Fairness in academic course timetabling
- 493 Downloads
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.
KeywordsCurriculum-based course timetabling Max–min fairness Fairness index
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.
- Abdullah, S., Burke, E. K., & McCollum, B. (2007). A hybrid evolutionary approach to the university course timetabling problem. In IEEE congress on evolutionary computation (CEC) (pp. 1764–1768). doi: 10.1109/CEC.2007.4424686.
- Asín Acha, R., & Nieuwenhuis, R. (2010). Curriculum-based course timetabling with SAT and MaxSAT. In Proceedings of the 8th international conference on the practice and theory of automated timetabling (PATAT) (pp. 42–56).Google Scholar
- Bertsekas, D. P., & Gallager, R. (1992). Data networks (2nd ed.). Upper Saddle River: Prentice Hall.Google Scholar
- Bullnheimer, B. (1998). An examination scheduling model to maximize students study time. In Proceedings of the 2nd international conference on the practice and theory of automated timetabling (PATAT) (pp. 78–91). doi: 10.1007/BFb0055882.
- Constantino, A. A., de Melo, E. L., Romao, W., & Landa-Silva, D. (2011). A heuristic algorithm for nurse scheduling with balanced preference satisfaction. In Proceedings of the IEEE symposium on computational intelligence in scheduling (CISched) (pp. 39–45). doi: 10.1109/SCIS.2011.5976549.
- Di Gaspero, L., McCollum, B., Schaerf, A. (2007). The second international timetabling competition (ITC-2007): Curriculum-based course timetabling (Track 3). Tech. Rep. QUB/IEEE/Tech/ITC2007/CurriculumCTT/v1.0/1, School of Electronics, Electrical Engineering and Computer Science, Queens University, Belfast (UK).Google Scholar
- Di Gaspero, L., & Schaerf, A. (2008). Hybrid local search techniques for the generalized balanced academic curriculum problem. In Proceedings of the 5th international workshop on hybrid metaheuristics (HM) (pp. 146–157). doi: 10.1007/978-3-540-88439-2_11.
- Di Gaspero, L., & Schaerf, A. (2012). Curriculum-based course timetabling site. http://satt.diegm.uniud.it/ctt/.
- Feldman, A., & Serrano, R. (2006). Welfare economics and social choice theory (2nd ed.). New York, NY: Springer. doi: 10.1007/0-387-29368-X.
- Jain, R. K., Chiu, D. M. W., & Hawe, W. R. (1984). A quantitative measure of fairness and discrimination for resource allocation in shared computer systems. Tech. Rep. DEC-TR-301, Digital Equipment Corporation.Google Scholar
- Kostuch, P. (2004). The university course timetabling problem with a three-phase approach. In Proceedings of the 5th international conference on the practice and theory of automated timetabling (PATAT) (pp. 109–125). doi: 10.1007/11593577_7.
- Lapin, L. (1990). Probability and statistics for modern engineering. Long Grove: Waveland Press.Google Scholar
- McCollum, B., Schaerf, A., Paechter, B., McMullan, P., Lewis, R., Parkes, A. J., Di Gaspero, L., Qu, R., & Burke, E. K. (2010). Setting the research agenda in automated timetabling: The second international timetabling competition. INFORMS Journal on Computing, 22, 120–130. doi: 10.1287/ijoc.1090.0320.CrossRefGoogle Scholar
- Merlot, L. T. G., Boland, N., Hughes, B. D., & Stuckey, P. J. (2002). A hybrid algorithm for the examination timetabling problem. In Proceedings of the 4th international conference on the practice and theory of automated timetabling (PATAT) (pp. 207–231). doi: 10.1007/978-3-540-45157-0_14.
- Mühlenthaler, M., & Wanka, R. (2012). Fairness in academic timetabling. In Proceedings of the 9th international conference on the practice and theory of automated timetabling (PATAT) (pp. 114–130).Google Scholar
- Muklason, A., Parkes, A. J., McCollum, B., & Özcan, E. (2013). Initial results on fairness in examination timetabling. In Proceedings of the 6th multidisciplinary international conference on scheduling: Theory and applications (MISTA) (pp. 777–780).Google Scholar
- Ogryczak, W. (2010). Bicriteria models for fair and efficient resource allocation. In Proceedings of the 2nd international conference on social informatics (SocInfo) (pp. 140–159). doi: 10.1007/978-3-642-16567-2_11.
- Ogryczak, W., & Wierzbicki, A. (2004). On multi-criteria approaches to bandwidth allocation. Control and Cybernetics, 33, 427–448.Google Scholar
- Rawls, J. (1999). A theory of justice, revised edn. Cambridge: Belknap Press of Harvard University Press.Google Scholar
- Smet, P., Martin, S., & Ouelhadj, D., Özcan, E., & Vanden Berghe, G. (2012). Investigation of fairness measures for nurse rostering. In Proceedings of the 9th international conference on the practice and theory of automated timetabling (PATAT) (pp. 369–372).Google Scholar
- Soomer, M. J., & Koole, G. M. (2008). Fairness in the aircraft landing problem. In Proceedings of the Anna Valicek competition 2008.Google Scholar
- Thompson, J., & Dowsland, K. A. (1996). General cooling schedules for a simulated annealing based timetabling system. In Proceedings of the 1st international confernce on the practice and theory of automated timetabling (PATAT) (pp. 345–363). doi: 10.1007/3-540-61794-9_70.
- Tuga, M., Berretta, R., & Mendes, A. (2007). A hybrid simulated annealing with Kempe chain neighborhood for the university timetabling problem. In Proceedings of the 6th ACIS international conference on computer and information science (ACIS-ICIS) (pp. 400–405). doi: 10.1109/ICIS.2007.25.