Abstract
This paper advocates approaching timetable construction from the algorithms and complexity perspective, in which analysis of the specific problem under study is used to find efficient algorithms for some of its aspects, or to relate it to other problems. Examples are given of problem analyses leading to relaxations, phased approaches, very large-scale neighbourhood searches, bipartite matchings, ejection chains, and connections with standard NP-complete problems. Although a thorough treatment is not possible in a paper of this length, it is hoped that the examples will encourage timetabling researchers to explore further with a view to utilising some of the techniques in their own work.
Similar content being viewed by others
References
Ahuja, R., Ergun, Ö., Orlin, J., & Punnen, A. (2002). A survey of very large-scale neighbourhood search techniques. Discrete Applied Mathematics, 123, 75–102.
Beasley, J. E. (1993). Lagrangean relaxation. In C. R. Reeves (Ed.), Modern heuristic techniques for combinatorial problems. Oxford: Blackwell Sci.
Burke, E. K., & Gendreau, M. (2008). In Proceedings, PATAT 2008, seventh international conference on the practice and theory of automated timetabling, Montreal.
Burke, E. K., Marecek, J. Parkes, A. J., & Rudová, H. (2008). A branch-and-cut procedure for Udine course timetabling. In Proceedings, PATAT 2008, seventh international conference on the practice and theory of automated timetabling, Montreal.
Carter, M. W. (2000). A comprehensive course timetabling and student scheduling system at the University of Waterloo. In Lecture notes in computer science: Vol. 2079. Practice and theory of automated timetabling III, third international conference, selected papers, PATAT 2000, Konstanz, Germany (pp. 64–81). Berlin: Springer.
Csima, J. & Gotlieb, C. C. (1964). Tests on a computer method for constructing school timetables. Communications of the ACM, 7, 160–163.
De Werra, D. (1971). Construction of school timetables by flow methods. INFOR—Canadian Journal of Operations Research and Information Processing, 9, 12–22.
Dowsland, K. A. (1993). Simulated annealing. In C. R. Reeves (Ed.), Modern heuristic techniques for combinatorial problems. Oxford: Blackwell Sci.
Easton, K., Nemhauser, G., & Trick, M. (2003). Solving the travelling tournament problem: a combined integer programming and constraint programming approach. In Lecture notes in computer science: Vol. 2740. Practice and theory of automated timetabling IV, fourth international conference, selected papers, PATAT 2002, Gent, Belgium, August 2002 (pp. 100–109). Berlin: Springer.
Glover, F. (1996). Ejection chains, reference structures and alternating path methods for traveling salesman problems. Discrete Applied Mathematics, 65, 223–253.
Glover, F., & Laguna, M. (1998). Tabu search. Norwell: Kluwer Academic.
Gotlieb, C. C. (1962). The construction of class-teacher timetables. In Proc. IFIP congress, pp. 73–77.
Kingston, J. H. (2008). Resource assignment in high school timetabling. In PATAT 2008, seventh international conference on the practice and theory of automated timetabling, Montreal.
Kirkpatrick, S. Gellat, C. D., & Vecchi, M. P. (1983). Optimization by simulated annealing. Science, 220, 671–680.
Kostuch, P. (2005). The university course timetabling problem with a three-phase approach. In Lecture notes in computer science: Vol. 3616. Practice and theory of automated timetabling V. 5th international conference, PATAT 2004, Pittsburgh, PA (pp. 109–125). Berlin: Springer.
Martin, R. K. (1999). Large scale linear and integer optimization: a unified approach. Norwell: Kluwer Academic.
Meyers, C., & Orlin, J. B. (2007). Very large-scale neighbourhood search techniques in timetabling problems. In Lecture notes in computer science: Vol. 3867. Practice and theory of automated timetabling VI, sixth international conference, PATAT 2006, Brno, Czech Republic (pp. 24–39). Berlin: Springer.
Müller, T., Rudová, H., & Barták, R. (2005). Minimal perturbation problem in course timetabling. In Lecture notes in computer science: Vol. 3616. Practice and theory of automated timetabling V, 5th international conference, PATAT 2004, Pittsburgh, PA (pp. 126–146). Berlin: Springer.
Murray, K., Müller, T., & Rudová, H. (2007). Modeling and solution of a complex university course timetabling problem. In Lecture notes in computer science: Vol. 3867. Practice and theory of automated timetabling VI, sixth international conference, PATAT 2006, Brno, Czech Republic (pp. 189–209). Berlin: Springer.
Papadimitriou, C. H., & Steiglitz, K. (1982). Combinatorial optimization: algorithms and complexity. New York: Prentice Hall.
Ribeiro, C. C., & Urrutia, S. (2004). Heuristics for the mirrored travelling tournament problem. In Proceedings, PATAT 2004, 5th international conference on the practice and theory of automated timetabling, Pittsburgh, PA (pp. 323–341).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kingston, J.H. Timetable construction: the algorithms and complexity perspective. Ann Oper Res 218, 249–259 (2014). https://doi.org/10.1007/s10479-012-1160-z
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10479-012-1160-z