IDEAS home Printed from https://ideas.repec.org/a/spr/jsched/v22y2019i6d10.1007_s10951-019-00617-7.html
   My bibliography  Save this article

On the parameterized tractability of the just-in-time flow-shop scheduling problem

Author

Listed:
  • Danny Hermelin

    (Ben-Gurion University of the Negev)

  • Dvir Shabtay

    (Ben-Gurion University of the Negev)

  • Nimrod Talmon

    (Ben-Gurion University of the Negev)

Abstract

We study the parameterized complexity of a set of flow-shop scheduling problems in which the objective is to maximize the weighted number of just-in-time jobs. Our analysis focuses on the case where the number of due dates is considerably smaller than the number of jobs and thus can be considered as a parameter. We prove that the two-machine problem is W[1]-hard with respect to this parameter, even if all processing times on the second machine are of unit length, while the problem is in XP when parameterized by the number of machines combined with the number of different due dates. We then move on to study the tractability of the problem when combining the number of different due dates with either the number of different weights or the number of different processing times on the first machine. We prove that in both cases the problem is fixed-parameter tractable for the two-machine case and is W[1]-hard for three or more machines.

Suggested Citation

  • Danny Hermelin & Dvir Shabtay & Nimrod Talmon, 2019. "On the parameterized tractability of the just-in-time flow-shop scheduling problem," Journal of Scheduling, Springer, vol. 22(6), pages 663-676, December.
    • Handle: RePEc:spr:jsched:v:22:y:2019:i:6:d:10.1007_s10951-019-00617-7
    DOI: 10.1007/s10951-019-00617-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10951-019-00617-7
    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/s10951-019-00617-7?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. White, Richard E. & Prybutok, Victor, 2001. "The relationship between JIT practices and type of production system," Omega, Elsevier, vol. 29(2), pages 113-124, April.
    2. Kenneth R. Baker & Gary D. Scudder, 1990. "Sequencing with Earliness and Tardiness Penalties: A Review," Operations Research, INFORMS, vol. 38(1), pages 22-36, February.
    3. Kovalyov, Mikhail Y. & Ng, C.T. & Cheng, T.C. Edwin, 2007. "Fixed interval scheduling: Models, applications, computational complexity and algorithms," European Journal of Operational Research, Elsevier, vol. 178(2), pages 331-342, April.
    4. Shabtay, Dvir, 2012. "The just-in-time scheduling problem in a flow-shop scheduling system," European Journal of Operational Research, Elsevier, vol. 216(3), pages 521-532.
    5. Dvir Shabtay & George Steiner, 2012. "Scheduling to Maximize the Number of Just-in-Time Jobs: A Survey," Springer Optimization and Its Applications, in: Roger Z. Ríos-Mercado & Yasmín A. Ríos-Solís (ed.), Just-in-Time Systems, chapter 0, pages 3-20, Springer.
    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. Danny Hermelin & Dvir Shabtay & Chen Zelig & Michael Pinedo, 2022. "A general scheme for solving a large set of scheduling problems with rejection in FPT time," Journal of Scheduling, Springer, vol. 25(2), pages 229-255, April.
    2. 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.
    3. Shabtay, Dvir & Gilenson, Miri, 2023. "A state-of-the-art survey on multi-scenario scheduling," European Journal of Operational Research, Elsevier, vol. 310(1), pages 3-23.
    4. Klaus Heeger & Danny Hermelin & George B. Mertzios & Hendrik Molter & Rolf Niedermeier & Dvir Shabtay, 2023. "Equitable scheduling on a single machine," Journal of Scheduling, Springer, vol. 26(2), pages 209-225, April.
    5. Dvir Shabtay, 2023. "A new perspective on single-machine scheduling problems with late work related criteria," Annals of Operations Research, Springer, vol. 322(2), pages 947-966, March.

