IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v174y2017i3d10.1007_s10957-017-1147-7.html
   My bibliography  Save this article

Polynomial Time Approximation Scheme for Two Parallel Machines Scheduling with a Common Due Date to Maximize Early Work

Author

Listed:
  • Malgorzata Sterna

    (Poznan University of Technology)

  • Kateryna Czerniachowska

    (Poznan University of Technology)

Abstract

We study the scheduling problem with a common due date on two parallel identical machines and the total early work criterion. The problem is known to be NP-hard. We prove a few dominance properties of optimal solutions of this problem. Their proposal was inspired by the results of some auxiliary computational experiments. Test were performed with the dynamic programming algorithm and list algorithms. Then, we propose the polynomial time approximation scheme, based on structuring problem input. Moreover, we discuss the relationship between the early work criterion and the related late work criterion. We compare the computational complexity and approximability of scheduling problems with both mentioned objective functions.

Suggested Citation

  • Malgorzata Sterna & Kateryna Czerniachowska, 2017. "Polynomial Time Approximation Scheme for Two Parallel Machines Scheduling with a Common Due Date to Maximize Early Work," Journal of Optimization Theory and Applications, Springer, vol. 174(3), pages 927-944, September.
    • Handle: RePEc:spr:joptap:v:174:y:2017:i:3:d:10.1007_s10957-017-1147-7
    DOI: 10.1007/s10957-017-1147-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-017-1147-7
    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/s10957-017-1147-7?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. M. Y. Kovalyov & C. N. Potts & L. N. van Wassenhove, 1994. "A Fully Polynomial Approximation Scheme for Scheduling a Single Machine to Minimize Total Weighted Late Work," Mathematics of Operations Research, INFORMS, vol. 19(1), pages 86-93, February.
    2. Xin Chen & Malgorzata Sterna & Xin Han & Jacek Blazewicz, 2016. "Scheduling on parallel identical machines with late work criterion: Offline and online cases," Journal of Scheduling, Springer, vol. 19(6), pages 729-736, December.
    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. Sterna, Malgorzata, 2011. "A survey of scheduling problems with late work criteria," Omega, Elsevier, vol. 39(2), pages 120-129, April.
    5. Blazewicz, Jacek & Pesch, Erwin & Sterna, Malgorzata & Werner, Frank, 2005. "The two-machine flow-shop problem with weighted late work criterion and common due date," European Journal of Operational Research, Elsevier, vol. 165(2), pages 408-415, September.
    6. A. M. A. Hariri & C. N. Potts & L. N. Van Wassenhove, 1995. "Single Machine Scheduling to Minimize Total Weighted Late Work," INFORMS Journal on Computing, INFORMS, vol. 7(2), pages 232-242, May.
    7. Jacek Błażewicz & Klaus H. Ecker & Erwin Pesch & Günter Schmidt & Jan Węglarz, 2007. "Handbook on Scheduling," International Handbooks on Information Systems, Springer, number 978-3-540-32220-7, September.
    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. Pascale Bendotti & Luca Brunod Indrigo & Philippe Chrétienne & Bruno Escoffier, 2024. "Resource leveling: complexity of a unit execution time two-processor scheduling variant and related problems," Journal of Scheduling, Springer, vol. 27(6), pages 587-606, December.
    2. 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.
    3. 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.
    4. Shi-Sheng Li & Jin-Jiang Yuan, 2020. "Single-machine scheduling with multi-agents to minimize total weighted late work," Journal of Scheduling, Springer, vol. 23(4), pages 497-512, August.
    5. Yunhong Min & Byung-Cheon Choi & Myoung-Ju Park & Kyung Min Kim, 2023. "A parallel-machine scheduling problem with an antithetical property to maximize total weighted early work," 4OR, Springer, vol. 21(3), pages 421-437, September.
    6. Yi-Chun Wang & Ji-Bo Wang, 2023. "Study on Convex Resource Allocation Scheduling with a Time-Dependent Learning Effect," Mathematics, MDPI, vol. 11(14), pages 1-20, July.
    7. Sterna, Małgorzata, 2021. "Late and early work scheduling: A survey," Omega, Elsevier, vol. 104(C).
    8. Xiaofei Liu & Yajie Li & Weidong Li & Jinhua Yang, 2023. "Combinatorial approximation algorithms for the maximum bounded connected bipartition problem," Journal of Combinatorial Optimization, Springer, vol. 45(1), pages 1-21, January.
    9. Chen, Rubing & Geng, Zhichao & Lu, Lingfa & Yuan, Jinjiang & Zhang, Yuan, 2022. "Pareto-scheduling of two competing agents with their own equal processing times," European Journal of Operational Research, Elsevier, vol. 301(2), pages 414-431.
    10. Chen, Xin & Liang, Yage & Sterna, Małgorzata & Wang, Wen & Błażewicz, Jacek, 2020. "Fully polynomial time approximation scheme to maximize early work on parallel machines with common due date," European Journal of Operational Research, Elsevier, vol. 284(1), pages 67-74.
    11. Györgyi, Péter & Kis, Tamás, 2020. "A common approximation framework for early work, late work, and resource leveling problems," European Journal of Operational Research, Elsevier, vol. 286(1), pages 129-137.

