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Minimizing the weighted sum of maximum earliness and maximum tardiness in a single-agent and two-agent form of a two-machine flow shop scheduling problem

Author

Listed:
  • Vahid Nasrollahi

    (Isfahan University of Technology)

  • Ghasem Moslehi

    (Isfahan University of Technology)

  • Mohammad Reisi-Nafchi

    (Isfahan University of Technology)

Abstract

In the past decade, multi-agent scheduling studies have become more widespread. However, the evaluation of these issues in the flow shop scheduling environment has received almost no attention. In this article, we investigate two problems. One problem is a common due date problem of constrained two-agent scheduling of jobs in a two-machine flow shop environment to minimize the weighted sum of maximum earliness and maximum tardiness of first-agent jobs and restrictions of non-eligibility on the tardiness of second-agent jobs. Another problem is a single-agent form of the two-agent problem when the number of second-agent jobs is zero. So, an optimal algorithm with polynomial time complexity is presented for the single-agent problem. For the two-agent problem, after it was shown to have minimum complexity of ordinary NP-hardness, a branch and bound algorithm, based on efficient lower and upper bounds and dominance rules, was developed. The computational results show that the algorithm can solve the large-size instances optimally.

Suggested Citation

  • Vahid Nasrollahi & Ghasem Moslehi & Mohammad Reisi-Nafchi, 2022. "Minimizing the weighted sum of maximum earliness and maximum tardiness in a single-agent and two-agent form of a two-machine flow shop scheduling problem," Operational Research, Springer, vol. 22(2), pages 1403-1442, April.
    • Handle: RePEc:spr:operea:v:22:y:2022:i:2:d:10.1007_s12351-020-00577-3
    DOI: 10.1007/s12351-020-00577-3
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    References listed on IDEAS

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    1. Wenchang Luo & Lin Chen & Guochuan Zhang, 2012. "Approximation schemes for two-machine flow shop scheduling with two agents," Journal of Combinatorial Optimization, Springer, vol. 24(3), pages 229-239, October.
    2. Yunqiang Yin & T. C. E. Cheng & Du-Juan Wang & Chin-Chia Wu, 2017. "Two-agent flowshop scheduling to maximize the weighted number of just-in-time jobs," Journal of Scheduling, Springer, vol. 20(4), pages 313-335, August.
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    5. Hamilton Emmons & George Vairaktarakis, 2013. "The Two-Machine Flow Shop," International Series in Operations Research & Management Science, in: Flow Shop Scheduling, edition 127, chapter 0, pages 21-66, Springer.
    6. Ghasem Moslehi & Mehdi Mahnam & Majid Amin-Nayeri & Amir Azaron, 2010. "A branch-and-bound algorithm to minimise the sum of maximum earliness and tardiness in the single machine," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 8(4), pages 458-482.
    7. Hamilton Emmons & George Vairaktarakis, 2013. "Flow Shop Scheduling," International Series in Operations Research and Management Science, Springer, edition 127, number 978-1-4614-5152-5, December.
    8. Perez-Gonzalez, Paz & Framinan, Jose M., 2014. "A common framework and taxonomy for multicriteria scheduling problems with interfering and competing jobs: Multi-agent scheduling problems," European Journal of Operational Research, Elsevier, vol. 235(1), pages 1-16.
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