Abstract
The school timetabling problem, although less complicated than its counterpart for the university, still provides a ground for interesting and innovative approaches that promise solutions of high quality. In this work, a Shift Assignment Problem is solved first and work shifts are assigned to teachers. In the sequel, the actual Timetabling Problem is solved while the optimal shift assignments that resulted from the previous problem help in defining the values for the cost coefficients in the objective function. Both problems are modelled using Integer Programming and by this combined approach we succeed in modelling all operational and practical rules that the Hellenic secondary educational system imposes. The resulting timetables are conflict free, complete, fully compact and well balanced for the students. They also handle simultaneous, collaborative and parallel teaching as well as blocks of consecutive lectures for certain courses. In addition, they are highly compact for the teachers, satisfy the teachers’ preferences at a high degree, and assign core courses towards the beginning of each day.
Similar content being viewed by others
References
Abramson, D. (1991). Constructing school timetables using simulated annealing: Sequential and parallel algorithms. Management Science, 37, 98–113.
Asratian, A. S., & de Werra, D. (2002). A generalized class-teacher model for some timetabling problem. European Journal of Operational Research, 143, 531–542.
Avella, P., & Vasilev, I. (2005). A computational study of a cutting plane algorithm for university course timetabling. Journal of Scheduling, 8, 497–514.
Birbas, T., Daskalaki, S., & Housos, E. (1997a). Timetabling for Greek High Schools. Journal of Operational Research Society, 48, 1191–1200.
Birbas, T., Daskalaki, S., & Housos, E. (1997b). Course and teacher scheduling in Hellenic High Schools. In Proc. of the 4th Balkan conference on operational research, Thessaloniki, Greece.
Birbas, T., Daskalaki, S., & Housos, E. (1999). Rescheduling process of a school timetable: the case of the Hellenic High Schools & Lyceums. In Proc. of the 5th international conference of the decision sciences institute, Athens, Greece.
Burke, E. K., & Ross, P. (1996). Practice & theory of automated timetabling. Lecture notes in computer science (Vol. 1153). Berlin: Springer.
Burke, E. K., & Carter, M. W. (1998). Practice & theory of automated timetabling II. Lecture notes in computer science (Vol. 1408). Berlin: Springer.
Burke, E. K., & Erben, W. (2001). Practice & theory of automated timetabling III. Lecture notes in computer science (Vol. 2079). Berlin: Springer.
Burke, E. K., & Trick, M. (2005). Practice & theory of automated timetabling V. Lecture notes in computer science (Vol. 3616). Berlin: Springer.
Burke, E. K., & Rudova, H. (2007). Practice & theory of automated timetabling VI. Lecture notes in computer science (Vol. 3867). Berlin: Springer.
Burke, E. K., & Petrovic, S. (2002). Recent research directions in automated timetabling. European Journal of Operational Research, 140(2), 266–280.
Burke, E. K., & De Causmaecker, P. (2003). Practice & theory of automated timetabling IV. Lecture notes in computer science (Vol. 2740). Berlin: Springer.
Burke, E. K., Kendall, G., & Soubiega, A. (2003a). A tabu-search hyper-heuristic for timetabling and rostering. Journal of Heuristics, 9(6), 451–470.
Burke, E. K., de Werra, D., & Kingston, J. (2003b). Applications in timetabling. In J. Yellen & J. Grossman (Eds.), Handbook of graph theory. Boca Raton: Chapman & Hall/CRC.
Burke, E. K., MacCarthy, B., Petrovic, S., & Qu, R. (2003c). Knowledge discovery in a hyper-heuristic using case-based reasoning for course timetabling. In E. K. Burke & P. De Causmaecker (Eds.), Lecture notes in computer science : Vol. 2740. Practice & theory of automated timetabling IV (pp. 276–287). Berlin: Springer.
Burke, E. K., Petrovic, S., & Qu, R. (2006). Case-based heuristic selection for timetabling problems. Journal of Scheduling, 9, 99–113.
Cangalovic, M., & Schreuder, J. A. M. (1991). Exact coloring algorithm for weighted graph applied to timetabling problems with lectures of different length. European Journal of Operational Research, 51(2), 248–258.
Carter, M. W., & Laporte, G. (1996). Recent developments in practical examination timetabling. In E. K. Burke & P. Ross (Eds.), Lecture notes in computer science : Vol. 1153. Practice & theory of automated timetabling (pp. 3–21). Berlin: Springer.
Carter, M. W., & Laporte, G. (1998). Recent developments in practical course timetabling. In E. K. Burke & M. W. Carter (Eds.), Lecture notes in computer science : Vol. 1408. Practice & theory of automated timetabling (pp. 3–19). Berlin: Springer.
Carter, M. W., Laporte, G., & Lee, S. T. (1996). Examination timetabling: algorithmic strategies and applications. Journal of the Operational Research Society, 47, 373–383.
Colorni, A., Dorigo, M., & Maniezzo, V. (1990). Genetic algorithms: a new approach to the timetable problem. NATO ASI series (Vol. F82, pp. 235–239). Berlin: Springer.