    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. Chen, Xin & Liang, Yage & Sterna, Małgorzata & Wang, Wen & Błażewicz, Jacek, 2020. "Fully polynomial time approximation scheme to maximize early work on parallel machines with common due date," European Journal of Operational Research, Elsevier, vol. 284(1), pages 67-74.
    2. Rubing Chen & Jinjiang Yuan & C.T. Ng & T.C.E. Cheng, 2019. "Single‐machine scheduling with deadlines to minimize the total weighted late work," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(7), pages 582-595, October.
    3. Sterna, Małgorzata, 2021. "Late and early work scheduling: A survey," Omega, Elsevier, vol. 104(C).
    4. Shi-Sheng Li & Jin-Jiang Yuan, 2020. "Single-machine scheduling with multi-agents to minimize total weighted late work," Journal of Scheduling, Springer, vol. 23(4), pages 497-512, August.
    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.
    6. Shabtay, Dvir & Mosheiov, Gur & Oron, Daniel, 2022. "Single machine scheduling with common assignable due date/due window to minimize total weighted early and late work," European Journal of Operational Research, Elsevier, vol. 303(1), pages 66-77.
    7. Mosheiov, Gur & Oron, Daniel & Shabtay, Dvir, 2021. "Minimizing total late work on a single machine with generalized due-dates," European Journal of Operational Research, Elsevier, vol. 293(3), pages 837-846.
    8. 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.
    9. 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.
    10. Sang, Yao-Wen & Wang, Jun-Qiang & Sterna, Małgorzata & Błażewicz, Jacek, 2023. "Single machine scheduling with due date assignment to minimize the total weighted lead time penalty and late work," Omega, Elsevier, vol. 121(C).
    11. Györgyi, Péter & Kis, Tamás, 2020. "A common approximation framework for early work, late work, and resource leveling problems," European Journal of Operational Research, Elsevier, vol. 286(1), pages 129-137.
    12. 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.
    13. Ruyan He & Jinjiang Yuan, 2020. "Two-Agent Preemptive Pareto-Scheduling to Minimize Late Work and Other Criteria," Mathematics, MDPI, vol. 8(9), pages 1-18, September.
    14. 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.
    15. Xin Chen & Malgorzata Sterna & Xin Han & Jacek Blazewicz, 2016. "Scheduling on parallel identical machines with late work criterion: Offline and online cases," Journal of Scheduling, Springer, vol. 19(6), pages 729-736, December.
    16. 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.
    17. Yuan Zhang & Jinjiang Yuan, 2019. "A note on a two-agent scheduling problem related to the total weighted late work," Journal of Combinatorial Optimization, Springer, vol. 37(3), pages 989-999, April.
    18. Xin Chen & Sergey Kovalev & Małgorzata Sterna & Jacek Błażewicz, 2021. "Mirror scheduling problems with early work and late work criteria," Journal of Scheduling, Springer, vol. 24(5), pages 483-487, October.
    19. Sterna, Malgorzata, 2011. "A survey of scheduling problems with late work criteria," Omega, Elsevier, vol. 39(2), pages 120-129, April.
    20. Justkowiak, Jan-Erik & Kovalev, Sergey & Kovalyov, Mikhail Y. & Pesch, Erwin, 2023. "Single machine scheduling with assignable due dates to minimize maximum and total late work," European Journal of Operational Research, Elsevier, vol. 308(1), pages 76-83.

    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:joptap:v:174:y:2017:i:3:d:10.1007_s10957-017-1147-7. 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.