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Recent developments in practical course timetabling

  • Michael W. Carter
  • Gilbert Laporte
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1408)

Abstract

Course timetabling is a multi-dimensional NP-Complete problem that has generated hundreds of papers and thousands of students have attempted to solve it for their own school. In this paper, we describe the major components of the course timetabling problem. We discuss some of the primary types of algorithms that have been applied to these problems. We provide a series of tables listing papers in refereed journals that have either implemented a solution or tested their algorithm on real data. We made no attempt to provide a qualitative comparison. We restricted our presentation to a description of the types of technique used and the size of problem solved We have not included commercial software vendors

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References

  1. 1.
    Abramson, D., “Constructing School Timetables Using Simulated Annealing: Sequential and Parallel Algorithms”, Man. Sci. 37, No. 1, pp. 98–113., 1991.MathSciNetGoogle Scholar
  2. 2.
    Adamidis, P. and Arapakis, P., “Weekly Lecture Timetabling with Genetic Algorithms”, PATAT ’91.Google Scholar
  3. 3.
    Aarts, E. and Lenstra, J.K., Local Search in Combinatorial Optimization, Wiley, Chichester, 1997.MATHGoogle Scholar
  4. 4.
    Aubin, J. and Ferland, J.A., “A Large Scale Timetabling Problem”, Computers & Operations Research 16, No. 1, pp. 67–77, 1989.MATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    Azevedo, F. and Barahona, P., “Timetabling in Constraint Logic Programming”, Proceedings of World Congress on Expert Systems’94.Google Scholar
  6. 6.
    Bloomfield, S.D. and McSharry, M.M., “Preferential Course Scheduling”, Interfaces 9, No. 4, pp. 24–31, August 1979.CrossRefGoogle Scholar
  7. 7.
    Carter, M.W., “A Lagrangian Relaxation Approach to the Classroom Assignment Problem”, INFOR 27, No. 2, pp. 230–246, 1989.MATHGoogle Scholar
  8. 8.
    Carter, M.W. and Tovey, C.A., “When Is the Classroom Assignment Problem Hard?”, Oper. Res. 40, Supp. No. 1, pp. S28–S39, 1992.MATHGoogle Scholar
  9. 9.
    Carter, M.W., Laporte, G. and Lee, S.Y., “Examination Timetabling: Algorithmic Strategies and Applications”, J. of Operational Research Society 47, No. 3, 373–383, March 1996.CrossRefGoogle Scholar
  10. 10.
    Carter, M.W. and Laporte, G., “Recent Developments in Practical Examination Timetabling”, in Practice and Theory of Automated Timetabling, Springer-Verlag Lecture Notes in Computer Science 1153, Burke & Ross, eds., 1996.Google Scholar
  11. 11.
    Chahal, N. and de Werra, D., “An Interactive System for Constructing Timetables on a PC”, EJOR 40, pp. 32–37, 1989.MATHCrossRefGoogle Scholar
  12. 12.
    Chan, H.W., Lau, C.K., and Sheung, J., “Practical School Timetabling: A Hybrid Approach Using Solution Synthesis and Iterative Repair”, in Practice and Theory of Automated Timetabling, Springer-Verlag Lecture Notes in Computer Science, Burke & Carter, eds., 1998.Google Scholar
  13. 13.
    Cheng,C, Kang,L., Leung,N. and White, G.M., “Investigations of a Constraint Logic Programming Approach to University Timetabling”, in Practice and Theory of Automated Timetabling, Springer-Verlag Lecture Notes in Computer Science 1153, Burke & Ross, eds., 1996.Google Scholar
  14. 14.
    Colorni A., Dorigo M. and Maniezzo V., “Genetic Algorithms — A New Approach to the Timetable Problem”, Lecture Notes in Computer Science — NATO ASI Series, Vol. F 82, Combinatorial Optimization, (Akgul et al eds), Springer-Verlag, pp 235–239. 1990. (1992?)Google Scholar
  15. 15.
    Cooper, T.B. and Kingston, J.H., “The Solution of Real Instances of the Timetabling Problem”, The Computer Journal, vol 36, no 7, pp 645–653, 1993.CrossRefGoogle Scholar
  16. 16.
    Corne, D., and Ross, P., “Peckish Initialization Strategies for Evolutionary Timetabling”, in Practice and Theory of Automated Timetabling, Springer-Verlag Lecture Notes in Computer Science 1153, Burke & Ross, eds., 1996.Google Scholar
  17. 17.
    Costa, D., “A Tabu Search Algorithm for Computing an Operational Timetable”, European J. of Operational Res. 76, pp. 98–110, 1994.MATHCrossRefGoogle Scholar
