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Approximability of scheduling problems with resource consuming jobs

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  • Péter Györgyi
  • Tamás Kis

Abstract

The paper presents new approximability results for single machine scheduling problems with jobs requiring some non-renewable resources (like raw materials, energy, or money) beside the machine. Each resource has an initial stock and additional supplies over time. A feasible schedule specifies a starting time for each job such that no two jobs overlap in time, and when a job is started, enough resources are available to cover its requirements. The goal is to find a feasible schedule of minimum makespan. This problem is strongly NP-hard. Recently, the authors of this paper have proposed a PTAS for the special case with a single non-renewable resource and with a constant number of supply dates, as well as an FPTAS for the special case with two supply dates and one resource only. In this paper we prove APX-hardness of the problem when the number of resources is part of the input, and new polynomial time approximation schemes are devised for some variants, including (1) job release dates, and more than one, but constant number of resources and resource supply dates, and (2) only one resource, arbitrary number of supply dates and job release dates, but with resource requirements proportional to job processing times. Copyright Springer Science+Business Media New York 2015

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  • 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.
    • Handle: RePEc:spr:annopr:v:235:y:2015:i:1:p:319-336:10.1007/s10479-015-1993-3
    DOI: 10.1007/s10479-015-1993-3
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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.
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    6. Briskorn, Dirk & Choi, Byung-Cheon & Lee, Kangbok & Leung, Joseph & Pinedo, Michael, 2010. "Complexity of single machine scheduling subject to nonnegative inventory constraints," European Journal of Operational Research, Elsevier, vol. 207(2), pages 605-619, December.
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    Cited by:

    1. Matthias Bentert & Robert Bredereck & Péter Györgyi & Andrzej Kaczmarczyk & Rolf Niedermeier, 2023. "A multivariate complexity analysis of the material consumption scheduling problem," Journal of Scheduling, Springer, vol. 26(4), pages 369-382, August.
    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. Györgyi, Péter & Kis, Tamás, 2017. "Approximation schemes for parallel machine scheduling with non-renewable resources," European Journal of Operational Research, Elsevier, vol. 258(1), pages 113-123.
    4. 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.
    5. Davari, Morteza & Ranjbar, Mohammad & De Causmaecker, Patrick & Leus, Roel, 2020. "Minimizing makespan on a single machine with release dates and inventory constraints," European Journal of Operational Research, Elsevier, vol. 286(1), pages 115-128.

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