Three methods used to solve an examination timetable problem

  • Jean Paul Boufflet
  • Stéphane Nègre
Tabu Search and Simulated Annealing
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1153)


This paper describes the problem of examination timetables at the University of Technology of Compiègne and the solutions we devised. The problem we faced was drawing up a week-long the examination timetable, taking into account a number of different constraints. These constraints are administrative, physical and related to preferences. Three tools were developed to solve this practical problem. The first tool is an exact method based on a tree search, the second is based on the tabu technique, and the third is an interactive computer aided design system. The most effective is the tree search method, but the tabu search technique may be a convenient alternative for several reasons. The computer aided design system can be used if all the automatic techniques fail. In the first part of this paper we describe the problem. In the second part we present a model using a reduction of the problem and relaxed constraints. Next, the three methods are described, and we briefly present the related problem of the assignment of invigilators. The results we present in the fourth part show that there exists no solution which takes into account all the constraints. We have solved the related problem of invigilator assignment using the well known out-of-kilter method. Computational results are presented.


graph colouring techniques tabu search implementation interactive vs. batch timetabling 


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  1. [AUS 76]
    AUST, RJ.; An Improvement Algorithm for School Timetabling. Computer J. Vol. 19, N∘ 4 pages 339–343, 1976.Google Scholar
  2. [BOU 92a]
    BOUFFLET, J. P.; Mémoire de doctorat “Emplois du temps dans un environnement fortement contraint: exemple de l'U.T.C”. Thèse de Doctorat en Contrôle des Systèmes de l'Université de Technologie de Compiègne, Génie Informatique, 20 février 1992.Google Scholar
  3. [BOU 92b]
    BOUFFLET, J. P. et TRIGANO, P.; “CELAME: Un Outil d'Aide à la Conception des Emplois du Temps de L'Université de Technologie de Compiègne”. ERGO IA'92, Ergonomie et Informatique Avancée, Biarritz France, 1992.Google Scholar
  4. [BRE 79]
    BRELAZ, D.; New Methods to Color the Vertices of a Graph. Communication of the ACM, Vol. 22, N∘4, pp 251–256, April 1979.Google Scholar
  5. [CAN 89]
    CANGALOVIC, M. and SCHREUDER, A. M.; Exact Colouring Algorithm for Weighted Graphs applied to Timetabling Problems with Lectures of different lengths. European Journal of Operational Research, Vol. 51, pp 248–258, 1991.Google Scholar
  6. [CAR 86]
    CARTER, M. W.; A Survey of Practical Applications of Examination Timetabling Algorithms. Operations research vol 34, N∘2, pages 193–202, 1986.Google Scholar
  7. [EDM 72]
    EDMONDS, J. and KARP, R. M.; “Theoretical improvements in algorithmic efficiency for network flow problems”; Journal of the ACM Vol 19, N∘2 pp 248–264.Google Scholar
  8. [FER 83]
    FERLAND,J et Roy, S et TRAN GIA LOC; Quadratic Assignment Models for Examination Timetabling and Game Scheduling; Publication N∘ 485, Université de Montréal, 1983.Google Scholar
  9. [FER 85]
    FERLAND,J et Roy, S et TRAN GIA LOC; The Timetabling Problem. Publication N∘ 531, Université de Montréal, 1985.Google Scholar
  10. [GLO 88]
    GLOVER, F.; TABU Search. CAAI Report 88-3, University of Colorado, Boulder, 1988.Google Scholar
  11. [GLO 90]
    GLOVER, F.; TABU Search: a Tutorial. Interface, Vol. 20, pp 74–94, 1990.Google Scholar
  12. [HER 87]
    HERTZ, A. and DE WERRA, D.; Using Tabu Search Techniques For Graph Colouring. Computing Vol. 39, pp 345–351, 1987.Google Scholar
  13. [HER 89]
    HERTZ, A.; Coloration des Sommets d'un Graphe et son Application à la Confection d'Horaire. Thèse N∘ 785, Ecole Polytechnique Fédérale de Lausanne, 1989.Google Scholar
  14. [NEG 93]
    NEGRE, S.; Algorithmes de Coloration de Graphe: Application à la Conception des Emplois du Temps de la Semaine d'Examen de l'Université de Technologie de Compiègne. Rapport de DEA de Contrôle des Systèmes, URA 817 Heudiasyc, Université de Technologie de Compiègne, 1993.Google Scholar
  15. [SCH 80]
    SCHMIDT, G. and STRÖHLEIN, T.; Timetable Construction an annoted Bibliography. Comput J Vol. 23, N∘ 4, pages 307–316, 1980.Google Scholar
  16. [TRI 84]
    TRIPATHY, A.; School Timetabling-A case in large binary integer linear programming. Management science Vol. 30, pages 1473–1489, 1984.Google Scholar
  17. [VDV 92]
    VI CAO, N. and Du MERLE, O. and VIAL, J. P.; Un Système de Confection Automatisée d'Horaires d'Examens; Revue des Sytème de Décision, Vol. 1, N∘4, pp 377–399, Editions Hermes, 1992.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Jean Paul Boufflet
    • 1
  • Stéphane Nègre
    • 1
  1. 1.Dpt Génie InformatiqueURA CNRS 817 Heudiasyc Université de Technologie de Compiègne (UTC)Compiegne CédexFrance

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