Skip to main content

Investigations of a constraint logic programming approach to university timetabling

  • Resoning About Constrainsts
  • Conference paper
  • First Online:
Practice and Theory of Automated Timetabling (PATAT 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1153))

Abstract

The casting of university timetables is a problem which combines classical numerical scheduling techniques with important human considerations. It will be argued here that since the application involves the preferences of humans, the problem is qualitatively different than similar problems involving inanimate objects. The humane and profane facets are combined in this study by using the constraint logic programming approach. The constraints are hierarchical: the primary constraints are rigidly enforced and the secondary constraints are relaxed according to their priority if a solution cannot be found. We present a solution based on a Prolog description of the constraints and goals. Two working implementations are described, one using an IBM mainframe and one using a personal computer. Tests with synthetic data and real data from a university have shown that good timetables can be cast using this method in a reasonable amount of time.

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. D. Abramson, “Constructing School Timetables Using Simulated Annealing: Sequential and Parallel Algorithms,” Management Science, vol. 37, no. 1, pp. 98–113, Jan. 1991.

    Google Scholar 

  2. Nagraj Balakrishnan, Abilio Lucena, and Richard T. Wong, “Scheduling Examinations to Reduce Second-Order Conflicts,” Computers Ops. Res., vol. 19, no. 5, pp. 353–361, 1992.

    Google Scholar 

  3. Alan Borning, Bjorn Freeman-Benson, and Molly Wilson, “Constraint Hierarchies,” Lisp and Symbolic Computation, vol. 5, pp. 223–270, 1992.

    Google Scholar 

  4. D. Brelaz, “New Methods to Color the Vertices of a Graph,” Comm. A.C.M., vol. 22, no. 4, pp. 251–256, 1979.

    Google Scholar 

  5. J.E. Brookes, Timetable Planning, Heinemann Educational Books, London, U.K., 1980.

    Google Scholar 

  6. J. Randall Brown, “Chromatic Scheduling and the Chromatic Number Problem,” Management Science, vol. 19, pp. 456–463, 1972.

    Google Scholar 

  7. C. Carmel and M. Itzovitz, “A Comprehensive University Planner Implemented in a 5th Generation Language,” Proceedings of 33rd Annual College and Administrative Comptuer Users Conference, pp. 418–428, Los Angeles, Calif., 1988.

    Google Scholar 

  8. M.W. Carter, “A Survey of Practical Applications of Examination Timetabling Algorithms,” Operations Research, vol. 34, no. 2, pp. 193–202, Mar–Apr. 1986.

    Google Scholar 

  9. Michael W. Carter, “A Lagrangian Relaxation Approach to the Classroom Assignment Problem,” INFOR, vol. 27, no. 2, pp. 230–245, 1989.

    Google Scholar 

  10. M.W. Carter and C.A. Tovey, “When Is the Classroom Assignment Problem Hard?,” Working Paper #89-03, Department of Industrial Engineering, University of Toronto, 1989.

    Google Scholar 

  11. Richard A. Dempsey and Henry P. Traverso, Scheduling the Secondary School, Nat. Assoc. of Secondary School Principals, Reston, Virginia, U.S.A., 1983.

    Google Scholar 

  12. M. Dincbas, H. Simonis, and P. van Hentenryck, “Solving a Cutting-Stock Program in Constraint Logic Programming,” Proc. of Fifth Int. Conf. and Symp. on Logic Programming, vol. 1, The MIT Press, Cambridge, Massachusetts, 1988.

    Google Scholar 

  13. F.D.J. Dunstan, “Sequential Colorings of Graphs,” Proceedings of the 5th British Combined Conference, pp. 151–158, Aberdeen, England, 1975.

    Google Scholar 

  14. Ronen Feldman and Martin Charles Golumbic, “Interactive Scheduling as a Constraint Satisfiability Problem,” Annals of Mathematics and Artificial Intelligence, vol. 1, pp. 49–73, 1990.

    Google Scholar 

  15. J.A. Ferland and S. Roy, “Timetabling Problem for University as Assignment of Activities to Resources,” Computers & Operations Research, vol. 12, no. 2, pp. 207–218, 1985.

    Google Scholar 

  16. A. Hertz, “Tabu Search for large scale timetabling problems,” Eur. J. Op. Res., vol. 54, pp. 39–47, 1991.

    Google Scholar 

  17. Le Kang and George M. White, “A Logic Approach to the Resolution of Constraints in Timetabling,” Eur. J. Op. Res., vol. 61, no. 3, pp. 306–317, 1992.

    Google Scholar 

  18. Vahid Lotfi and Robert Cerveny, “A Final-exam-scheduling Package,” J. Opl. Res. Soc., vol. 42, no. 3, pp. 205–216, 1991.

