainic, Teodor Gabriel & Gendreau, Michel & Rei, Walter, 2017. "The Benders decomposition algorithm: A literature review," European Journal of Operational Research, Elsevier, vol. 259(3), pages 801-817.
    24. Rasul Esmaeilbeigi & Bahman Naderi & Parisa Charkhgard, 2016. "New formulations for the setup assembly line balancing and scheduling problem," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(2), pages 493-518, March.
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