Skip to main content

Mathematical Model for Scheduling Problems: A Compatibility Test on University Course Timetabling Problem

  • Conference paper
  • First Online:
Proceedings of the 8th International Conference on Computational Science and Technology

Abstract

The study presents the application of a general mathematical model previously developed for another set of timetabling problem which is the University Course Timetabling (UCT). The aim of this study is to extend the validation process of the formulated model using a standard Mixed Integer Linear Programming (MILP). A real public university course timetabling problem was used as our case study. All data was gathered and analysed before embedded to the general model and solved optimally using the AIMMS mathematical software with CPLEX as the solver to a personal laptop of 2.20 GHz and 4.95 GB RAM. The data consists of 27 programmes, 449 core courses, 59 rooms and 70 time slots. An optimal standard university course timetable was produced within a few minutes of CPU time. Optimality denotes that the courses were assigned to the preferred slots and rooms, while fulfilling requirements such as the university’s policies, and other demands of all parties involved. With the timetable produced, it is proven of the capability of the mathematical model developed in solving timetabling problems.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 229.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 299.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 299.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Dorneles AP, Araujo OCB, Buriolm LS (2014) A fix-and-optimize heuristic for the high school timetabling problem. Comput Oper Res 52:29–38

    Google Scholar 

  2. Aizam NAH, Sithamparam T, General basic 0-1 integer Programming Model for Timetabling Problems (2016) Special Issue: The 10th IMT-GT International conference on mathematics, statistics and its applications 2014 (ICMSA 2014). Malaysian J Math Sci 10(S):143–154

    Google Scholar 

  3. Aizam NAH, Uvaraja V (2015) Generic model for timetabling problems by integer linear programming approach. Int J Math Comput Phys Electr Comput Eng 9(12):668–675

    Google Scholar 

  4. Aizam NAH, Ismail ZF, Kovindan P (2019) General mathematical model and timetabling problems: expansion and application to real-time timetabling. In: Proceedings of the international conference on mathematical sciences and technology (MATHTECH2018): Innovative technologies for mathematics & mathematics for technological innovation, 2184,040010

    Google Scholar 

  5. Aizam NAH, Leong SPS (2016) Integrating mathematical model and scheduling problem. In: International conference on mathematics, engineering and industrial application 2016 (ICoMEIA2016). Proceeding of the 2nd international conference on mathematics, engineering and industrial applications 2016, vol 1775(1), p 030065

    Google Scholar 

  6. Aizam NAH, Leong SPS (2016) Extended basic integer programming models for multiple scheduling problems, vol 1750, p 030038. https://doi.org/10.1063/1.4954574

  7. Asmuni H (2008) Fuzzy methodologies for automated university timetabling solution construction and evaluation, Ph.D. Thesis. School of Computer Science University of Nottingham

    Google Scholar 

  8. Aziz NLA, Aizam NAH (2017, August) University course timetabling and the requirements: Survey in several universities in the east-coast of Malaysia. In: AIP conference proceeding, vol 1870(1), p 040013. AIP Publishing LLC

    Google Scholar 

  9. Aizam NAH, Caccetta L (2014) Computational models for timetabling problem. Numer Algebra Control Optim 4(3):269–285

    Article  MathSciNet  Google Scholar 

  10. Demeester P, Bilgin B, De Causmaecker P, Vanden Berghe G (2012) A hyperheuristic approach to examination timetabling problems: benchmarks and a new problem from practice. J Sched 15(1):83–103

    Google Scholar 

  11. Woumans G, Boeck LD, Beliën J, Creemers S (2016) A column generation approach for solving the examination-timetabling problem. Eur J Oper Res 253(1):178–194

    Article  MathSciNet  Google Scholar 

  12. Razak HA, Ibrahim Z, Hussin NM (2010, March) Bipartite graph edge coloring approach to course timetabling. In: 2010 International conference on information retrieval & knowledge management (CAMP). IEEE, pp 229–234

    Google Scholar 

  13. Tavakoli MM, Shirouyehzad H, Lotfi FH, Najafi SE (2020) Proposing a novel heuristic algorithm for university course timetabling problem with the quality of courses rendered approach: a case study. Alex Eng J