Colorni, A., Dorigo, M., & Maniezzo, V. (1998). Metaheuristics for high school timetabling. Computational Optimization and Applications, 9(3), 275–298.
Costa, D. (1994). A tabu search algorithm for computing an operational timetable. European Journal of Operational Research, 76, 98–110.
de Gans, O. B. (1981). A computer timetabling system for secondary schools in the Netherlands. European Journal of Operational Research, 7, 175–182.
de Werra, D. (1985). An introduction to timetabling. European Journal of Operational Research, 19, 151–162.
de Werra, D. (1997). The combinatorics of timetabling. European Journal of Operational Research, 96, 504–513.
de Werra, D., Asratian, A. S., & Durand, S. (2002). Complexity of some special types of timetabling problems. Journal of Scheduling, 5, 171–183.
Daskalaki, S., & Birbas, T. (2005). Efficient solutions for a university timetabling problem through integer programming. European Journal of Operational Research, 160, 106–120.
Daskalaki, S., Birbas, T., & Housos, E. (2004). An integer programming formulation for a case study in university timetabling. European Journal of Operational Research, 153, 117–135.
Deris, S. B., Omatu, S., Ohta, H., & Samat, P. (1997). University timetabling by constraint-based reasoning: a case study. Journal of the Operational Research Society, 48, 1178–1190.
Dimopoulou, M., & Miliotis, P. (2001). Implementation of a university course and examination timetabling system. European Journal of Operational Research, 130, 202–213.
Drexl, A., & Salewski, F. (1997). Distribution requirements and compactness constraints in school timetabling. European Journal of Operational Research, 102, 193–214.
Even, S., Itai, A., & Shamir, A. (1976). On the complexity of timetabling and multicommodity flow problems. SIAM Journal of Computation, 5, 691–703.
Hertz, A. (1992). Find a feasible course schedule using Tabu search. Discrete Applied Mathematics, 35, 255–270.
Junginger, W. (1986). Timetabling in Germany—a survey. Interfaces, 16, 66–74.
Kingston, J. H. (2005). A tiling algorithm for high school timetabling. In E. K. Burke & M. Trick (Eds.), Lecture notes in computer science : Vol. 3616. Practice & theory of automated timetabling V (pp. 208–225). Berlin: Springer.
Lawrie, N. H. (1969). An integer linear programming model of a school timetabling problem. Computer Journal, 12, 307–316.
Learning and Teaching Scotland (2006). www.ltscotland.org.uk/ictineducation/professionaldevelopment/management/timetabling.
Neufeld, G. A., & Tartar, J. (1974). Graph coloring conditions for the existence of solutions to the timetable problem. Communications of the ACM, 17(8), 450–453.
Ostermann, R., & de Werra, D. (1983). Some experiments with a timetabling system. OR Spectrum, 3, 199–204.
Papoutsis, K., Valouxis, C., & Housos, E. (2003). A column generation approach for the timetabling problem of Greek high schools. Journal of Operational Research Society, 54, 230–238.
Petrovic, S., & Burke, E. K. (2004). University timetabling. In J. Y.-T. Leung (Ed.). Handbook of scheduling: algorithms, models and performance analysis. Boca Raton: Chapman & Hall/CRC (Chap. 45).
Schaerf, A. (1999a). A survey of automated timetabling. Artificial Intelligence Review, 13(2), 87–127.
Schaerf, A. (1999b). Local search techniques for large high-school timetabling problems. IEEE Transactions on Systems, Man, and Cybernetics, 29(4), 368–377.
Schimmelpfeng, K., & Helber, S. (2007). Application of a real-world university-course timetabling model solved by integer programming. OR Spectrum, 29(4), 783–803.
ten Eikelder, H. M. M., & Willemen, R. J. (2001). Some complexity aspects of secondary school timetabling problems. In E. K. Burke & W. Erben (Eds.), Lecture notes in computer science : Vol. 2079. Practice & theory of automated timetabling III (pp. 3–17). Berlin: Springer.
Tripathy, A. (1992). Computerized decision aid for timetabling—a case analysis. Discrete Applied Mathematics, 35(3), 313–323.
Valouxis, C., & Housos, E. (2003). Constraint programming approach for school timetabling. Computers & Operations Research, 30(10), 1555–1572.
Yoshikawa, M., Kaneko, K., Yamanouchi, T., & Watanabe, M. (1996). A constraint-based high school scheduling system. IEEE Expert, 11(1), 63–72 (see also IEEE Intelligent Systems and Their Applications).
Author information
Authors and Affiliations
Corresponding author
Additional information
Dr. Birbas is currently the Director for Primary and Secondary Education in the Region of Western Greece.
Rights and permissions
About this article
Cite this article
Birbas, T., Daskalaki, S. & Housos, E. School timetabling for quality student and teacher schedules. J Sched 12, 177–197 (2009). https://doi.org/10.1007/s10951-008-0088-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10951-008-0088-2