  18. 18.
    Davis, L. and Ritter, L., “Schedule Optimization with Probabilistic Search”, Proceedings of the 3rd IEEE Conference on Artificial Intelligence Applications, Orlando, Florida, USA, pp. 231–236, IEEE, 1987.Google Scholar
  19. 19.
    de Gans, O.B., “A Computer Timetabling System for Secondary Schools in The Netherlands”, EJOR 7, 175–182, 1981.CrossRefGoogle Scholar
  20. 20.
    de Werra, D., “Construction of School Timetables by Flow Methods”, INFOR 9, No.1, 1971, 12–22.MATHGoogle Scholar
  21. 21.
    Dinkel, J.J., Mote, J. and Venkataramanan, M.A., “An Efficient Decision Support System for Academic Course Scheduling”, Operations Research 37, No. 6, pp. 853–864, 1989.Google Scholar
  22. 22.
    Dyer, J.S. and Mulvey, J.M., “Computerized Scheduling and Planning”, New Directions for Institutional Research 13, pp. 67–86, 1977.Google Scholar
  23. 23.
    Elmohamed, S., Coddington, P., and Fox, G., “A Comparison of Annealing Techniques for Academic Course Scheduling”, in Practice and Theory of Automated Timetabling, Springer-Verlag Lecture Notes in Computer Science, Burke & Carter, eds., 1998.Google Scholar
  24. 24.
    Erben,W. and Keppler, J., “A Genetic Algorithm Solving a Weekly Course Timetabling Problem”, in Practice and Theory of Automated Timetabling, Springer-Verlag Lecture Notes in Computer Science 1153, Burke & Ross, eds., 1996.Google Scholar
  25. 25.
    Fahrion, R. and Dollansky, G., “Construction of University Faculty Timetables Using Logic Programming”, Discrete Applied Mathematics 35, No. 3, pp. 221–236, 1992.MATHCrossRefGoogle Scholar
  26. 26.
    Glassey, C.R. and Mizrach, M., “A Decision Support System for Assigning Classes to Rooms”, Interfaces 16, No. 5, pp. 92–100, 1986.Google Scholar
  27. 27.
    Gosselin, K. and Truchon, M., “Allocation of Classrooms by Linear Programming”, J. Operational Research Soc. 37, No. 6, 561–569, 1986.CrossRefGoogle Scholar
  28. 28.
    Graves, R.L., Schrage, L. and Sankaran, J., “An Auction Method for Course Registration”, Interfaces 23, No. 5, pp 81–92, September–October 1993.Google Scholar
  29. 29.
    Gueret,G., Jussien,N., Boizumault,P. and Prins, C., “Building University Timetables Using Constraint Logic Programming”, in Practice and Theory of Automated Timetabling, Springer-Verlag Lecture Notes in Computer Science 1153, Burke & Ross, eds., 1996.Google Scholar
  30. 30.
    Henz,M. and Wurtz,J., “Using Oz for College Timetabling”, in Practice and Theory of Automated Timetabling, Springer-Verlag Lecture Notes in Computer Science 1153, Burke & Ross, eds., 1996.Google Scholar
  31. 31.
    Hertz, A., “Tabu Search for Large Scale Timetabling Problems”, EJOR 54, pp. 39–47, 1991.MATHCrossRefGoogle Scholar
  32. 32.
    Jaffar, J. and Maher, M.J., “Constraint Logic Programming: A Survey”, Journal of Logic Programming 19/20, pp. 503–581, 1994.MathSciNetCrossRefGoogle Scholar
  33. 33.
    Kang, L. and White, G.M., “A Logic Approach to the Resolution of Constraints in Timetabling”, European Journal of Operational Research 61, pp. 306–317, 1992.MATHCrossRefGoogle Scholar
  34. 34.
    Kang, L., Von Schoenberg, G.H. and White, G.M., 1Complete University Timetabling Using Logicl, Computers and Education, 17 No. 2, pp. 145–153, 1991.CrossRefGoogle Scholar
  35. 35.
    Lajos, G., “Complete University Modular Timetabling Using Constraint Logic Programming”, in Practice and Theory of Automated Timetabling, Springer-Verlag Lecture Notes in Computer Science 1153, Burke & Ross, eds., 1996.Google Scholar
  36. 36.
    Laporte, G. and Desroches, S., “The Problem of Assigning Students to Course Sections in a Large Engineering School”, Comp. & Ops. Res. 13, No. 4, pp. 387–394, 1986.CrossRefGoogle Scholar
  37. 37.
    McClure, R.H. and Wells, C.E., “A Mathematical Programming Model for Faculty Course Assignments”, Decision Sciences 15, No. 3, pp. 409–420, 1984.Google Scholar
  38. 38.
    Miyaji, I., Ohno, K. and Mine, H., Solution Method for Partitioning Students into Groupsl, European Journal of Operational Research, 33, No. 1, pp. 82–90. 616, 1981.Google Scholar
  39. 39.
    Nepal, T., Melville, S.W., and Ally, M.I., “A Brute Force and Heuristics Approach to Tertiary Timetabling”, in Practice and Theory of Automated Timetabling, Springer-Verlag Lecture Notes in Computer Science, Burke & Carter, eds., 1998.Google Scholar
