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Two-machine flow shop problem with unit-time operations and conflict graph

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  • Nour El Houda Tellache
  • Mourad Boudhar

Abstract

This paper addresses the problem of scheduling, on a two-machine flow shop, a set of unit-time operations subject to the constraints that some conflicting jobs cannot be scheduled simultaneously on different machines. In the context of our study, these conflicts are modelled by general graphs. The problem of minimising the maximum completion time (makespan) is known to be NP-hard in the strong sense. We propose a mixed-integer linear programming (MILP) model. Then, we develop a branch and bound algorithm based on new lower and upper bound procedures. We further provide a computer simulation to measure the performance of the proposed approaches. The computational results show that the branch and bound algorithm outperforms the MILP model and can solve instances of size up to 20,000 jobs.

Suggested Citation

  • Nour El Houda Tellache & Mourad Boudhar, 2017. "Two-machine flow shop problem with unit-time operations and conflict graph," International Journal of Production Research, Taylor & Francis Journals, vol. 55(6), pages 1664-1679, March.
    • Handle: RePEc:taf:tprsxx:v:55:y:2017:i:6:p:1664-1679
    DOI: 10.1080/00207543.2016.1206672
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    References listed on IDEAS

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    1. Bendraouche, Mohamed & Boudhar, Mourad & Oulamara, Ammar, 2015. "Scheduling: Agreement graph vs resource constraints," European Journal of Operational Research, Elsevier, vol. 240(2), pages 355-360.
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    Cited by:

    1. Zhuang, Yanling & Zhou, Yun & Yuan, Yufei & Hu, Xiangpei & Hassini, Elkafi, 2022. "Order picking optimization with rack-moving mobile robots and multiple workstations," European Journal of Operational Research, Elsevier, vol. 300(2), pages 527-544.
    2. Yong Chen & Yinhui Cai & Longcheng Liu & Guangting Chen & Randy Goebel & Guohui Lin & Bing Su & An Zhang, 2022. "Path cover with minimum nontrivial paths and its application in two-machine flow-shop scheduling with a conflict graph," Journal of Combinatorial Optimization, Springer, vol. 43(3), pages 571-588, April.
    3. Nour El Houda Tellache & Mourad Boudhar, 2018. "Flow shop scheduling problem with conflict graphs," Annals of Operations Research, Springer, vol. 261(1), pages 339-363, February.

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