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A constraint program for solving the job-shop problem

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Principles and Practice of Constraint Programming — CP96 (CP 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1118))

Abstract

In this paper, a method within the framework of propagation of interval constraints and based on the branch- and-bound optimization scheme for solving the job-shop scheduling problem will be presented. The goal is to provide a constraint program which is clean, flexible and robust. The design of the constraint program is based on an idea of sorting the release and due dates of tasks, which is a successful application of a previous but not yet published work on a distinct integers constraint. Based on the sorting constraint, by assembling redundant constraints and applying an efficient search strategy, the current program for the job-shop problem can solve the ten 10 × 10 instances in the paper of Applegate and Cook (1991) in satisfactory computational time. Moreover, good results have been achieved on some harder instances.

This work has been supported by the Esprit Project Acclaim nℴ 7195

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References

  1. Applegate, D. and Cook, B. A Computational Study of the Job Shop Scheduling Problem, Operations Research Society of America, vol 3, no 2, 1991.

    Google Scholar 

  2. Baptiste, P., Le Pape, C. and Nuijten, W. Constraint-based Optimization and Approximation for Job Shop Scheduling, Proc. of the IJCAI 95 workshop on Intelligent Manufacturing Systems, Montréal, 1995.

    Google Scholar 

  3. Benhamou, F. and Older, W. J. Applying Interval Arithmetic to Real, Integer and Boolean Constraints, to appear in the Journal of Logic Programming.

    Google Scholar 

  4. Carlier, J. and Pinson, E. An algorithm for solving the job shop problem, Management Science, vol 35, no 2, February 1989.

    Google Scholar 

  5. Carlier, J. and Pinson, E., Adjustment of heads and tails for the Job-shop problem, European Journal of Operational Research, 78:146–161, 1994.

    Google Scholar 

  6. Caseau, Y. and Laburthe, F. Improved CLP scheduling with task intervals, Proc. of the 11th International Conference on Logic Programming, 1994.

    Google Scholar 

  7. Caseau, Y. and Laburthe, F. Disjuctive scheduling with task intervals, LIENS Technical Report n∘ 95-25, 1995.

    Google Scholar 

  8. Cleary, J. Logical Arithmetic, Future Computing Systems, Vol 2, No 2, 1987.

    Google Scholar 

  9. Colmerauer, A., An introduction to Prolog III, in Communications of the ACM, 33(7):69, July 1990.

    Google Scholar 

  10. Lee J. and van Emden, M. Adapting CLP(R) to Floating point Arithmetic, in Proc. of the Fifth Generation Computer Systems Conference, Tokyo, Japan, 1992.

    Google Scholar 

  11. Lenstra, J.K. and Rinnooy Kan, A.H.G., Computational Complexity of Discrete Optimization Problems, Annals of Discrete Mathematics 4, 121–140, 1979.

    Google Scholar 

  12. Mackworth, A.K., Consistency in Networks of Relations, in Artificial Intelligence 8, p 99–118, 1977.

    Google Scholar 

  13. Muth, J.F. and Thompson, G.L. Industrial Scheduling, Prentice Hall, Engleclood Cliffs, N.J, 1963.

    Google Scholar 

  14. Older, W.J., Van Emden, M. and Swinkels, F. Getting to the Real Problem:experience with BNR Prolog in OR, in Proceedings of the Third International Conference on the Practical Applications of Prolog,(PAP'95), Paris, April, 1995, Alinmead Software Ltd., ISBN 0-952-55540-9.

    Google Scholar 

  15. Older, W.J. and Vellino, A. Constraint Arithmetic on Real Intervals, Constraint Logic Programming: Selected Research, F. Benhamou and A. Colmerauer (eds), MIT Press, 1992.

    Google Scholar 

  16. Van Hentenryck, P., Simonis, H. and Dincbas, D., Constraint satisfaction using constraint logic programming, Artificial Intelligence, vol 58, no.1–3, p113–157, December 1992.

    Google Scholar 

  17. Zhou, J. Solving the job-shop problem by constraint programming, Proc. of the post-ILPS'95 workshop on Interval Constraints, Portland Oregon, December 1995.

    Google Scholar 

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Eugene C. Freuder

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© 1996 Springer-Verlag Berlin Heidelberg

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Zhou, J. (1996). A constraint program for solving the job-shop problem. In: Freuder, E.C. (eds) Principles and Practice of Constraint Programming — CP96. CP 1996. Lecture Notes in Computer Science, vol 1118. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61551-2_97

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  • DOI: https://doi.org/10.1007/3-540-61551-2_97

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  • Print ISBN: 978-3-540-61551-4

  • Online ISBN: 978-3-540-70620-5

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