Abstract
The Open-Shop Problem is a hard problem that can be solved using Constraint Programming or Operation Research methods. Existing techniques are efficient at reducing the search tree but they usually do not consider the absolute ordering of the tasks. In this work, we develop a new propagator for the One-Machine Non-Preemptive Problem, the basic constraint for the Open-Shop Problem. This propagator takes this additional information into account allowing, in most cases, a reduction of the search tree. The underlying principle is to use shaving on the positions. Our propagator applies on one machine or one job and its time complexity is in \(\mathcal{O}(N^2 \log N)\), where N is either the number of jobs or machines. Experiments on the Open-Shop Problem show that the propagator adds pruning to state-of-the-art constraint satisfaction techniques to solve this problem.
This is a preview of subscription content, log in via an institution to check access.
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
Carlier, J., Pinson, E.: An algorithm for solving the job-shop problem. Management Science 35(2), 164–176 (1989)
Applegate, D., Cook, B.: A computational study of the job shop scheduling problem. ORSA J. Comput. 3(2), 149–156 (1991)
Carlier, J., Pinson, E.: Adjustment of heads and tails for the job-shop problem. European J. Oper. Res. 78, 146–161 (1994)
Caseau, Y., Laburthe, F.: Improved CLP scheduling with task intervals. In: Proc. 11th Intl. Conf. on Logic Programming (1994)
Carlier, J., Pinson, E.: A practical use of Jackson’s preemptive schedule for solving the job-shop problem. Ann. Oper. Res. 26, 269–287 (1990)
Dorndorf, U., Pesch, E., Phan-Huy, T.: Solving the open shop scheduling problem. J. Scheduling 4, 157–174 (2001)
Vilim, P.: \(\mathcal{O}(n \log n)\) filtering algorithms for unary resource constraint. In: Régin, J.-C., Rueher, M. (eds.) CPAIOR 2004. LNCS, vol. 3011, pp. 335–347. Springer, Heidelberg (2004)
Martin, P., Shmoys, D.: A new approach to computing optimal schedules for the job-shop scheduling problem. In: Cunningham, W.H., Queyranne, M., McCormick, S.T. (eds.) IPCO 1996. LNCS, vol. 1084, Springer, Heidelberg (1996)
Zhou, J.: A permutation-based approach for solving the job-shop problem. Constraints 2, 185–213 (1997)
Nuijten, W., Le Pape, C.: Constraint-based job shop scheduling with ILOG Scheduler. J. Heuristics 3, 271–286 (1998)
Wolf, A.: Better propagation for non-preemptive single-resource constraint problems. In: Faltings, B.V., Petcu, A., Fages, F., Rossi, F. (eds.) CSCLP 2004. LNCS (LNAI), vol. 3419, pp. 201–215. Springer, Heidelberg (2005)
Guéret, C., Prins, C.: A new lower bound for the open-shop problem. Annals of Operation Research 92, 165–183 (1999)
Jackson, J.R.: An extension of Johnson’s results on job lot scheduling. Naval Research Logistics Quarterly 3, 201–203 (1956)
Baptiste, P., Le Pape, C., Nuijten, W.: Constraint-based scheduling. Kluwer Academic Publishers, Dordrecht (2001)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Monette, JN., Deville, Y., Dupont, P. (2007). A Position-Based Propagator for the Open-Shop Problem. In: Van Hentenryck, P., Wolsey, L. (eds) Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems. CPAIOR 2007. Lecture Notes in Computer Science, vol 4510. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72397-4_14
Download citation
DOI: https://doi.org/10.1007/978-3-540-72397-4_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72396-7
Online ISBN: 978-3-540-72397-4
eBook Packages: Computer ScienceComputer Science (R0)