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Elective course planning

Author

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  • Kristiansen, Simon
  • Sørensen, Matias
  • Stidsen, Thomas R.

Abstract

Efficient planning increasingly becomes an indispensable tool for management of both companies and public organizations. This is also the case for high school management in Denmark, because the growing individual freedom of the students to choose courses makes planning much more complex. Due to reforms, elective courses are today an important part of the curriculum, and elective courses are a good way to make high school education more attractive for the students. In this article, the problem of planning the elective courses is modeled using integer programming and three different solution approaches are suggested, including a Branch-and-Price framework using partial Dantzig-Wolfe decomposition. Explicit Constraint Branching is used to enhance the solution process, both on the original IP model and in the Branch-and-Price algorithm. To the best of our knowledge, no exact algorithm for the Elective Course Planning Problem has been described in the literature before. The proposed algorithms are tested on data sets from 98 of the 150 high schools in Denmark. The tests show that for the majority of the problems, the optimal solution can be obtained within the one hour time bound. Furthermore the suggested algorithms achieve better results than the currently applied meta-heuristic.

Suggested Citation

  • Kristiansen, Simon & Sørensen, Matias & Stidsen, Thomas R., 2011. "Elective course planning," European Journal of Operational Research, Elsevier, vol. 215(3), pages 713-720, December.
    • Handle: RePEc:eee:ejores:v:215:y:2011:i:3:p:713-720
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    References listed on IDEAS

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    1. de Werra, D., 1985. "An introduction to timetabling," European Journal of Operational Research, Elsevier, vol. 19(2), pages 151-162, February.
    2. François Vanderbeck, 2000. "On Dantzig-Wolfe Decomposition in Integer Programming and ways to Perform Branching in a Branch-and-Price Algorithm," Operations Research, INFORMS, vol. 48(1), pages 111-128, February.
    3. Arabinda Tripathy, 1984. "School Timetabling---A Case in Large Binary Integer Linear Programming," Management Science, INFORMS, vol. 30(12), pages 1473-1489, December.
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    8. Tomáš Müller & Keith Murray, 2010. "Comprehensive approach to student sectioning," Annals of Operations Research, Springer, vol. 181(1), pages 249-269, December.
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    Cited by:

    1. Simon Kristiansen & Thomas R. Stidsen, 2016. "Elective course student sectioning at Danish high schools," Annals of Operations Research, Springer, vol. 239(1), pages 99-117, April.
    2. Aslan, Ayse & Ursavas, Evrim & Romeijnders, Ward, 2023. "A Precedence Constrained Knapsack Problem with Uncertain Item Weights for Personalized Learning Systems," Omega, Elsevier, vol. 115(C).
    3. Aslan, Ayse & Bakir, Ilke & Vis, Iris F.A., 2020. "A dynamic thompson sampling hyper-heuristic framework for learning activity planning in personalized learning," European Journal of Operational Research, Elsevier, vol. 286(2), pages 673-688.

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