Solving job shop scheduling with setup times through constraint-based iterative sampling: an experimental analysis

  • Angelo Oddi
  • Riccardo Rasconi
  • Amedeo Cesta
  • Stephen F. Smith
Article

Abstract

This paper presents a heuristic algorithm for solving a job-shop scheduling problem with sequence dependent setup times and min/max separation constraints among the activities (SDST-JSSP/max). The algorithm relies on a core constraint-based search procedure, which generates consistent orderings of activities that require the same resource by incrementally imposing precedence constraints on a temporally feasible solution. Key to the effectiveness of the search procedure is a conflict sampling method biased toward selection of most critical conflicts and coupled with a non-deterministic choice heuristic to guide the base conflict resolution process. This constraint-based search is then embedded within a larger iterative-sampling search framework to broaden search space coverage and promote solution optimization. The efficacy of the overall heuristic algorithm is demonstrated empirically both on a set of previously studied job-shop scheduling benchmark problems with sequence dependent setup times and by introducing a new benchmark with setups and generalized precedence constraints.

Keywords

Random-restart Constraint-based reasoning Job-shop scheduling Setup times Generalized precedence constraints 

Mathematics Subject Classifications (2010)

68T20 68M20 68W20 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Adams, J., Balas, E., Zawack, D.: The shifting bottleneck procedure for job shop scheduling. Manage. Sci. 34(3), 391–401 (1988)MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Allahverdi, A., Soroush, H.: The significance of reducing setup times/setup costs. Eur. J. Oper. Res. 187(3), 978–984 (2008)MATHCrossRefGoogle Scholar
  3. 3.
    Allahverdi, A., Ng, C., Cheng, T., Kovalyov, M.: A survey of scheduling problems with setup times or costs. Eur. J. Oper. Res. 187(3), 985–1032 (2008)MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Artigues, C., Feillet, D.: A branch and bound method for the job-shop problem with sequence-dependent setup times. Ann. Oper. Res. 159(1), 135–159 (2008)MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Balas, E., Simonetti, N., Vazacopoulos, A.: Job shop scheduling with setup times, deadlines and precedence constraints. J. Sched. 11(4), 253–262 (2008)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Birattari, M.: Race: Racing methods for the selection of the best. http://CRAN.R-project.org/package=race, R package version 0.1.58 (2010)
  7. 7.
    Birattari, M., Stützle, T., Paquete, L., Varrentrapp, K.,: A racing algorithm for configuring metaheuristics. In: GECCO, pp. 11–18 2002Google Scholar
  8. 8.
    Brucker, P., Jurisch, B., Sievers, B.: A branch and bound algorithm for the job-shop scheduling problem. Discrete Appl. Math. 49(1–3), 107–127 (1994)MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Brucker, P., Thiele, O.: A branch & bound method for the general-shop problem with sequence dependent setup-times. OR Spectrum 18(3), 145–161 (1996)MathSciNetMATHGoogle Scholar
  10. 10.
    Brucker, P., Lenstra, J., Kan, A.R.: Complexity of machine scheduling problems. Ann. Discrete Math. 1, 343–362 (1977)CrossRefGoogle Scholar
  11. 11.
    Cambazard, H., Hebrard, E., Barry, O., Papadopoulos, A.: Local search and constraint programming for the post-enrolment-based course timetabling problem. In: PATAT ’08—Proceedings of the 7th International Conference on the Practice and Theory of Automated Timetabling (2008)Google Scholar
  12. 12.
    Cesta, A., Oddi, A., Smith, S.F.: A constraint-based method for project scheduling with time windows. J. Heuristics 8(1), 109–136 (2002)MATHCrossRefGoogle Scholar
  13. 13.
    Cheng, C., Smith, S.: Generating feasible schedules under complex metric constraints. In: Proceedings 12th National Conference on AI (AAAI-94) (1994)Google Scholar
  14. 14.
    Dechter, R., Meiri, I., Pearl, J.: Temporal constraint networks. Artif. Intell. 49, 61–95 (1991)MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    Demirkol, E., Mehta, S., Uzsoy, R.: Benchmarks for shop scheduling problems. Eur. J. Oper. Res. 109(1), 137–141 (1998)MATHCrossRefGoogle Scholar
  16. 16.
    Focacci, F., Laborie, P., Nuijten, W.: Solving scheduling problems with setup times and alternative resources. In: AIPS, pp. 92–111 (2000)Google Scholar
  17. 17.
    González, M.A., Vela, C.R., Varela, R.: A Tabu search algorithm to minimize lateness in scheduling problems with setup times. In: Proceedings of the CAEPIA-TTIA 2009 13th Conference of the Spanish Association on Artificial Intellegence (2009)Google Scholar
  18. 18.
    Montanari, U.: Networks of constraints: fundamental properties and applications to picture processing. Inf. Sci. 7, 95–132 (1974)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Nowicki, E., Smutnicki, C.: An advanced tabu search algorithm for the job shop problem. J. Sched. 8(2), 145–159 (2005)MathSciNetMATHCrossRefGoogle Scholar
  20. 20.
    Oddi, A., Smith, S.: Stochastic procedures for generating feasible schedules. In: Proceedings 14th National Conference on AI (AAAI-97), pp. 308–314 (1997)Google Scholar
  21. 21.
    Ovacik, I., Uzsoy, R.: Exploiting shop floor status information to schedule complex job shops. J. Manuf. Syst. 13(2), 73–84 (1994)CrossRefGoogle Scholar
  22. 22.
    Ovacik, I., Uzsoy, R.: Decomposition Methods for Complex Factory Scheduling Problems. Kluwer Academic, Dordrecht (1997)CrossRefGoogle Scholar
  23. 23.
    Policella, N., Cesta, A., Oddi, A., Smith, S.: From precedence constraint posting to partial order schedules. AI Commun. 20(3), 163–180 (2007)MathSciNetMATHGoogle Scholar
  24. 24.
    R Development Core Team (2010) R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria, http://www.R-project.org/. ISBN 3-900051-07-0 (2010)
  25. 25.
    Sotskov, Y.N., Shakhlevich, N.V.: Np-hardness of shop-scheduling problems with three jobs. Discrete Appl. Math. 59(3), 237–266 (1995). doi:10.1016/0166-218X(93)E0169-Y MathSciNetMATHCrossRefGoogle Scholar
  26. 26.
    Vela, C.R., Varela, R., González, MA.: Local search and genetic algorithm for the job shop scheduling problem with sequence dependent setup times. J. Heuristics 16(2):139–165 (2008). http://www.springerlink.com/index/10.1007/s10732-008-9094-y CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Angelo Oddi
    • 1
  • Riccardo Rasconi
    • 1
  • Amedeo Cesta
    • 1
  • Stephen F. Smith
    • 2
  1. 1.Istituto di Scienze e Tecnologie della CognizioneConsiglio Nazionale delle RicercheRomeItaly
  2. 2.Robotics InstituteCarnegie Mellon UniversityPittsburghUSA

Personalised recommendations