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A branch and bound method for the job-shop problem with sequence-dependent setup times

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  • Christian Artigues
  • Dominique Feillet

Abstract

This paper deals with the job-shop scheduling problem with sequence-dependent setup times. We propose a new method to solve the makespan minimization problem to optimality. The method is based on iterative solving via branch and bound decisional versions of the problem. At each node of the branch and bound tree, constraint propagation algorithms adapted to setup times are performed for domain filtering and feasibility check. Relaxations based on the traveling salesman problem with time windows are also solved to perform additional pruning. The traveling salesman problem is formulated as an elementary shortest path problem with resource constraints and solved through dynamic programming. This method allows to close previously unsolved benchmark instances of the literature and also provides new lower and upper bounds. Copyright Springer Science+Business Media, LLC 2008

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  • Christian Artigues & Dominique Feillet, 2008. "A branch and bound method for the job-shop problem with sequence-dependent setup times," Annals of Operations Research, Springer, vol. 159(1), pages 135-159, March.
    • Handle: RePEc:spr:annopr:v:159:y:2008:i:1:p:135-159:10.1007/s10479-007-0283-0
    DOI: 10.1007/s10479-007-0283-0
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    Cited by:

    1. Carlos Mencía & María Sierra & Ramiro Varela, 2013. "Depth-first heuristic search for the job shop scheduling problem," Annals of Operations Research, Springer, vol. 206(1), pages 265-296, July.
    2. Velez, Sara & Dong, Yachao & Maravelias, Christos T., 2017. "Changeover formulations for discrete-time mixed-integer programming scheduling models," European Journal of Operational Research, Elsevier, vol. 260(3), pages 949-963.
    3. Tomasz Gawroński, 2012. "Optimization of setup times in the furniture industry," Annals of Operations Research, Springer, vol. 201(1), pages 169-182, December.
    4. Diarmuid Grimes & Emmanuel Hebrard, 2015. "Solving Variants of the Job Shop Scheduling Problem Through Conflict-Directed Search," INFORMS Journal on Computing, INFORMS, vol. 27(2), pages 268-284, May.
    5. Ansis Ozolins, 2020. "Bounded dynamic programming algorithm for the job shop problem with sequence dependent setup times," Operational Research, Springer, vol. 20(3), pages 1701-1728, September.
    6. Gaby Pinto & Yariv Ben-Dov & Gad Rabinowitz, 2013. "Formulating and solving a multi-mode resource-collaboration and constrained scheduling problem (MRCCSP)," Annals of Operations Research, Springer, vol. 206(1), pages 311-339, July.
    7. Sascha Cauwelaert & Cyrille Dejemeppe & Pierre Schaus, 2020. "An Efficient Filtering Algorithm for the Unary Resource Constraint with Transition Times and Optional Activities," Journal of Scheduling, Springer, vol. 23(4), pages 431-449, August.
    8. Dario Medić & Srećko Krile & Igor Jelaska & Rino Bošnjak, 2021. "Adriatic Sea Hub Ports Feeder Service Optimization Using Multi-Criteria Decision-Making Methods," Sustainability, MDPI, vol. 13(21), pages 1-12, November.
    9. Amir Elalouf, 2014. "Fast approximation algorithms for routing problems with hop-wise constraints," Annals of Operations Research, Springer, vol. 222(1), pages 279-291, November.
    10. Zhe Liu & Shurong Li, 2022. "A numerical method for interval multi-objective mixed-integer optimal control problems based on quantum heuristic algorithm," Annals of Operations Research, Springer, vol. 311(2), pages 853-898, April.

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