Industrial Engineering and Management Systems

Korean Institute of Industrial Engineers (대한산업공학회)
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An Integer Programming Model for a Complex University Timetabling Problem: A Case Study

  • Prabodanie, R.A. Ranga (Department of Industrial Management, Faculty of Applied Sciences, Wayamba University of Sri Lanka)
  • Received : 2016.05.26
  • Accepted : 2016.11.14
  • Published : 2017.03.30
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Abstract

A binary integer programming model is proposed for a complex timetabling problem in a university faculty which conducts various degree programs. The decision variables are defined with fewer dimensions to economize the model size of large scale problems and to improve modeling efficiency. Binary matrices are used to incorporate the relationships between the courses and students, and the courses and teachers. The model includes generally applicable constraints such as completeness, uniqueness, and consecutiveness; and case specific constraints. The model was coded and solved using Open Solver which is an open-source optimizer available as an Excel add-in. The results indicate that complicated timetabling problems with large numbers of courses and student groups can be formulated more efficiently with fewer numbers of variables and constraints using the proposed modeling framework. The model could effectively generate timetables with a significantly lower number of work hours per week compared to currently used timetables. The model results indicate that the particular timetabling problem is bounded by the student overlaps, and both human and physical resource constraints are insignificant.

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References

  1. Abdullah, S. and Turabieh, H. (2012), On the use of multi neighbourhood structures within a tabu-based memetic approach to university timetabling problems, Inform, Sciences, 191, 146-168.
  2. Agustin-Blas, L. E., Salcedo-Sanz, S., Ortiz-Garcia, E. G., Portilla-Figueras, A., and Perez-Bellido, A. M. (2009), Hybrid grouping genetic algorithm for assigning students to preferred laboratory groups, Expert System Applications, 36(3), 7234-7241. https://doi.org/10.1016/j.eswa.2008.09.020
  3. Akkoyunlu, E. A. (1973), A linear algorithm for computing the optimum university timetable, The Computer Journal, 16(4), 347-350. https://doi.org/10.1093/comjnl/16.4.347
  4. Aladag, A. H., Hocaoglu, G., and Basaran, M. A. (2009), The effect of neighbourhood structures on tabu search algorithm in solving course timetabling problem, Expert System Applications, 36(10), 12349-12356. https://doi.org/10.1016/j.eswa.2009.04.051
  5. Badoni, R. P., Gupta, D. K., and Mishra, P. (2014), A new hybrid algorithm for university course timetabling problem using events based on groupings of students, Computers & Industrial Engineering, 78, 12-25. https://doi.org/10.1016/j.cie.2014.09.020
  6. Bakir, M. A. and Akshop, C. (2008), A 0-1 integer programming approach to a university timetabling problem, Hacettepe Journal of Mathematics and Statistics, 37(1), 41-55.
  7. Basir, N., Ismail. W., and Norwawi, N. (2013), A simulated annealing for Tahmidi course timetabling, Procedia Technology, 11, 437-445. https://doi.org/10.1016/j.protcy.2013.12.213
  8. Bellio, R., Ceschia, S., Gaspero, L. D., Schaerf, A., and Urli, T. (2016), Feature-based tuning of simulated annealing applied to the curriculum-based course timetabling problem, Computers & Operation Research, 65, 83-92. https://doi.org/10.1016/j.cor.2015.07.002
  9. Bolaji, A. L., Khader, A. T., Al-Betar, M. A., and Awadallah, M. A. (2014), University course timetabling using hybridized artificial bee colony with hill climbing optimizer, Journal of Computational Science, 5(5), 809-818. https://doi.org/10.1016/j.jocs.2014.04.002
  10. Boland, N., Hughes, B. D., Merlot, L. T. G., and Stuckey, P. J. (2006), New integer linear programming approaches for course timetabling, Computers & Operation Research 35(7), 2209-2233. https://doi.org/10.1016/j.cor.2006.10.016
  11. Broek, J. V. D., Hurkens, C., and Woeginger, G. (2009), Timetabling problems at the TU Eindhoven, European Journal of Operational Research, 196(3), 877-885. https://doi.org/10.1016/j.ejor.2008.04.038
  12. Burke, E. K., Elliman, D. G., and Weare, R. F. (1994), A university timetabling system based on Graph colouring and constraint manipulation, Journal of Research on Computing in Education, 27, 1-18. https://doi.org/10.1080/08886504.1994.10782112
