Abstract
In this paper, we propose an integer-programming relaxation for obtaining lower bounds for the curriculum-based course timetabling problem in which weekly assignments for courses to rooms and periods are considered. The model is a pattern formulation where a pattern is an assignment of a course into a set of periods on one day. Different preprocessing techniques are implemented to reduce the number of variables, and valid inequalities are derived and added to the model. The proposed model is tested on 21 real-world data instances. On 17 of these instances, the best known solutions have been proven optimal, and out of the remaining four, our model improves the lower bounds for three of them.
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Acknowledgements
The authors would like to thank the anonymous reviewers for their valuable feedback to improve the manuscript. Niels-Christian Fink Bagger acknowledges the Innovation Fund Denmark for its financial support. Guy Desaulniers and Jacques Desrosiers acknowledge the Natural Sciences and Engineering Research Council of Canada for its financial support. For the same reason, Jacques Desrosiers also thanks the HEC Montréal Foundation.
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Bagger, NC.F., Desaulniers, G. & Desrosiers, J. Daily course pattern formulation and valid inequalities for the curriculum-based course timetabling problem. J Sched 22, 155–172 (2019). https://doi.org/10.1007/s10951-018-0582-0
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DOI: https://doi.org/10.1007/s10951-018-0582-0