Advertisement

Fairness in Academic Course Timetabling

Chapter
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 678)

Abstract

In this chapter we will focus on models and algorithms for creating fair course timetables. For this purpose we consider the distribution of the timetable quality over the stakeholders. We propose two different problem formulations based on different fairness models: lexicographic max-min fairness and jain’s fairness index. We further propose and evaluate a Simulated Annealing-based algorithm for creating optimized timetables in the first model and investigate the tradeoff between fairness and overall timetable quality using the second model.

Keywords

Assignment Problem Soft Constraint Fairness Index Timetabling Problem Total Penalty 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Bibliography

  1. [BDCDGS12]
    Bonutti, A., De Cesco, F., Di Gaspero, L., Schaerf, A.: Benchmarking curriculum-based course timetabling: formulations, data formats, instances, validation, and results. Ann. Oper. Res. 194(1), 59–70 (2012). doi: 10.1007/s10479-010-0707-0 CrossRefGoogle Scholar
  2. [BDM09]
    Burkard, R.E., Dell’Amico, M., Martello, S.: Assignment Problems. Society for Industrial and Applied Mathematics, Philadelphia (2009)CrossRefGoogle Scholar
  3. [BFT11]
    Bertsimas, D., Farias, V.F., Trichakis, N.: The price of fairness. Oper. Res. 59(1), 17–31 (2011). doi: 10.1287/opre.1100.0865 CrossRefGoogle Scholar
  4. [BR91]
    Burkard, R.E., Rendl, F.: Lexicographic bottleneck problems. Oper. Res. Lett. 10, 303–308 (1991). doi: 10.1016/0167-6377(91)90018-K CrossRefGoogle Scholar
  5. [BSMD08]
    Bandyopadhyay, S., Saha, S., Maulik, U., Deb, K.: A simulated annealing-based multiobjective optimization algorithm: AMOSA. IEEE Trans. Evol. Comput. 12, 269–283 (2008). doi: 10.1109/TEVC.2007.900837 CrossRefGoogle Scholar
  6. [Bul98]
    Bullnheimer, B.: 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 (1998). doi: 10.1007/BFb0055882
  7. [BZ80]
    Burkard, R.E., Zimmermann, U.: Weakly admissible transformations for solving algebraic assignment and transportation problems. Math. Progam. Study 12, 1–18 (1980). doi: 10.1007/BFb0120884 CrossRefGoogle Scholar
  8. [CdMRLS11]
    Constantino, A.A., de Melo, E.L., Romao, W., Landa-Silva, D.: A heuristic algorithm for nurse scheduling with balanced preference satisfaction. In: Proceedings of IEEE Symposium on Computational Intelligence in Scheduling (CISched), pp. 39–45 (2011). doi: 10.1109/SCIS.2011.5976549
  9. [Chi89]
    Chiu, R., Jain, D.-M.: Analysis of the increase and decrease algorithms for congestion avoidance in computer networks. Comput. Netw. ISDN Syst. 17, 1–14 (1989)CrossRefGoogle Scholar
  10. [CM01]
    Castro, C., Manzano, S.: Variable and value ordering when solving balanced academic curriculum problems. In: 6th Workshop of the ERCIM WG on Constraints (2001)Google Scholar
  11. [DCPT99]
    Della Croce, F., Paschos, V.T., Tsoukias, A.: An improved general procedure for lexicographic bottleneck problems. Oper. Res. Lett. 24(4), 187–194 (1999). doi: 10.1016/S0167-6377(99)00013-9 CrossRefGoogle Scholar
  12. [DGMS07]
    Di Gaspero, L., McCollum, B., Schaerf, A.: The second international timetabling competition (ITC-2007): curriculum-based course timetabling (Track 3). In: Proceedings of the 1st International Workshop on Scheduling, a Scheduling Competition (SSC) (2007)Google Scholar
  13. [DGS]
    Di Gaspero, L., Schaerf, A.: Curriculum-based course timetabling web-site. http://satt.diegm.uniud.it/ctt/ (2013). Accessed Sept 2013
  14. [DVY03]
    De Veciana, G., Yang, X.: Fairness, incentives and performance in peer-to-peer networks. Seeds 250(300), 350 (2003)Google Scholar
