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On a borderline between the NP-hard and polynomial-time solvable cases of the flow shop with job-dependent storage requirements

Author

Listed:
  • Alexander Kononov

    (Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences)

  • Julia Memar

    (University of Technology Sydney)

  • Yakov Zinder

    (University of Technology Sydney)

Abstract

The paper is concerned with the two-machine flow shop, where each job requires an additional resource (referred to as storage space) from the start of its first operation till the end of its second operation. The storage requirement of a job is determined by the processing time of its first operation. At any point in time, the total consumption of this additional resource cannot exceed a given limit (referred to as the storage capacity). The goal is to minimise the makespan, i.e. to minimise the time needed for the completion of all jobs. This problem is NP-hard in the strong sense. The paper analyses how the parameter - a lower bound on the storage capacity specified in terms of the processing times, affects the computational complexity.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:83:y:2022:i:3:d:10.1007_s10898-021-01097-w
    DOI: 10.1007/s10898-021-01097-w
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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, December.
    2. 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.
    3. 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.
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