Abstract
Overload checking, forbidden regions, edge finding, and not-first/not-last detection are well-known propagation rules to prune the start times of tasks which have to be processed without any interruption and overlapping on an exclusively available resource, i.e. machine. We show that these rules are correct and that “sweeping” over task intervals is an efficient and sufficient technique to achieve maximal pruning with respect to all these propagation rules. All the presented algorithms have quadratic time and linear space complexity with respect to the number of tasks. To our knowledge, this is the first presentation where the correctness of all these rules is proved and where it is shown and proved that the combination of these algorithms achieves the same pruning of the start times achieved by other algorithms with cubic time and quadratic space complexity.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Applegate, D., Cook, W.: A computational study of the job-shop scheduling problem. ORSA Journal on Computing 27(3), 149–156 (1991)
Baptiste, P.: A Theoretical and Experimental Study of Resource Constraint Propagation. PhD thesis, Université de Technologie de Compiègne, UMR CNRS 6599 Heudiasyc (1998)
Baptiste, P., le Pape, C., Nuijten, W.: Constraint-Based Scheduling. International Series in Operations Research & Management Science, vol. 39. Kluwer Academic Publishers, Dordrecht (2001)
Beldiceanu, N., Carlsson, M.: Sweep as a generic pruning technique applied to the non-overlapping rectangles constraint. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 377–391. Springer, Heidelberg (2001)
Beldiceanu, N., Carlsson, M.: A new multi-resource cumulatives constraint with negative heights. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, pp. 63–79. Springer, Heidelberg (2002)
Carlier, J., Pinson, E.: An algorithm for solving the job-shop problem. Management Science (2), 164–176 (1989)
Caseau, Y., Laburthe, F.: Improved CLP scheduling with task intervals. In: van Hentenryck, P. (ed.) Proceedings of the Eleventh International Conference on Logic Programming, ICLP 1994, pp. 369–383. MIT Press, Cambridge (1994)
Thompson, G.L., Fisher, H.: Probabilistic learning combinations of local job-shop scheduling rules. In: Thompson, G.L., Muth, J.F. (eds.) Industrial Scheduling, pp. 225–251. Prentice Hall, Englewood Cliffs (1963)
Balas, E., Adams, J., Zawack, D.: The shifting bottleneck procedure for job shop scheduling. Management Science 34, 391–401 (1988)
Lawrence, S.: Resource constrained project scheduling: an experimental investigation of heuristic scheduling techniques (supplement). Technical report, Graduate School of Industrial Administration, Carnegie-Mellon University, Pittsburgh, Pennsylvania (1984)
Preparata, F.P., Ian Shamos, M.: Computational Geometry, An Introduction. In: Texts and Monographs in Computer Science. Springer, Heidelberg (1985)
Vaccari, R., Storer, R.H., Wu, S.D.: New search spaces for sequencing instances with application to job shop scheduling. Management Science, 1495–1509 (1992)
Yamada, T., Nakano, R.: A genetic algorithm applicable to large-scale job-shop instances. In: Manner, R., Manderick, B. (eds.) Parallel instance solving from nature 2, pp. 281–290. North-Holland, Amsterdam (1992)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wolf, A. (2003). Pruning while Sweeping over Task Intervals. In: Rossi, F. (eds) Principles and Practice of Constraint Programming – CP 2003. CP 2003. Lecture Notes in Computer Science, vol 2833. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45193-8_50
Download citation
DOI: https://doi.org/10.1007/978-3-540-45193-8_50
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20202-8
Online ISBN: 978-3-540-45193-8
eBook Packages: Springer Book Archive