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Fairness in academic course timetabling

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Abstract

We consider the problem of creating fair course timetables in the setting of a university. The central idea is that undesirable arrangements in the course timetable, i.e., violations of soft constraints, should be distributed in a fair way among the stakeholders. We propose and discuss in detail two fair versions of the popular curriculum-based course timetabling (CB-CTT) problem, the MMF-CB-CTT problem and the JFI-CB-CTT problem, which are based on max–min fairness (MMF) and Jain’s fairness index (JFI), respectively. For solving the MMF-CB-CTT problem, we present and experimentally evaluate an optimization algorithm based on simulated annealing. We introduce three different energy difference measures and evaluate their impact on the overall algorithm performance. The proposed algorithm improves the fairness on 20 out of 32 standard instances compared to the known best timetables. The JFI-CB-CTT problem formulation focuses on the trade-off between fairness and the aggregated soft constraint violations. Here, our experimental evaluation shows that the known best solutions to 32 CB-CTT standard instances are quite fair with respect to JFI. Our experiments show that the fairness can often be improved at the cost of only a small increase in the overall amount of penalty.

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Notes

  1. Very recently, Antony Philips managed to further improve the total penalty by one for comp21 . This solution matches the known lower bound and is thus optimal, see (Di Gaspero and Schaerf 2012).

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Acknowledgements

We would like to thank the anonymous referees for their constructive comments and valuable remarks on this paper. Research funded in parts by the School of Engineering of the University of Erlangen-Nuremberg.

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  1. Department of Computer Science, University of Erlangen-Nuremberg, Cauerstraß e 11, 90459, Erlangen, Germany

    Moritz Mühlenthaler & Rolf Wanka

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  1. Moritz Mühlenthaler
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Correspondence to Moritz Mühlenthaler.

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This is the extended version of Mühlenthaler and Wanka (2012) presented on PATAT 2012.

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Mühlenthaler, M., Wanka, R. Fairness in academic course timetabling. Ann Oper Res 239, 171–188 (2016). https://doi.org/10.1007/s10479-014-1553-2

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