    Google Scholar 

  19. Michael Lucks, “A Constraint Satisfaction Algorithm for the Automated Decryption of Simple Substitution Ciphers,” Lecture Notes in Computer Science, vol. 403, pp. 132–144, Springer-Verlag, 1990.

    Google Scholar 

  20. Rick Mayoh, “Mission Impossible: Drawing up NHL Schedule,” Ottawa Citizen, Ottawa, Canada, Jan. 15, 1992.

    Google Scholar 

  21. Steven Minton, Mark D. Johnston, Andrew B. Philips, and Philip Laird, “Minimizing Conflicts: A Heuristic Repair Method for Constraint Satisfaction and Scheduling Problems,” Artificial Intelligence, vol. 58, no. 1–3, pp. 161–205, Dec. 1992.

    Google Scholar 

  22. J.M. Mulvey, “A Classroom/Time Assignment Model,” Eur. J. Op. Res., vol. 9, pp. 64–70, 1982.

    Google Scholar 

  23. J.E.L. Peck, R. Osterman, and D. De Werra, “Some Experiments with a Timetabling System,” OR Spektrum, vol. 3, pp. 199–204, 1982.

    Google Scholar 

  24. J. Peemoller, “A Correction to Brelaz's Modification of Brown's Colouring Algorithm,” Comm. A.C.M., vol. 26, pp. 595–597, 1983.

    Google Scholar 

  25. Anthony Saville, Instructional Programming: Issues and Innovations in School Scheduling, Charles E. Merrill Publishing Co., Columbus, Ohio, U.S.A., 1973.

    Google Scholar 

  26. G. Schmidt and T. Stróhlein, “Timetable construction — an annotated bibliography,” Comp. J., vol. 23, no. 4, pp. 307–316, 1980.

    Google Scholar 

  27. S.M. Selim, “An Algorithm for Producing Course and Lecture Timetables,” Comput. Educ., vol. 7, no. 2, pp. 101–108, 1983.

    Google Scholar 

  28. Gardner Swenson, Donald Keys, and J. Lloyd Trump, Providing for Flexibility in Scheduling and Instruction, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1966.

    Google Scholar 

  29. E.M. Timmreck, “Scheduler — A Program that Uses Instructor and Student Preferences to Form Timetables,” Comp. Sci. Tech. Report #3, Univ. of Wisconsin, 1967.

    Google Scholar 

  30. R.G. Veitsch and J.C. Wilson, An Introduction to PROLOG Programming with WPROLOG — Univ. of Waterloo PROLOG Interpreter for VM/SP CMS, WATCOM Products, Inc., Waterloo, Canada, 1986.

    Google Scholar 

  31. Christopher M. White and Kenneth A. Bowen, ALS Prolog User's Guide and Reference Manual.

    Google Scholar 

  32. George M. White and Pak-Wah Chan, “Towards the Construction of Optimal Examination Schedules,” INFOR, vol. 17, no. 3, pp. 219–229, 1979.

    Google Scholar 

  33. George M. White and Michel Haddad, “An Heuristic Method for Optimizing Examination Schedules Which Have Day and Night Courses,” Comput. Educ., vol. 7, no. 4, pp. 235–238, 1983.

    Google Scholar 

  34. George M. White and Simon K.S. Wong, “Interactive Timetabling in Universities,” Comput. Educ., vol. 12, no. 4, pp. 521–529, 1988.

    Google Scholar 

  35. W. Deane Wiley and Lloyd K. Bishop, The Flexibly Scheduled High School, Parker Publishing Co., West Nyack, N.Y., 1968.

    Google Scholar 

  36. Michael Woitass, “Coordination of Intelligent Office Agents — Applied to Meeting Scheduling,” Proc. of the IFIP WG8.4 Conf. on Multi-User Interfaces and Applications, pp. 371–387, Elsevier Science Publishers, Sep. 1990.

    Google Scholar 

  37. Masazumi Yoshikawa, Kazuya Kaneko, Yuriko Nomura, and Masanobu Watanabe, “A Constraint-Based Appeoach to High-School Timetabling Problems: A Case Study,” Proc. Twelfth Nat. Conf. on Artificial Intellegence (AAAI-94), Seattle, WA, Jul. 31–Aug. 4, 1994.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Edmund Burke Peter Ross

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Cheng, C., Kang, L., Leung, N., White, G.M. (1996). Investigations of a constraint logic programming approach to university timetabling. In: Burke, E., Ross, P. (eds) Practice and Theory of Automated Timetabling. PATAT 1995. Lecture Notes in Computer Science, vol 1153. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61794-9_55

Download citation

  • DOI: https://doi.org/10.1007/3-540-61794-9_55

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61794-5

  • Online ISBN: 978-3-540-70682-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics