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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

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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.

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Acknowledgements

The research of the first author was supported by the program of fundamental scientific researches of the SB RAS, project 0314-2019-0014.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

    Alexander Kononov

  2. University of Technology Sydney, PO Box 123, Broadway, NSW, 2007, Australia

    Julia Memar & Yakov Zinder

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  1. Alexander Kononov
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  2. Julia Memar
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  3. Yakov Zinder
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Correspondence to Julia Memar.

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Kononov, A., Memar, J. & Zinder, Y. On a borderline between the NP-hard and polynomial-time solvable cases of the flow shop with job-dependent storage requirements. J Glob Optim 83, 445–456 (2022). https://doi.org/10.1007/s10898-021-01097-w

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  • DOI: https://doi.org/10.1007/s10898-021-01097-w

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