  13. Cacchiani, V., Caprara, A., Roberti, R., and Toth, P. (2013), A new lower bound for curriculum-based course timetabling, Computers & Operation Research, 40(10), 2466-2477. https://doi.org/10.1016/j.cor.2013.02.010
  14. Cangalovic, M. and Schreuder, J. A. M. (1991), Exact coloring algorithms for weighted graphs applied to timetabling problems with lectures of different lengths, European Journal of Operational Research, 51(2), 248-258. https://doi.org/10.1016/0377-2217(91)90254-S
  15. Ceschia, S., Gaspero, L. D., and Schaerf, A. (2012), Design, engineering, and experimental analysis of a simulated annealing approach to the post-enrolment course timetabling problem, Computers & Operation Research, 39(7), 1615-1624. https://doi.org/10.1016/j.cor.2011.09.014
  16. Daskalaki, S., Birbas, T., and Housos, E. (2004), An IP formulation for a case study in university timetabling, European Journal of Operational Research, 153(1), 117-135. https://doi.org/10.1016/S0377-2217(03)00103-6
  17. Deris, S. B., Omatu, S., Ohta, H., and Samat, P. A. B. D. (1997), University timetabling by Constraint based reasoning: A case study, Journal of the Operational Research Society, 48(12), 1178-1190. https://doi.org/10.1057/palgrave.jors.2600469
  18. Dimopoulou, M. and Miliotis, P. (2001), Implementation of a university course and examination timetabling system, European Journal of Operational Research, 130(1), 202-213. https://doi.org/10.1016/S0377-2217(00)00052-7
  19. Domenech, B. and Lusa, A. (2015), A MILP model for the teacher assignment problem considering teachers' preferences, European Journal of Operational Research, 249(3), 1153-1160. https://doi.org/10.1016/j.ejor.2015.08.057
  20. Hochbaum, D. S. (1997), Approximation algorithms for NP-hard problems. PWS Publishing Company, Boston, MA.
  21. Ismayilova, A. A., Sagir, M., and Gasimov, R. N. (2007), A multiobjective faculty-course-time slot assignment problem with preferences, Mathematical and Computer Modelling, 46(7-8), 1017-1029. https://doi.org/10.1016/j.mcm.2007.03.012
  22. Lawrie, N. L. (1969), An integer linear programming model of a school timetabling problem, The Computer Journal, 12, 307-316. https://doi.org/10.1093/comjnl/12.4.307
  23. Lu, Z. and Hao, J. K. (2010), Adaptive tabu search for course timetabling, European Journal of Operational Research, 200(1), 235-244. https://doi.org/10.1016/j.ejor.2008.12.007
  24. Mahiba, A. A. and Durai, C. A. D. (2012), Genetic Algorithm with Search Bank Strategies for University Course Timetabling Problem, Procedia Engineering, 38, 253-263. https://doi.org/10.1016/j.proeng.2012.06.033
  25. Martin, C. H. (2004), Ohio University's college of business uses integer programming to schedule classes, Interfaces, 34, 460-465. https://doi.org/10.1287/inte.1040.0106
  26. Mason, A. J. (2011), OpenSolver -An open source add-in to solve linear and integer programmes in Excel. In: Klatte D, Luthi HJ, Schmedders K (eds) Operations Research Proceedings, Springer, Berlin Heidelberg, 401-406.
  27. Miranda, J., Rey, P. A., and Robles, J. M. (2012), UdpSkeduler: A web architecture based decision support system for course and classroom scheduling, Decision Support Systems, 52(2), 505-513. https://doi.org/10.1016/j.dss.2011.10.011
  28. Mirrazavi, S. K., Mardle, S. J., and Tamiz, M. (2003), A two-phase multiple objective approach to university timetabling utilizing optimization and evolutionary solution methodologies, Journal of the Operational Research Society, 54(11), 1155-1166. https://doi.org/10.1057/palgrave.jors.2601628
  29. Panagiotis, S., Vigla, E., and Karaboyas, F. (1998), Nearly optimum timetable construction through CLP and intelligent search, International Journal of Artificial Intelligence Tools, 7(4), 415-442. https://doi.org/10.1142/S0218213098000196
  30. Phillips, A. E., Waterer, H., Ehrgott, M., and Ryan, D. M. (2015), Integer programming methods for largescale practical classroom assignment problems, Computers & Operations Research, 53, 42-53. https://doi.org/10.1016/j.cor.2014.07.012
  31. Schimmelpfeng, K. and Helber, S. (2007), Application of a real-world university-course timetabling model solved by integer programming, OR Spectrum, 29(4), 783-803. https://doi.org/10.1007/s00291-006-0074-z
  32. Tripathy, A. (1980), A Lagrangian relaxation approach to course timetabling, Journal of the Operational Research Society, 31(7), 599-603. https://doi.org/10.1057/jors.1980.116
  33. Vermuyten, H., Lemmens, S., Marques, I., and Belien, J. (2015), Developing compact course timetables with optimized student flows, European Journal of Operational Research, 251(2), 651-661. https://doi.org/10.1016/j.ejor.2015.11.028

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