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Preprocessing and an improved MIP model for examination timetabling

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  • Taha Arbaoui
  • Jean-Paul Boufflet
  • Aziz Moukrim

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. Copyright Springer Science+Business Media New York 2015

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  • Taha Arbaoui & Jean-Paul Boufflet & Aziz Moukrim, 2015. "Preprocessing and an improved MIP model for examination timetabling," Annals of Operations Research, Springer, vol. 229(1), pages 19-40, June.
    • Handle: RePEc:spr:annopr:v:229:y:2015:i:1:p:19-40:10.1007/s10479-015-1832-6
    DOI: 10.1007/s10479-015-1832-6
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    References listed on IDEAS

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    1. Barry McCollum & Paul McMullan & Andrew Parkes & Edmund Burke & Rong Qu, 2012. "A new model for automated examination timetabling," Annals of Operations Research, Springer, vol. 194(1), pages 291-315, April.
    2. Barry McCollum & Andrea Schaerf & Ben Paechter & Paul McMullan & Rhyd Lewis & Andrew J. Parkes & Luca Di Gaspero & Rong Qu & Edmund K. Burke, 2010. "Setting the Research Agenda in Automated Timetabling: The Second International Timetabling Competition," INFORMS Journal on Computing, INFORMS, vol. 22(1), pages 120-130, February.
    3. Abdul Rahman, Syariza & Bargiela, Andrzej & Burke, Edmund K. & Özcan, Ender & McCollum, Barry & McMullan, Paul, 2014. "Adaptive linear combination of heuristic orderings in constructing examination timetables," European Journal of Operational Research, Elsevier, vol. 232(2), pages 287-297.
    4. Turabieh, Hamza & Abdullah, Salwani, 2011. "An integrated hybrid approach to the examination timetabling problem," Omega, Elsevier, vol. 39(6), pages 598-607, December.
    5. E.K. Burke & J.P. Newall, 2004. "Solving Examination Timetabling Problems through Adaption of Heuristic Orderings," Annals of Operations Research, Springer, vol. 129(1), pages 107-134, July.
    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.
    7. Edmund Burke & Jakub Mareček & Andrew Parkes & Hana Rudová, 2012. "A branch-and-cut procedure for the Udine Course Timetabling problem," Annals of Operations Research, Springer, vol. 194(1), pages 71-87, April.
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    Cited by:

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    2. De Boeck, Liesje & Beliën, Jeroen & Creemers, Stefan, 2016. "A column generation approach for solving the examination-timetabling problemAuthor-Name: Woumans, Gert," European Journal of Operational Research, Elsevier, vol. 253(1), pages 178-194.

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