  40. 40.
    Ng, W.-Y., “TESS: An Interactive Support System for School Timetabling”, Information Technology in Educational Management for the Schools of the Future, Fung et al (ed.), Chapman and Hall, pp. 131–137, 1997.Google Scholar
  41. 41.
    Osman, I.H. and Laporte, G., “Metaheuristics: A Bibliography. G. Laporte and I.H. Osman (eds), Metaheuristics in Combinatorial Optimization”, Annals of Operations Research 63, pp. 513–623, Baltzer, Amsterdam, 1996.Google Scholar
  42. 42.
    Ostermann, R. and de Werra, D., “Some Experiments with a Timetabling System”, OR Spektrum 3, pp. 199–204, 1982.CrossRefGoogle Scholar
  43. 43.
    Paechter, B., Cumming, A. and Luchian, H., “The Use of Local Search Suggestion Lists for Improving the Solution of Timetable Problems with Evolutionary Algorithms”, In Proceedings of the AISB Workshop on Evolutionary Computing, Sheffield, England, April 3–7, 1995.Google Scholar
  44. 44.
    Papoulias, D.B., “The Assignment-to-days problem in a School Time-table, a Heuristic Approach”, EJOR 4, pp. 31–41, 1980.CrossRefGoogle Scholar
  45. 45.
    Poutain, D., “Constraint Logic Programming”, Byte 20, pp. 159–160, 1995.Google Scholar
  46. 46.
    Ram,V. and Scogings, C., “Automated Time Table Generation Using Multiple Context Reasoning with Truth Maintenance”, in Practice and Theory of Automated Timetabling, Springer-Verlag Lecture Notes in Computer Science 1153, Burke & Ross, eds., 1996.Google Scholar
  47. 47.
    Rankin, R.C., “Automatic Timetabling in Practice”, in Practice and Theory of Automated Timetabling, Springer-Verlag Lecture Notes in Computer Science 1153, Burke & Ross, eds., 1996.Google Scholar
  48. 48.
    Reeves, C.R., 1Modern Heuristic Techniques for Combinatorial Problems 1, Blackwell, Oxford, 1993.Google Scholar
  49. 49.
    Rich, D.C., “A Smart Genetic Algorithm for University Timetabling”, in Practice and Theory of Automated Timetabling, Springer-Verlag Lecture Notes in Computer Science 1153, Burke & Ross, eds., 1996.Google Scholar
  50. 50.
    Ross, P., Corne, D. and Fang, H.-L., “Successful Lecture Timetabling with Evolutionary Algorithms”, Dept of A.I. Working Paper, University of Edinburg, 1994.Google Scholar
  51. 51.
    Sabin, G.C.W. and Winter, G.K., “The Impact of Automated Timetabling on Universities — A Case Study”, J. Operational Research Soc. 37, No.7, pp. 689–693, 1986.CrossRefGoogle Scholar
  52. 52.
    Sampson, S.E., Freeland, J.R. and Weiss, E.N., “Class Scheduling to Maximize Participant Satisfaction”, Interfaces 25, No. 3, pp. 30–41, May–June 1995.Google Scholar
  53. 53.
    Schaerf, A., “Tabu Search Techniques for Large High-School Timetabling Problems”, Comp. Science/Dept. of Interactive Systems, CS-R9611, Centrum voor Wiskunde en Informatica, SMC, Netherlands Organization for Scientific Researchm 1996.Google Scholar
  54. 54.
    Schniederjans, M.J. and Kim, G.C., “A Goal Programming Model to Optimize Departmental Preference in Course Assignments”, Comput. Opns. Res. 14, No. 2, pp. 87–96, 1987.CrossRefGoogle Scholar
  55. 55.
    Selim, S.M., “An Algorithm for Constructing a Unversity Faculty Timetable”, Comput. Educ. 6, No. 4, pp. 323–334., 1982.CrossRefGoogle Scholar
  56. 56.
    White, G.M., and Zhang, J., “Generating Complete University Timetables by Combining Tabu Search with Constraint Logic”, in Practice and Theory of Automated Timetabling, Springer-Verlag Lecture Notes in Computer Science, Burke & Carter, eds., 1998.Google Scholar
  57. 57.
    Wright, M., “School Timetabling using Heuristic Search”, Journal of the Operational Research Society, Vol. 47, pp. 347–357, 1996.CrossRefGoogle Scholar
  58. 58.
    Yoshikawa, M., Kaneko, K., Yamanouchi, T. and Watanabe, N., “A Constraint-Based High School Scheduling System”, IEEE Expert, Vol. 11, No. 1, IEEE Coputer Society, Los Alamitos, CA., pp. 63–72, February 1996.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Michael W. Carter
    • 1
  • Gilbert Laporte
    • 2
  1. 1.Department of Mechanical and Industrial EngineeringUniversity of TorontoToronto
  2. 2.GERAD école des Hautes études Commerciales de MontréalMontréalCanada

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