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The University Examination And Course Timetabling Problem With Integer Programming

  • Received : 2019.08.29
  • Accepted : 2019.09.18
  • Published : 2019.09.30

Abstract

In this paper, we study the university timetabling problem, which consists of two subproblems, the university course timetabling problem and the examination timetabling problem. Given a set of classrooms, students, teachers, and lectures, the problem is to assign a number of courses (and examinations) to suitable timeslots and classrooms while satisfying the given set of constraints. We discuss the modeling and solution approaches to construct course and examination timetables for one of the largest Korean university. By using binary integer programming formulations, we describe these two complex real-world problems. Then, we propose a solution method, called NOGOOD, to solve the examination timetabling model. The computation results show that NOGOOD finds the optimal examination schedule for the given instance. Although we consider a specific instance of the university timetabling problem, the methods we use can be applicable to modeling and solving other timetabling problems.

Keywords

References

  1. M.W. Carter, "A Survey of Practical Applications of Examination Timetabling Algorithms," Operations Research, Vol. 34, No. 2, pp.193-202, March-April 1986. https://doi.org/10.1287/opre.34.2.193
  2. A. Schaerf, “A Survey of Automated Timetabling,” Artificial Intelligence Review, Vol. 13, No. 2, pp. 87-127, April 1999. https://doi.org/10.1023/A:1006576209967
  3. H. Babaei, J. Karimpour, and A. Hadidi, "A Survey of Approaches for University Course Timetabling Problem," Computers & Industrial Engineering, Vol. 86, pp. 43-59, August 2015. https://doi.org/10.1016/j.cie.2014.11.010
  4. M. Dimopoulou, and P. Miliotis, “Implementation of a University Course and Examination Timetabling System,” European Journal of Operational Research, Vol. 130, No. 1, pp. 202-213, April 2001. https://doi.org/10.1016/S0377-2217(00)00052-7
  5. M.R. Garey, and D.S. Johnson, "Computers and Intractability - A Guide to the Theory of NP-compleness," Freeman, San Francisco, 1979.
  6. M. Cangalovic, and J.A.M. Schreuder, “Exact Coloring Algorithms for Weighted Graphs Applied to Timetabling Problems with Lectures of Different Lengths,” European Journal of Operational Research, Vol. 51, No. 2, pp. 248-258, March 1991. https://doi.org/10.1016/0377-2217(91)90254-S
  7. D. De Werra, "Some Combinatorial Models for Course Scheduling," Practice and Theory of Automated Timetabling, ser. Springer, Lecture Notes in Computer Science, Vol. 1153, pp. 296-308, 1996. https://doi.org/10.1007/3-540-61794-9_67
  8. D. De Werra, "The Combinatorics of Timetabling", European Journal of Operational Research, Vol. 96, No. 3, pp. 504-513, February 1997. https://doi.org/10.1016/S0377-2217(96)00111-7
  9. S. Daskalaki, and T. Birbas, “Efficient Solutions for University Timetabling Problem through Integer Programming,” European Journal of Operational Research, Vol. 160, No. 1, pp. 106-120, January 2005. https://doi.org/10.1016/j.ejor.2003.06.023
  10. N. Boland, B.D. Hughes, L.T.G. Merlot, and P.J. Stuckey, “New Integer Linear Programming Approaches for Course Timetabling,” Computers and Operations Research, Vol. 35, No. 7, pp. 2209-2233, July 2008. https://doi.org/10.1016/j.cor.2006.10.016
  11. S.A. MirHassani, “A Computational Approach to Enhancing Course Timetabling with Integer Programming,” Applied Mathematics and Computation, Vol. 175, No. 1, pp. 814-822, April 2006. https://doi.org/10.1016/j.amc.2005.07.039
