IDEAS home Printed from https://ideas.repec.org/a/spr/jsched/v22y2019i6d10.1007_s10951-019-00601-1.html
   My bibliography  Save this article

Minimizing total weighted completion time on a single machine subject to non-renewable resource constraints

Author

Listed:
  • Péter Györgyi

    (Hungarian Academy of Sciences)

  • Tamás Kis

    (Hungarian Academy of Sciences)

Abstract

In this paper, we describe new complexity results and approximation algorithms for single-machine scheduling problems with non-renewable resource constraints and the total weighted completion time objective. This problem is hardly studied in the literature. Beyond some complexity results, only a fully polynomial-time approximation scheme (FPTAS) is known for a special case. In this paper, we discuss some polynomially solvable special cases and also show that under very strong assumptions, such as the processing time, the resource consumption and the weight is the same for each job; minimizing the total weighted completion time is still NP-hard. In addition, we also propose a 2-approximation algorithm for this variant and a polynomial-time approximation scheme (PTAS) for the case when the processing time equals the weight for each job, while the resource consumptions are arbitrary.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jsched:v:22:y:2019:i:6:d:10.1007_s10951-019-00601-1
    DOI: 10.1007/s10951-019-00601-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10951-019-00601-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10951-019-00601-1?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. Slowinski, Roman, 1984. "Preemptive scheduling of independent jobs on parallel machines subject to financial constraints," European Journal of Operational Research, Elsevier, vol. 15(3), pages 366-373, March.
    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. 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.
    5. Wayne E. Smith, 1956. "Various optimizers for single‐stage production," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 3(1‐2), pages 59-66, March.
    6. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. 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.
    3. 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.
    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.
    5. Lidong Wu & Cong-Dian Cheng, 2016. "On single machine scheduling with resource constraint," Journal of Combinatorial Optimization, Springer, vol. 31(2), pages 491-505, February.
    6. 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.
    7. Marieke Quant & Marc Meertens & Hans Reijnierse, 2008. "Processing games with shared interest," Annals of Operations Research, Springer, vol. 158(1), pages 219-228, February.
    8. Lili Liu & Guochun Tang & Baoqiang Fan & Xingpeng Wang, 2015. "Two-person cooperative games on scheduling problems in outpatient pharmacy dispensing process," Journal of Combinatorial Optimization, Springer, vol. 30(4), pages 938-948, November.
    9. van Beek, Andries & Malmberg, Benjamin & Borm, Peter & Quant, Marieke & Schouten, Jop, 2021. "Cooperation and Competition in Linear Production and Sequencing Processes," Discussion Paper 2021-011, Tilburg University, Center for Economic Research.
    10. Reijnierse, Hans & Borm, Peter & Quant, Marieke & Meertens, Marc, 2010. "Processing games with restricted capacities," European Journal of Operational Research, Elsevier, vol. 202(3), pages 773-780, May.
    11. Borm, Peter & Fiestras-Janeiro, Gloria & Hamers, Herbert & Sanchez, Estela & Voorneveld, Mark, 2002. "On the convexity of games corresponding to sequencing situations with due dates," European Journal of Operational Research, Elsevier, vol. 136(3), pages 616-634, February.
    12. Rubing Chen & Jinjiang Yuan, 2020. "Single-machine scheduling of proportional-linearly deteriorating jobs with positional due indices," 4OR, Springer, vol. 18(2), pages 177-196, June.
    13. Ravindran Vijayalakshmi, Vipin & Schröder, Marc & Tamir, Tami, 2024. "Minimizing total completion time with machine-dependent priority lists," European Journal of Operational Research, Elsevier, vol. 315(3), pages 844-854.
    14. Hanane Krim & Rachid Benmansour & David Duvivier & Daoud Aït-Kadi & Said Hanafi, 2020. "Heuristics for the single machine weighted sum of completion times scheduling problem with periodic maintenance," Computational Optimization and Applications, Springer, vol. 75(1), pages 291-320, January.
    15. M. Musegaas & P. E. M. Borm & M. Quant, 2018. "On the convexity of step out–step in sequencing games," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 68-109, April.
    16. Musegaas, M. & Borm, P.E.M. & Quant, M., 2015. "Step out–Step in sequencing games," European Journal of Operational Research, Elsevier, vol. 246(3), pages 894-906.
    17. Atay, Ata & Trudeau, Christian, 2024. "Queueing games with an endogenous number of machines," Games and Economic Behavior, Elsevier, vol. 144(C), pages 104-125.
    18. Miri Gilenson & Dvir Shabtay & Liron Yedidsion & Rohit Malshe, 2021. "Scheduling in multi-scenario environment with an agreeable condition on job processing times," Annals of Operations Research, Springer, vol. 307(1), pages 153-173, December.
    19. Agnetis, Alessandro & Chen, Bo & Nicosia, Gaia & Pacifici, Andrea, 2019. "Price of fairness in two-agent single-machine scheduling problems," European Journal of Operational Research, Elsevier, vol. 276(1), pages 79-87.
    20. Yang, Guangjing & Sun, Hao & Hou, Dongshuang & Xu, Genjiu, 2019. "Games in sequencing situations with externalities," European Journal of Operational Research, Elsevier, vol. 278(2), pages 699-708.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jsched:v:22:y:2019:i:6:d:10.1007_s10951-019-00601-1. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.