    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. Janiak, Adam & Janiak, Władysław A. & Krysiak, Tomasz & Kwiatkowski, Tomasz, 2015. "A survey on scheduling problems with due windows," European Journal of Operational Research, Elsevier, vol. 242(2), pages 347-357.
    2. Yunqiang Yin & T. C. E. Cheng & Du-Juan Wang & Chin-Chia Wu, 2017. "Two-agent flowshop scheduling to maximize the weighted number of just-in-time jobs," Journal of Scheduling, Springer, vol. 20(4), pages 313-335, August.
    3. Yaron Leyvand & Dvir Shabtay & George Steiner & Liron Yedidsion, 2010. "Just-in-time scheduling with controllable processing times on parallel machines," Journal of Combinatorial Optimization, Springer, vol. 19(3), pages 347-368, April.
    4. Baruch Mor & Gur Mosheiov, 2022. "Single machine scheduling to maximize the weighted number of on-time jobs with job-rejection," Operational Research, Springer, vol. 22(3), pages 2707-2719, July.
    5. Shabtay, Dvir & Gilenson, Miri, 2023. "A state-of-the-art survey on multi-scenario scheduling," European Journal of Operational Research, Elsevier, vol. 310(1), pages 3-23.
    6. Shabtay, Dvir & Steiner, George & Zhang, Rui, 2016. "Optimal coordination of resource allocation, due date assignment and scheduling decisions," Omega, Elsevier, vol. 65(C), pages 41-54.
    7. Scherrer-Rathje, Maike & Boyle, Todd A. & Deflorin, Patricia, 2009. "Lean, take two! Reflections from the second attempt at lean implementation," Business Horizons, Elsevier, vol. 52(1), pages 79-88.
    8. Prabuddha De & Jay B. Ghosh & Charles E. Wells, 1994. "Due‐date assignment and early/tardy scheduling on identical parallel machines," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(1), pages 17-32, February.
    9. X. Cai & F. S. Tu, 1996. "Scheduling jobs with random processing times on a single machine subject to stochastic breakdowns to minimize early‐tardy penalties," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(8), pages 1127-1146, December.
    10. Li, Y. & Ip, W. H. & Wang, D. W., 1998. "Genetic algorithm approach to earliness and tardiness production scheduling and planning problem," International Journal of Production Economics, Elsevier, vol. 54(1), pages 65-76, January.
    11. Ge Yu & Sheldon H. Jacobson, 2020. "Primal-dual analysis for online interval scheduling problems," Journal of Global Optimization, Springer, vol. 77(3), pages 575-602, July.
    12. Ip, W. H. & Yung, K. L. & Wang, Dingwei, 2004. "A branch and bound algorithm for sub-contractor selection in agile manufacturing environment," International Journal of Production Economics, Elsevier, vol. 87(2), pages 195-205, January.
    13. Kate, H.A. ten & Wijngaard, J. & Zijm, W.H.M., 1995. "Minimizing weighted total earliness, total tardiness and setup costs," Research Report 95A37, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    14. T C E Cheng & L Kang & C T Ng, 2004. "Due-date assignment and single machine scheduling with deteriorating jobs," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(2), pages 198-203, February.
    15. Ventura, Jose A. & Radhakrishnan, Sanjay, 2003. "Single machine scheduling with symmetric earliness and tardiness penalties," European Journal of Operational Research, Elsevier, vol. 144(3), pages 598-612, February.
    16. C N Potts & V A Strusevich, 2009. "Fifty years of scheduling: a survey of milestones," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(1), pages 41-68, May.
    17. Jayaram, Jayanth & Das, Ajay & Nicolae, Mariana, 2010. "Looking beyond the obvious: Unraveling the Toyota production system," International Journal of Production Economics, Elsevier, vol. 128(1), pages 280-291, November.
    18. Slotnick, Susan A., 2011. "Order acceptance and scheduling: A taxonomy and review," European Journal of Operational Research, Elsevier, vol. 212(1), pages 1-11, July.
    19. Huynh Tuong, Nguyen & Soukhal, Ameur & Billaut, Jean-Charles, 2010. "A new dynamic programming formulation for scheduling independent tasks with common due date on parallel machines," European Journal of Operational Research, Elsevier, vol. 202(3), pages 646-653, May.
    20. Kolahan, F. & Liang, M., 1998. "An adaptive TS approach to JIT sequencing with variable processing times and sequence-dependent setups," European Journal of Operational Research, Elsevier, vol. 109(1), pages 142-159, August.

    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_s10951-019-00617-7. 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.