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An exact solution with an improved running time for the routing flow shop problem with two machines

Author

Listed:
  • Ilya Chernykh

    (Sobolev Institute of Mathematics
    Novosibirsk State University)

  • Alexander Kononov

    (Sobolev Institute of Mathematics)

  • Sergey Sevastyanov

    (Sobolev Institute of Mathematics)

Abstract

We present an improved analysis of the running time of a dynamic program for the routing flow shop problem with two machines on an asymmetric network. Our analysis is based on structural properties of optimal schedules and significantly improves the bound on the running time of the algorithm obtained in the conference version of our paper (Chernykh, Kononov, and Sevastyanov, in: Kononov, A. et al. (eds) Mathematical optimization theory and operations research. MOTOR 2020. Lecture notes in computer science, Springer, Switzerland, 2020). To the best of our knowledge, our polynomial-time algorithm (under the assumption that the number of network nodes is bounded by any constant) is the first positive result on the complexity of the routing flow shop problem with an arbitrary structure of the transportation network, even in the case of a symmetric network. This result contrasts with the complexity of the two-machine routing open shop problem, which is NP-hard even on the two-node network.

Suggested Citation

  • Ilya Chernykh & Alexander Kononov & Sergey Sevastyanov, 2024. "An exact solution with an improved running time for the routing flow shop problem with two machines," Journal of Scheduling, Springer, vol. 27(4), pages 329-340, August.
    • Handle: RePEc:spr:jsched:v:27:y:2024:i:4:d:10.1007_s10951-023-00784-8
    DOI: 10.1007/s10951-023-00784-8
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    References listed on IDEAS

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    1. 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.
    2. Yu, Wei & Liu, Zhaohui & Wang, Leiyang & Fan, Tijun, 2011. "Routing open shop and flow shop scheduling problems," European Journal of Operational Research, Elsevier, vol. 213(1), pages 24-36, August.
    3. Averbakh, Igor & Berman, Oded & Chernykh, Ilya, 2006. "The routing open-shop problem on a network: Complexity and approximation," European Journal of Operational Research, Elsevier, vol. 173(2), pages 531-539, September.
    4. Igor Averbakh & Oded Berman, 1999. "A Simple Heuristic for m-Machine Flow-Shop and its Applications in Routing-Scheduling Problems," Operations Research, INFORMS, vol. 47(1), pages 165-170, February.
    5. Igor Averbakh & Oded Berman, 1996. "Routing Two-Machine Flowshop Problems on Networks with Special Structure," Transportation Science, INFORMS, vol. 30(4), pages 303-314, November.
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