IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v30y2015i3d10.1007_s10878-013-9643-7.html
   My bibliography  Save this article

Approximation algorithms for maximizing the weighted number of early jobs on a single machine with non-availability intervals

Author

Listed:
  • Imed Kacem

    (Université de Lorraine)

  • Hans Kellerer

    (University of Graz)

  • Yann Lanuel

    (Université de Lorraine)

Abstract

In this paper we consider the maximization of the weighted number of early jobs on a single machine with non-availability constraints. We deal with the resumable and the non-resumable cases. We show that the resumable version of this problem has a fully polynomial time approximation scheme (FPTAS) even if the number of the non-availability intervals is variable and a subset of jobs has deadlines instead of due dates. For the non-resumable version we remark that the problem cannot admit an FPTAS even if all due dates are equal and only one non-availability interval occurs. Nevertheless, we show in this case that it admits a polynomial time approximation scheme (PTAS) for a constant number of non-availability intervals and arbitrary due dates.

Suggested Citation

  • Imed Kacem & Hans Kellerer & Yann Lanuel, 2015. "Approximation algorithms for maximizing the weighted number of early jobs on a single machine with non-availability intervals," Journal of Combinatorial Optimization, Springer, vol. 30(3), pages 403-412, October.
  • Handle: RePEc:spr:jcomop:v:30:y:2015:i:3:d:10.1007_s10878-013-9643-7
    DOI: 10.1007/s10878-013-9643-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-013-9643-7
    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/s10878-013-9643-7?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. E. L. Lawler & J. M. Moore, 1969. "A Functional Equation and its Application to Resource Allocation and Sequencing Problems," Management Science, INFORMS, vol. 16(1), pages 77-84, September.
    2. Schmidt, Gunter, 2000. "Scheduling with limited machine availability," European Journal of Operational Research, Elsevier, vol. 121(1), pages 1-15, February.
    3. C. N. Potts & L. N. Van Wassenhove, 1992. "Single Machine Scheduling to Minimize Total Late Work," Operations Research, INFORMS, vol. 40(3), pages 586-595, June.
    4. Sartaj Sahni, 1977. "General Techniques for Combinatorial Approximation," Operations Research, INFORMS, vol. 25(6), pages 920-936, December.
    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. Shi-Sheng Li & Ren-Xia Chen, 2022. "Minimizing total weighted late work on a single-machine with non-availability intervals," Journal of Combinatorial Optimization, Springer, vol. 44(2), pages 1330-1355, September.
    2. Yunqiang Yin & Jianyou Xu & T. C. E. Cheng & Chin‐Chia Wu & Du‐Juan Wang, 2016. "Approximation schemes for single‐machine scheduling with a fixed maintenance activity to minimize the total amount of late work," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(2), pages 172-183, 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. Koulamas, Christos & Kyparisis, George J., 2023. "A classification of dynamic programming formulations for offline deterministic single-machine scheduling problems," European Journal of Operational Research, Elsevier, vol. 305(3), pages 999-1017.
    2. Gerhard J. Woeginger, 2000. "When Does a Dynamic Programming Formulation Guarantee the Existence of a Fully Polynomial Time Approximation Scheme (FPTAS)?," INFORMS Journal on Computing, INFORMS, vol. 12(1), pages 57-74, February.
    3. Tzafestas, Spyros & Triantafyllakis, Alekos, 1993. "Deterministic scheduling in computing and manufacturing systems: a survey of models and algorithms," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 35(5), pages 397-434.
    4. Cheng, T. C. Edwin & Gordon, Valery S. & Kovalyov, Mikhail Y., 1996. "Single machine scheduling with batch deliveries," European Journal of Operational Research, Elsevier, vol. 94(2), pages 277-283, October.
    5. 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.
    6. J. M. van den Akker & J. A. Hoogeveen & S. L. van de Velde, 1999. "Parallel Machine Scheduling by Column Generation," Operations Research, INFORMS, vol. 47(6), pages 862-872, December.
    7. Akturk, M. Selim & Ghosh, Jay B. & Gunes, Evrim D., 2004. "Scheduling with tool changes to minimize total completion time: Basic results and SPT performance," European Journal of Operational Research, Elsevier, vol. 157(3), pages 784-790, September.
    8. Yuan Zhang & Jinjiang Yuan & Chi To Ng & Tai Chiu E. Cheng, 2021. "Pareto‐optimization of three‐agent scheduling to minimize the total weighted completion time, weighted number of tardy jobs, and total weighted late work," Naval Research Logistics (NRL), John Wiley & Sons, vol. 68(3), pages 378-393, April.
    9. Safer, Hershel M. & Orlin, James B., 1953-, 1995. "Fast approximation schemes for multi-criteria flow, knapsack, and scheduling problems," Working papers 3757-95., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    10. Shi-Sheng Li & Ren-Xia Chen, 2022. "Minimizing total weighted late work on a single-machine with non-availability intervals," Journal of Combinatorial Optimization, Springer, vol. 44(2), pages 1330-1355, September.
    11. Wang, Xiuli & Cheng, T.C.E., 2015. "A heuristic for scheduling jobs on two identical parallel machines with a machine availability constraint," International Journal of Production Economics, Elsevier, vol. 161(C), pages 74-82.
    12. Seyed Habib A. Rahmati & Abbas Ahmadi & Kannan Govindan, 2018. "A novel integrated condition-based maintenance and stochastic flexible job shop scheduling problem: simulation-based optimization approach," Annals of Operations Research, Springer, vol. 269(1), pages 583-621, October.
    13. Jiang, Yiwei & Wu, Mengjing & Chen, Xin & Dong, Jianming & Cheng, T.C.E. & Blazewicz, Jacek & Ji, Min, 2024. "Online early work scheduling on parallel machines," European Journal of Operational Research, Elsevier, vol. 315(3), pages 855-862.
    14. Willem E. de Paepe & Jan Karel Lenstra & Jiri Sgall & René A. Sitters & Leen Stougie, 2004. "Computer-Aided Complexity Classification of Dial-a-Ride Problems," INFORMS Journal on Computing, INFORMS, vol. 16(2), pages 120-132, May.
    15. 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.
    16. Hongying Li & Chunjie Su, 2011. "An optimal semi-online algorithm for 2-machine scheduling with an availability constraint," Journal of Combinatorial Optimization, Springer, vol. 22(2), pages 153-165, August.
    17. 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.
    18. Reha Uzsoy & Chung‐Yee Lee & Louis A. Martin‐Vega, 1992. "Scheduling semiconductor test operations: Minimizing maximum lateness and number of tardy jobs on a single machine," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(3), pages 369-388, April.
    19. Hnaien, Faicel & Yalaoui, Farouk & Mhadhbi, Ahmed, 2015. "Makespan minimization on a two-machine flowshop with an availability constraint on the first machine," International Journal of Production Economics, Elsevier, vol. 164(C), pages 95-104.
    20. Zhi-Long Chen & Nicholas G. Hall, 2010. "The Coordination of Pricing and Scheduling Decisions," Manufacturing & Service Operations Management, INFORMS, vol. 12(1), pages 77-92, April.

    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:30:y:2015:i:3:d:10.1007_s10878-013-9643-7. 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.