  15. [EF70]
    Edmonds, J., Fulkerson, D.R.: Bottleneck extrema. J. Combin. Theory 8(3), 299–306 (1970). doi: 10.1016/S0021-9800(70)80083-7 CrossRefGoogle Scholar
  16. [FS06]
    Feldman, A.M., Serrano, R.: Welfare Economics and Social Choice Theory, 2nd edn. Springer, New York (2006). doi: 10.1007/0-387-29368-X Google Scholar
  17. [Gin21]
    Gini, C.: Measurement of inequality of incomes. Econ. J. 31(121), 124–126 (1921). doi: 10.2307/2223319 CrossRefGoogle Scholar
  18. [GKR12]
    Gorski, J., Klamroth, K., Ruzika, S.: Generalized multiple objective bottleneck problems. Oper. Res. Lett. 40(4), 276–281 (2012)CrossRefGoogle Scholar
  19. [GT89]
    Gabow, H.N., Tarjan, R.E.: Faster scaling algorithms for network problems. SIAM J. Comput. 18(5), 1013–1036 (1989). doi: 10.1137/0218069 CrossRefGoogle Scholar
  20. [JCH84]
    Jain, R.K., Chiu, D.-M.W., Hawe, W.R.: A quantitative measure of fairness and discrimination for resource allocation in shared computer systems. Technical Report, DEC-TR-301, Digital Equipment Corporation (1984)Google Scholar
  21. [KAJ94]
    Koulamas, C., Antony, S.R., Jaen, R.: A survey of simulated annealing applications to operations research problems. Omega 22(1), 41–56 (1994). doi: 10.1016/0305-0483(94)90006-X CrossRefGoogle Scholar
  22. [KGV83]
    Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.: Optimization by simulated annealing. Science 220(4598), 671–680 (1983)CrossRefGoogle Scholar
  23. [KK06]
    Kumar, A., Kleinberg, J.M.: Fairness measures for resource allocation. SIAM J. Comput. 36(3), 657–680 (2006). doi: 10.1137/S0097539703434966 CrossRefGoogle Scholar
  24. [KMT98]
    Kelly, F.P., Maulloo, A.K., Tan, D.K.H.: Rate control for communication networks: shadow prices, proportional fairness and stability. J. Oper. Res. Soc. 49(3), 237–252 (1998)CrossRefGoogle Scholar
  25. [Kos05]
    Kostuch, P.: The university course timetabling problem with a three-phase approach. In: Burke, E.K., Trick, M. (eds.) Practice and Theory of Automated Timetabling. Lecture Notes in Computer Science, vol. 3616, pp. 109–125. Springer, Berlin/Heidelberg (2005). doi: 10.1007/11593577_7 CrossRefGoogle Scholar
  26. [KRT01]
    Kleinberg, J.M., Rabani, Y., Tardos, É.: Fairness in routing and load balancing. J. Comput. Syst. Sci. 63(1), 2–20 (2001). doi: 10.1006/jcss.2001.1752 CrossRefGoogle Scholar
  27. [KS60]
    Kapur, J.N., Saxena, H.C.: Mathematical Statistics. S. Chand and Company, New Delhi (1960)Google Scholar
  28. [LA87]
    van Laarhoven, P.J.M., Aarts, E.H.L.: Simulated Annealing: Theory and Applications. Kluwer Academic Publishers, Boston (1987)CrossRefGoogle Scholar
  29. [LC10]
    Lan, T., Chiang, M.: An axiomatic theory of fairness in network resource allocation. www.princeton.edu/~chiangm/fairness.pdf (2010). Extended version of [LKCS10]
  30. [LH10]
    Lü, Z., Hao, J.-K.: Adaptive tabu search for course timetabling. Eur. J. Oper. Res. 200(1), 235–244 (2010). doi: 10.1016/j.ejor.2008.12.007 CrossRefGoogle Scholar
  31. [LKCS10]
    Lan, T., Kao, D., Chiang, M., Sabharwal, A.: An axiomatic theory of fairness in network resource allocation. In: Proceedings of IEEE INFOCOM, pp. 1343–1351 (2010). doi: 10.1109/INFCOM.2010.5461911
  32. [LL10]
    Lach, G., Lübbecke, M.E.: Curriculum based course timetabling: new solutions to Udine benchmark instances. Ann. Oper. Res. 1–18 (2010). doi: 10.1007/s10479-010-0700-7
  33. [LL12]
    Lach, G., Lübbecke, M.E.: Curriculum based course timetabling: new solutions to Udine benchmark instances. Ann. Oper. Res. 194, 255–272 (2012). doi: 10.1007/s10479-010-0700-7 CrossRefGoogle Scholar
