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A tight approximation ratio of a list scheduling algorithm for a single-machine scheduling problem with a non-renewable resource

Author

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  • Susumu Hashimoto

    (Tokyo Institute of Technology)

  • Shinji Mizuno

    (Tokyo Institute of Technology)

Abstract

In this paper, we investigate an open problem by Györgyi and Kis for a single-machine scheduling problem with a non-renewable resource (NR-SSP) and total weighted completion time criterion. The problem is NP-hard, even if every job has the same processing time, and each weight is equal to its required amount of the resource. Györgyi and Kis prove that a simple list scheduling algorithm for this special case is a 3-approximation algorithm and conjecture that the algorithm for the case is a 2-approximation algorithm. We prove their conjecture. More strongly, we show that the approximation ratio is strictly less than 2 for any instance, and for any $$ \epsilon > 0 $$ ϵ > 0 , there exists an instance for which the approximation ratio is more than $$ 2-\epsilon $$ 2 - ϵ .

Suggested Citation

  • Susumu Hashimoto & Shinji Mizuno, 2021. "A tight approximation ratio of a list scheduling algorithm for a single-machine scheduling problem with a non-renewable resource," Journal of Scheduling, Springer, vol. 24(3), pages 259-267, June.
    • Handle: RePEc:spr:jsched:v:24:y:2021:i:3:d:10.1007_s10951-021-00681-y
    DOI: 10.1007/s10951-021-00681-y
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    References listed on IDEAS

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    1. Alexander Grigoriev & Martijn Holthuijsen & Joris van de Klundert, 2005. "Basic scheduling problems with raw material constraints," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(6), pages 527-535, September.
    2. Péter Györgyi & Tamás Kis, 2019. "Minimizing total weighted completion time on a single machine subject to non-renewable resource constraints," Journal of Scheduling, Springer, vol. 22(6), pages 623-634, December.
    3. Gafarov, Evgeny R. & Lazarev, Alexander A. & Werner, Frank, 2011. "Single machine scheduling problems with financial resource constraints: Some complexity results and properties," Mathematical Social Sciences, Elsevier, vol. 62(1), pages 7-13, July.
    4. Péter Györgyi & Tamás Kis, 2015. "Approximability of scheduling problems with resource consuming jobs," Annals of Operations Research, Springer, vol. 235(1), pages 319-336, December.
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