    Google Scholar 

  14. Yousef AH, Salama C, Jad MY, El-Gafy T, Matar M, Habashi SS (2016) A GPU based genetic algorithm solution for the timetabling problem. In: 2016 11th International conference on computer engineering & systems (ICCES). IEEE, pp 103–109

    Google Scholar 

  15. Matijaš VD, Molnar G, Čupić M, Jakobović D, Bašić BD (2010) University course timetabling using ACO: a case study on laboratory exercises. Knowledge based and intelligent information and engineering systems lecture notes in computer science, pp 100–110

    Google Scholar 

  16. Phillips AE, Walker CG, Ehrgott M, Ryan DM (2017) Integer programming for minimal perturbation problems in university course timetabling. Ann Oper Res 252(2):283–304

    Article  MathSciNet  Google Scholar 

  17. Aschinger M, Applebee S, Bucur A, Edmonds H, Hungerländer P, Maier K (2017) New constraints and features for the university course timetabling problem. In: Operations Research proceedings 2016 operations research proceedings, pp 95–101

    Google Scholar 

  18. Sánchez-Partida D, Martínez-Flores JL, Olivares-Benítez E (2014) An integer linear programming model for a university timetabling problem considering time windows and consecutive periods. J Appl Oper Res 6(3):158–173

    Google Scholar 

  19. Norgren E, Jonasson J (2016) Investigating a genetic algorithm-simulated annealing hybrid applied to university course timetabling problem: a comparative study between simulated annealing initialized with genetic algorithm. Genetic algorithm and simulated annealing (2016) [15 Oct 2018]. http://kth.diva-portal.org/smash/get/diva2:927039/FULLTEXT01.pdf

  20. Fonseca GH, Santos HG, Carrano EG, Stidsen TJ (2016) Modelling and solving university course timetabling problems through XHSTT. In: Patat’16 proceedings of the 11th International conference on the practice and theory of automated timetabling, pp 127–138

    Google Scholar 

  21. Aizam NAH, Abdul Aziz NL, Zaulir ZM (2019) New general university course timetabling model towards real problems: a comparison. J Adv Res Dyn Control Syst 11(12):244–257

    Google Scholar 

  22. MirHassani SA (2006) A computational approach to enhancing course timetabling with integer programming. Appl Math Comput 175(1):814–822

    MathSciNet  MATH  Google Scholar 

  23. Mushi AR, Chacha S (2013) Optimal solution strategy for university course timetabling problem. Int J Adv Res Comp Sci 4(2):35–40

    Google Scholar 

  24. Shiau D (2011) A hybrid particle swarm optimization for a university course scheduling problem with flexible preferences. Expert Syst Appl 38(1):235–248

    Article  Google Scholar 

  25. Abdelhalim EA, Khayat GA (2016) A Utilization-based genetic algorithm for solving the university timetabling problem (UGA). Alex Eng J 55(2):1395–1409

    Article  Google Scholar 

  26. Song T, Liu S, Tang X, Peng X, Chen M (2018) An iterated local search algorithm for the university course timetabling problem. Appl Soft Comput 68:597–608

    Article  Google Scholar 

  27. Kallrath J (ed) (2013) Modelling languages in mathematical optimization, vol 88

    Google Scholar 

  28. Bisschop JJ, Roelofs M (2006) AIMMS-User’s Guide.Lulu.com. http://download.aimms.com/aimms/download/manuals/AIMMS3OM_Background.pdf. 10 Sept 2017

Download references

Acknowledgements

This research was funded by the Ministry of Higher Education, under the Research Acculturation Grant Scheme, [RAGS/1/2014/SG04/UMT//3]. We would also like to express our sincere gratitude to the Academic Management Department of the selected public university for provisioning the expertise and data to carry out this study. Without their contribution, this study will not be promising enough to be applicable on real-life scheduling problems.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Nur Aidya Hanum Aizam .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Aizam, N.A.H., Ismail, Z.F., Yen, C.L.S. (2022). Mathematical Model for Scheduling Problems: A Compatibility Test on University Course Timetabling Problem. In: Alfred, R., Lim, Y. (eds) Proceedings of the 8th International Conference on Computational Science and Technology. Lecture Notes in Electrical Engineering, vol 835. Springer, Singapore. https://doi.org/10.1007/978-981-16-8515-6_10

Download citation

Publish with us

Policies and ethics