  34. [MOS+13]
    Martin, S., Ouelhadj, D., Smet, P., Berghe, G.V., Özcan, E.: Cooperative search for fair nurse rosters. Expert Syst. Appl. 40(16), 6674–6683 (2013). doi: 10.1016/j.eswa.2013.06.019 CrossRefGoogle Scholar
  35. [MPMÖ13]
    Muklason, A., Parkes, A.J., McCollum, B., Özcan, E.: Initial results on fairness in examination timetabling. In: Proceedings of 6th Multidisciplinary International Conference on Scheduling: Theory and Applications (MISTA), pp. 777–780, (2013)Google Scholar
  36. [Ogr10]
    Ogryczak, W.: Bicriteria models for fair and efficient resource allocation. In: Proceedings of 2nd International Conference on Social Informatics (SocInfo), pp. 140–159 (2010). doi: 10.1007/978-3-642-16567-2_11
  37. [Pen07]
    Pentico, D.W.: Assignment problems: a golden anniversary survey. Eur. J. Oper. Res. 176(2), 774–793 (2007). doi: 10.1016/j.ejor.2005.09.014 CrossRefGoogle Scholar
  38. [PS98]
    Papadimitriou, C.H., Steiglitz, K.: Combinatorial Optimization; Algorithms and Complexity. Dover Publications, New York (1998)Google Scholar
  39. [PZ11]
    Punnen, A.P., Zhang, R.: Quadratic bottleneck problems. Nav. Res. Logist. 58(2), 153–164 (2011). doi: 10.1002/nav.20446 CrossRefGoogle Scholar
  40. [Raw99]
    Rawls, J.: A Theory of Justice, revised edition. Belknap Press of Harvard University Press, Cambridge (1999)Google Scholar
  41. [SA98]
    Sokkalingam, P.T., Aneja, Y.P.: Lexicographic bottleneck combinatorial problems. Oper. Res. Lett. 23(1–2), 27–33 (1998). doi: 10.1016/S0167-6377(98)00028-5 CrossRefGoogle Scholar
  42. [SK08]
    Soomer, M.J., Koole, G.M.: Fairness in the aircraft landing problem. In: Proceedings of the Anna Valicek Competition (2008)Google Scholar
  43. [SMO+12]
    Smet, P., Martin, S., Ouelhadj, D., Özcan, E., Berghe, G.V.: 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 (2012)Google Scholar
  44. [TD96]
    Thompson, J.M., Dowsland, K.A.: General cooling schedules for a simulated annealing based timetabling system. In: Proceedings 1st International Conference on the Practice and Theory of Automated Timetabling (PATAT), pp. 345–363 (1996). doi: 10.1007/3-540-61794-9_70
  45. [TD98]
    Thompson, J.M., Dowsland, K.A.: A robust simulated annealing based examination timetabling system. Comput. Oper. Res. 25(7–8), 637–648 (1998). doi: 10.1016/S0305-0548(97)00101-9 CrossRefGoogle Scholar
  46. [UK11]
    Uchida, M., Kurose, J.: An information-theoretic characterization of weighted α-proportional fairness in network resource allocation. Inform. Sci. 181(18), 4009–4023 (2011). doi: 10.1016/j.ins.2011.05.001 CrossRefGoogle Scholar
  47. [Wil45]
    Wilcoxon, F.: Individual comparisons by ranking methods. Biometrics Bull. 1(6), 80–83 (1945). doi: 10.2307/3001968 CrossRefGoogle Scholar
  48. [Yag88]
    Yager, R.R.: On ordered weighted averaging aggregation operators in multicriteria decisionmaking. IEEE Trans. Syst. Man Cybern. 18(1), 183–190 (1988). doi: 10.1109/21.87068 CrossRefGoogle Scholar

Author’s Own Publications

  1. [MW12*]
    Mühlenthaler, M., Wanka, R.: Fairness in academic course timetabling. In: Proceedings of 9th International Conference on the Practice and Theory of Automated Timetabling (PATAT), pp. 114–130 (2012)Google Scholar
  2. [MW13*]
    Mühlenthaler, M., Wanka, R.: A decomposition of the max-min fair curriculum-based course timetabling problem. In: Proceedings of the 6th Multidisciplinary International Conference on Scheduling: Theory and Applications (MISTA), pp. 300–313 (2013)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Dept. of Computer Science 12University of Erlangen-NurembergErlangenGermany

Personalised recommendations