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Preprocessing and an improved MIP model for examination timetabling

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Abstract

We address the examination timetabling problem proposed in the second International Timetabling Competition (ITC2007). This paper presents new preprocessing stages and an improved mixed integer mathematical model. An exam-based conflict graph in which edges represent incompatibilities between exams is used. The preprocessing stages make use of the graph, together with hard constraints and room capacities, to reveal implicit constraints. Results show that the new preprocessing stages increase up to 106  % the number of conflict constraints an have more than doubled the size of the maximum clique. The improved mixed integer model comprises fewer constraints and is therefore more memory-efficient than the model presented after the competition. We propose valid inequalities based on cliques and a Data-dependent dual-feasible function to enhance our model. We run the tests on the twelve instances presented in the competition and the Yeditepe instances. The problem contains several criteria, which were also tested individually to help end users decide their respective importance. When our model and the original model are compared on the different instances, results show that the improved model yields better results for the majority of the cases and uses less memory.

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Acknowledgments

This work was carried out in the framework of the Labex MS2T, which was funded by the French Government, through the program “Investments for the future” managed by the National Agency for Research (Reference ANR-11-IDEX-0004-02). We would also like to thank the referees for their insightful comments that helped us improve the quality of this paper.

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Authors and Affiliations

  1. Sorbonne universités, Université de Technologie de Compiègne, CNRS, Heudiasyc UMR 7253, CS 60319, 60200, Compiègne cedex, France

    Taha Arbaoui, Jean-Paul Boufflet & Aziz Moukrim

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  1. Taha Arbaoui
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  2. Jean-Paul Boufflet
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  3. Aziz Moukrim
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Correspondence to Taha Arbaoui.

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Arbaoui, T., Boufflet, JP. & Moukrim, A. Preprocessing and an improved MIP model for examination timetabling. Ann Oper Res 229, 19–40 (2015). https://doi.org/10.1007/s10479-015-1832-6

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  • DOI: https://doi.org/10.1007/s10479-015-1832-6

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