IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v31y2016i4d10.1007_s10878-015-9836-3.html
   My bibliography  Save this article

New results on two-machine flow-shop scheduling with rejection

Author

Listed:
  • Liqi Zhang

    (Henan Agricultural University)

  • Lingfa Lu

    (Zhengzhou University)

  • Shisheng Li

    (Zhongyuan University of Technology)

Abstract

In this paper, we consider the off-line and on-line two-machine flow-shop scheduling problems with rejection. The objective is to minimize the sum of the makespan of accepted jobs and the total rejection penalty of rejected jobs. For the off-line version, Shabtay and Gasper (Comput Oper Res 39:1087–1096, 2012) showed that this problem is NP-hard and then provided a pseudo-polynomial-time algorithm, two 2-approximation algorithms and a fully polynomial-time approximation scheme. We further study some special cases in this paper. We show that this problem is still NP-hard even when all jobs have the same processing time on one of the machines or all jobs have the same rejection penalty. Furthermore, we also showed that this problem can be solved in polynomialtime algorithm when all jobs satisfy the agreeable condition on their processing times and rejection penalties. For the on-line version without rejection, Chen and Woeginger [in: Du DZ, Pardalos PM (eds.) Minimax and Applications, 1995] showed that the competitive ratio of any determined on-line algorithm is at least 2. We further show that the competitive ratio of any determined on-line algorithm is at least 2 even when all jobs have the same processing time on the first machine. Finally, for the on-line version with rejection, we present a class of on-line algorithms with the best-possible competitive ratio 2.

Suggested Citation

  • Liqi Zhang & Lingfa Lu & Shisheng Li, 2016. "New results on two-machine flow-shop scheduling with rejection," Journal of Combinatorial Optimization, Springer, vol. 31(4), pages 1493-1504, May.
    • Handle: RePEc:spr:jcomop:v:31:y:2016:i:4:d:10.1007_s10878-015-9836-3
    DOI: 10.1007/s10878-015-9836-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-015-9836-3
    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/s10878-015-9836-3?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. György Dósa & Yong He, 2006. "Scheduling with machine cost and rejection," Journal of Combinatorial Optimization, Springer, vol. 12(4), pages 337-350, December.
    2. George Steiner & Rui Zhang, 2011. "Revised Delivery-Time Quotation in Scheduling with Tardiness Penalties," Operations Research, INFORMS, vol. 59(6), pages 1504-1511, December.
    3. S. M. Johnson, 1954. "Optimal two‐ and three‐stage production schedules with setup times included," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 1(1), pages 61-68, March.
    4. Lu, Lingfa & Ng, C.T. & Zhang, Liqi, 2011. "Optimal algorithms for single-machine scheduling with rejection to minimize the makespan," International Journal of Production Economics, Elsevier, vol. 130(2), pages 153-158, April.
    5. Choi, Byung-Cheon & Chung, Jibok, 2011. "Two-machine flow shop scheduling problem with an outsourcing option," European Journal of Operational Research, Elsevier, vol. 213(1), pages 66-72, August.
    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. Baruch Mor & Gur Mosheiov & Dana Shapira, 2021. "Single machine lot scheduling with optional job-rejection," Journal of Combinatorial Optimization, Springer, vol. 41(1), pages 1-11, January.
    3. Shabtay, Dvir & Gerstl, Enrique, 2024. "Coordinating scheduling and rejection decisions in a two-machine flow shop scheduling problem," European Journal of Operational Research, Elsevier, vol. 316(3), pages 887-898.

