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A 5-parameter complexity classification of the two-stage flow shop scheduling problem with job dependent storage requirements

Author

Listed:
  • Yakov Zinder

    (University of Technology)

  • Alexandr Kononov

    (Sobolev Institute of Mathematics)

  • Joey Fung

    (BHP)

Abstract

The paper is concerned with the two-machine scheduling problem where each job is to be processed on the first-stage machine and after that on the second-stage machine. In order to be processed, each job requires storage space that it seizes at the start of its processing on the first-stage machine and releases only at the completion of processing on the second-stage machine. The storage space is limited and its consumption varies from job to job. The goal is to minimise the time needed for the completion of all jobs. All instances of the considered scheduling problem are classified by means of five parameters. This leads to the sixty four families of instances. For each family, the paper establishes its computational complexity and, in the case of polynomial-time solvability, presents a polynomial-time algorithm, constructing an optimal schedule.

Suggested Citation

  • Yakov Zinder & Alexandr Kononov & Joey Fung, 2021. "A 5-parameter complexity classification of the two-stage flow shop scheduling problem with job dependent storage requirements," Journal of Combinatorial Optimization, Springer, vol. 42(2), pages 276-309, August.
    • Handle: RePEc:spr:jcomop:v:42:y:2021:i:2:d:10.1007_s10878-021-00706-4
    DOI: 10.1007/s10878-021-00706-4
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    References listed on IDEAS

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    1. 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, April.
    2. Peter Brucker, 2007. "Scheduling Algorithms," Springer Books, Springer, edition 0, number 978-3-540-69516-5, February.
    3. S. M. Johnson, 1954. "Optimal two‐ and three‐stage production schedules with setup times included," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 1(1), pages 61-68, March.
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    Cited by:

    1. Geser, Philine & Le, Hoang Thanh & Hartmann, Tom & Middendorf, Martin, 2022. "On permutation schedules for two-machine flow shops with buffer constraints and constant processing times on one machine," European Journal of Operational Research, Elsevier, vol. 303(2), pages 593-601.
    2. Alexander Kononov & Julia Memar & Yakov Zinder, 2022. "On a borderline between the NP-hard and polynomial-time solvable cases of the flow shop with job-dependent storage requirements," Journal of Global Optimization, Springer, vol. 83(3), pages 445-456, July.

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