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A constraint generation approach for two-machine shop problems with jobs selection

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  • Della Croce, Federico
  • Koulamas, Christos
  • T'kindt, Vincent

Abstract

We consider job selection problems in two-stage flow shops and job shops. The aim is to select the best job subset with a given cardinality to minimize the makespan. These problems are known to be ordinary NP-hard and the current state of the art algorithms can solve flow shop problems with up to 3000 jobs. We introduce a constraint generation approach to the integer linear programming (ILP) formulation of these problems according to which the constraints associated with nearly all potential critical paths are relaxed and then only the ones violated by the relaxed solution are sequentially reinstated. The proposed approach is capable of solving problems with up to 100 000 jobs.

Suggested Citation

  • Della Croce, Federico & Koulamas, Christos & T'kindt, Vincent, 2017. "A constraint generation approach for two-machine shop problems with jobs selection," European Journal of Operational Research, Elsevier, vol. 259(3), pages 898-905.
    • Handle: RePEc:eee:ejores:v:259:y:2017:i:3:p:898-905
    DOI: 10.1016/j.ejor.2016.11.036
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    References listed on IDEAS

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    1. Panwalkar, S.S. & Koulamas, Christos, 2012. "An O(n2) algorithm for the variable common due date, minimal tardy jobs bicriteria two-machine flow shop problem with ordered machines," European Journal of Operational Research, Elsevier, vol. 221(1), pages 7-13.
    2. Lee, Kangbok & Choi, Byung-Cheon, 2011. "Two-stage production scheduling with an outsourcing option," European Journal of Operational Research, Elsevier, vol. 213(3), pages 489-497, September.
    3. Della Croce, Federico & Gupta, Jatinder N. D. & Tadei, Roberto, 2000. "Minimizing tardy jobs in a flowshop with common due date," European Journal of Operational Research, Elsevier, vol. 120(2), pages 375-381, January.
    4. Vincent T’kindt & Federico Della Croce & Jean-Louis Bouquard, 2007. "Enumeration of Pareto Optima for a Flowshop Scheduling Problem with Two Criteria," INFORMS Journal on Computing, INFORMS, vol. 19(1), pages 64-72, February.
    5. Choi, Byung-Cheon & Chung, Jibok, 2011. "Two-machine flow shop scheduling problem with an outsourcing option," European Journal of Operational Research, Elsevier, vol. 213(1), pages 66-72, August.
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    Cited by:

    1. Annear, Luis Mauricio & Akhavan-Tabatabaei, Raha & Schmid, Verena, 2023. "Dynamic assignment of a multi-skilled workforce in job shops: An approximate dynamic programming approach," European Journal of Operational Research, Elsevier, vol. 306(3), pages 1109-1125.
    2. Jinwen Ou, 2020. "Near-linear-time approximation algorithms for scheduling a batch-processing machine with setups and job rejection," Journal of Scheduling, Springer, vol. 23(5), pages 525-538, October.
    3. Mohamadreza Dabiri & Mehdi Yazdani & Bahman Naderi & Hassan Haleh, 2022. "Modeling and solution methods for hybrid flow shop scheduling problem with job rejection," Operational Research, Springer, vol. 22(3), pages 2721-2765, July.
    4. Amir Ahmadi-Javid & Nasrin Ramshe, 2019. "Designing flexible loop-based material handling AGV paths with cell-adjacency priorities: an efficient cutting-plane algorithm," 4OR, Springer, vol. 17(4), pages 373-400, December.

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