    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. Liqi Zhang & Lingfa Lu, 2016. "Parallel-machine scheduling with release dates and rejection," 4OR, Springer, vol. 14(2), pages 165-172, June.
    2. Peihai Liu & Xiwen Lu, 2020. "New approximation algorithms for machine scheduling with rejection on single and parallel machine," Journal of Combinatorial Optimization, Springer, vol. 40(4), pages 929-952, November.
    3. 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.
    4. Shabtay, Dvir & Gerstl, Enrique, 2024. "Coordinating scheduling and rejection decisions in a two-machine flow shop scheduling problem," European Journal of Operational Research, Elsevier, vol. 316(3), pages 887-898.
    5. S.S. Panwalkar & Milton L. Smith & Christos Koulamas, 2013. "Review of the ordered and proportionate flow shop scheduling research," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(1), pages 46-55, February.
    6. Wlodzimierz Szwarc & Jatinder N. D. Gupta, 1987. "A flow‐shop problem with sequence‐dependent additive setup times," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(5), pages 619-627, October.
    7. Yinfeng Xu & Rongteng Zhi & Feifeng Zheng & Ming Liu, 2022. "Competitive algorithm for scheduling of sharing machines with rental discount," Journal of Combinatorial Optimization, Springer, vol. 44(1), pages 414-434, August.
    8. Brammer, Janis & Lutz, Bernhard & Neumann, Dirk, 2022. "Permutation flow shop scheduling with multiple lines and demand plans using reinforcement learning," European Journal of Operational Research, Elsevier, vol. 299(1), pages 75-86.
    9. Della Croce, Federico & Koulamas, Christos & T'kindt, Vincent, 2017. "A constraint generation approach for two-machine shop problems with jobs selection," European Journal of Operational Research, Elsevier, vol. 259(3), pages 898-905.
    10. Vincent T’kindt & Federico Della Croce & Mathieu Liedloff, 2022. "Moderate exponential-time algorithms for scheduling problems," 4OR, Springer, vol. 20(4), pages 533-566, December.
    11. 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.
    12. Roberto Cordone & Pierre Hosteins & Giovanni Righini, 2018. "A Branch-and-Bound Algorithm for the Prize-Collecting Single-Machine Scheduling Problem with Deadlines and Total Tardiness Minimization," INFORMS Journal on Computing, INFORMS, vol. 30(1), pages 168-180, February.
    13. Vineet Jain & Tilak Raj, 2018. "An adaptive neuro-fuzzy inference system for makespan estimation of flexible manufacturing system assembly shop: a case study," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 9(6), pages 1302-1314, December.
    14. Golpîra, Hêriş, 2020. "Smart Energy-Aware Manufacturing Plant Scheduling under Uncertainty: A Risk-Based Multi-Objective Robust Optimization Approach," Energy, Elsevier, vol. 209(C).
    15. 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.
    16. Ma, Ran & Guo, Sainan & Miao, Cuixia, 2021. "A semi-online algorithm and its competitive analysis for parallel-machine scheduling problem with rejection," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    17. Na Geng & Letian Chen & Ran Liu & Yanhong Zhu, 2017. "Optimal patient assignment for W queueing network in a diagnostic facility setting," International Journal of Production Research, Taylor & Francis Journals, vol. 55(19), pages 5609-5631, October.
    18. A. G. Leeftink & R. J. Boucherie & E. W. Hans & M. A. M. Verdaasdonk & I. M. H. Vliegen & P. J. Diest, 2018. "Batch scheduling in the histopathology laboratory," Flexible Services and Manufacturing Journal, Springer, vol. 30(1), pages 171-197, June.
    19. Yadong Wang & Baoqiang Fan & Jingang Zhai & Wei Xiong, 2019. "Two-machine flowshop scheduling in a physical examination center," Journal of Combinatorial Optimization, Springer, vol. 37(1), pages 363-374, January.
    20. Chen, Xin & Miao, Qian & Lin, Bertrand M.T. & Sterna, Malgorzata & Blazewicz, Jacek, 2022. "Two-machine flow shop scheduling with a common due date to maximize total early work," European Journal of Operational Research, Elsevier, vol. 300(2), pages 504-511.

    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:jcomop:v:31:y:2016:i:4:d:10.1007_s10878-015-9836-3. 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.