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Flow shop scheduling problem with conflict graphs

Author

Listed:
  • Nour El Houda Tellache

    (USTHB University)

  • Mourad Boudhar

    (USTHB University)

Abstract

This paper addresses the problem of scheduling jobs on flow shops subject to constraints given by an undirected graph, in which each edge joins a pair of conflicting jobs that cannot be processed simultaneously on different machines. We first show that the problem of minimizing the maximum completion time (makespan) is NP-hard for several versions. Then, we present polynomial-time solvable cases. On the other hand, we propose heuristic approaches and lower bounds alongside with an experimental study.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:261:y:2018:i:1:d:10.1007_s10479-017-2560-x
    DOI: 10.1007/s10479-017-2560-x
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    References listed on IDEAS

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    1. Mohamed Bendraouche & Mourad Boudhar, 2016. "Scheduling with agreements: new results," International Journal of Production Research, Taylor & Francis Journals, vol. 54(12), pages 3508-3522, June.
    2. Nawaz, Muhammad & Enscore Jr, E Emory & Ham, Inyong, 1983. "A heuristic algorithm for the m-machine, n-job flow-shop sequencing problem," Omega, Elsevier, vol. 11(1), pages 91-95.
    3. Taillard, E., 1990. "Some efficient heuristic methods for the flow shop sequencing problem," European Journal of Operational Research, Elsevier, vol. 47(1), pages 65-74, July.
    4. M. R. Garey & D. S. Johnson & Ravi Sethi, 1976. "The Complexity of Flowshop and Jobshop Scheduling," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 117-129, May.
    5. 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.
    6. 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.
    7. B. J. Lageweg & J. K. Lenstra & A. H. G. Rinnooy Kan, 1978. "A General Bounding Scheme for the Permutation Flow-Shop Problem," Operations Research, INFORMS, vol. 26(1), pages 53-67, February.
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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. Lin Gui & Xinyu Li & Qingfu Zhang & Liang Gao, 2024. "A uniform sampling method for permutation space," Annals of Operations Research, Springer, vol. 338(2), pages 925-945, July.
    3. Said Aqil & Karam Allali, 2021. "On a bi-criteria flow shop scheduling problem under constraints of blocking and sequence dependent setup time," Annals of Operations Research, Springer, vol. 296(1), pages 615-637, January.
    4. 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.
    5. Xinyu Sun & Xin-Na Geng & Tao Liu, 2020. "Due-window assignment scheduling in the proportionate flow shop setting," Annals of Operations Research, Springer, vol. 292(1), pages 113-131, September.

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