  12. K. Schimmelpfeng, and S. Helber, "Application of a Real-world University Course Timetabling Model Solved by Integer Programming," OR Spectrum, Vol. 29, No.4, pp. 783-803, October 2007. https://doi.org/10.1007/s00291-006-0074-z
  13. S.M. Al-Yakoob, and H.D. Sherali, "Mathematical Models and Algorithms for a High School Timetabling Problem," Computers and Operations Research, Vol. 61, pp. 56-68, September 2015. https://doi.org/10.1016/j.cor.2015.02.011
  14. A. Hertz, “Tabu Search for Large Scale Timetabling Problems,” European Journal of Operational Research, Vol. 54, No. 1, pp. 39-47, September 1991. https://doi.org/10.1016/0377-2217(91)90321-L
  15. J. Aubin, and J.A. Ferland, “A Large Scale Timetabling Problem,” Computers and Operations Research, Vol. 16, No. 1, pp. 67-77, 1989. https://doi.org/10.1016/0305-0548(89)90053-1
  16. A.M. Barham, and J.B. Westwood, “A Simple Heuristic to Facilitate Course Timetabling,” Journal of the Operational Research Society, Vol. 29, No. 11, pp. 1055-1060, November 1978. https://doi.org/10.1057/jors.1978.237
  17. D. Johnson, “Timetabling University Examinations,” Journal of the Operational Research Society, Vol. 41, No. 1, pp. 39-47, January 1990. https://doi.org/10.1057/jors.1990.5
  18. M. Wright, “School Timetabling Using Heuristic Search,” Journal of the Operational Research Society, Vol. 47, No. 3, pp. 347-357, March 1996. https://doi.org/10.1057/jors.1996.34
  19. I.V. Katasaragkis, I.X. Tassopoulos, and G.N. Bleigiannis, "A Comparative Study of Modern Heuristics on The School Timetabling Problem," Algorithms, Vol. 8, No. 3, pp. 723-742, August 2015. https://doi.org/10.3390/a8030723
  20. A.L Bolaji, A.T. Khader, M.A. Al-Betar, and M.A. Awadallah, "University Course Timetabling Using Hybridized Artificial Bee Colony with Hill Climbing Optimizer," Journal of Computational Science, Vol. 5, No. 5, pp. 809-818, September 2014. https://doi.org/10.1016/j.jocs.2014.04.002
  21. B. Naderi, "Modeling and Scheduling University Course Timetabling Problems," International Journal of Research in Industrial Engineering, Vol. 5, No. 1-4 pp. 1-15, Autumn 2016.
  22. E.K. Burke, B. McCollum, A. Meisels, S. Petrovic, and R. Qu, “A Graph-based Hyper-heuristic for Educational Timetabling Problems,” European Journal of Operational Research, Vol. 176, No. 1, pp. 177-192, January 2007. https://doi.org/10.1016/j.ejor.2005.08.012
  23. P. De Causmaecker, P. Demeester, and G.V. Berghe, “A Decomposed Metaheuristic Approach for a Real-world University Timetabling Problem,” European Journal of Operational Research, Vol. 195, No. 1, pp. 307-318, May 2008. https://doi.org/10.1016/j.ejor.2008.01.043
  24. L. Zhang, and S. Lau, "Constructing university timetable using constraint satisfaction programming approach," Proceedings of the International Conference on Computational Intelligence for Modelling, Control and Automation and International Conference on Intelligent Agents, Web Technologies and Internet Commerce, Vienna, Austria, Vol. 2, pp. 55-60, November 2005.
  25. M.W. Carter, and G. Laporte, "Recent Developments in Practical Examination Timetabling," Practice and Theory of Automated Timetabling, ser. Springer, Lecture Notes in Computer Science, Vol. 1153, pp. 1-21, 1996. https://doi.org/10.1007/3-540-61794-9_49
  26. A. Akbulut, and G. Yilmaz, "University Exam Scheduling System Using Graph Coloring Algorithm and RFID Technology", International Journal of Innovation, Management and Technology, Vol. 4, No. 1, pp. 66-72, February 2013.