IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v284y2020i1p67-74.html
   My bibliography  Save this article

Fully polynomial time approximation scheme to maximize early work on parallel machines with common due date

Author

Listed:
  • Chen, Xin
  • Liang, Yage
  • Sterna, Małgorzata
  • Wang, Wen
  • Błażewicz, Jacek

Abstract

We study the scheduling problem on parallel identical machines in order to maximize the total early work, i.e. the parts of non-preemptive jobs executed before a common due date, and investigate mainly the model with a fixed number of machines, for which a dynamic programming approach and a fully polynomial time approximation scheme (FPTAS) are proposed. The proposal of these methods allowed us to establish the complexity and approximability status of this problem more exactly. Moreover, since our FPTAS can be also applied for the two-machine case, we improve considerably the result known in the literature for this model, in which a polynomial time approximation scheme (PTAS) was given. The new FPTAS has not only the best computational complexity, but also the much better approximation ratio than the PTAS. Finally, the theoretical studies are completed with computational experiments, performed for dynamic programming, PTAS and FPTAS, showing the high efficiencies of FPTAS both in terms of time consumption and solution quality.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:284:y:2020:i:1:p:67-74
    DOI: 10.1016/j.ejor.2019.12.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221719309877
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2019.12.003?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. Defever, Fabrice & Imbruno, Michele & Kneller, Richard, 2020. "Trade liberalization, input intermediaries and firm productivity: Evidence from China," Journal of International Economics, Elsevier, vol. 126(C).
    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. Jianfeng Ren & Yuzhong Zhang & Guo Sun, 2009. "The Np-Hardness Of Minimizing The Total Late Work On An Unbounded Batch Machine," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 26(03), pages 351-363.
    4. Spyros Galanis, 2021. "Speculative trade and the value of public information," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 23(1), pages 53-68, February.
    5. 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.
    6. 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.
    7. Sterna, Malgorzata, 2011. "A survey of scheduling problems with late work criteria," Omega, Elsevier, vol. 39(2), pages 120-129, April.
    8. Wu, Chin-Chia & Lee, Wen-Chiung, 2006. "Two-machine flowshop scheduling to minimize mean flow time under linear deterioration," International Journal of Production Economics, Elsevier, vol. 103(2), pages 572-584, October.
    9. Enrique Gerstl & Baruch Mor & Gur Mosheiov, 2019. "Scheduling on a proportionate flowshop to minimise total late work," International Journal of Production Research, Taylor & Francis Journals, vol. 57(2), pages 531-543, January.
    10. 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.
    11. 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.
    12. Shioura, Akiyoshi & Shakhlevich, Natalia V. & Strusevich, Vitaly A., 2018. "Preemptive models of scheduling with controllable processing times and of scheduling with imprecise computation: A review of solution approaches," European Journal of Operational Research, Elsevier, vol. 266(3), pages 795-818.
    13. Galanis, S. & Ioannou, C. & Kotronis, S., 2019. "Information Aggregation Under Ambiguity: Theory and Experimental Evidence," Working Papers 20/05, Department of Economics, City University London.
    14. 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.
    15. Paul Levine & Joseph Pearlman & Stephen Wright & Bo Yang, 2019. "Information, VARs and DSGE Models," School of Economics Discussion Papers 1619, School of Economics, University of Surrey.
    16. 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.
    17. Shang-Chia Liu & Jiahui Duan & Win-Chin Lin & Wen-Hsiang Wu & Jan-Yee Kung & Hau Chen & Chin-Chia Wu, 2018. "A Branch-and-Bound Algorithm for Two-Agent Scheduling with Learning Effect and Late Work Criterion," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(05), pages 1-24, October.
    18. 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.
    19. Mamageishvili, A. & Schlegel, J. C., 2019. "Optimal Smart Contracts with Costly Verification," Working Papers 19/13, Department of Economics, City University London.
    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. 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.
    2. 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.
    3. 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.
    4. Sterna, Małgorzata, 2021. "Late and early work scheduling: A survey," Omega, Elsevier, vol. 104(C).
    5. 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.
    6. 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.
    7. 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. Sterna, Małgorzata, 2021. "Late and early work scheduling: A survey," Omega, Elsevier, vol. 104(C).
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    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. 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. Liu, Changqing & He, Yigang & Peng, Guanghan, 2019. "The stabilization effect of self-delayed flux integral for two-lane lattice hydrodynamic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    13. Torres-Vargas, G. & Fossion, R. & Méndez-Bermúdez, J.A., 2020. "Normal mode analysis of spectra of random networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    14. Aldakheel, F. & Ismail, M.S. & Hughes, K.J. & Ingham, D.B. & Ma, L. & Pourkashanian, M. & Cumming, D. & Smith, R., 2020. "Gas permeability, wettability and morphology of gas diffusion layers before and after performing a realistic ex-situ compression test," Renewable Energy, Elsevier, vol. 151(C), pages 1082-1091.
    15. Zhu, Wen-Xing & Zhang, Jing-Yu & Song, Ze-Rui, 2019. "Study on braking process of vehicles at the signalized intersection based on car-following theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1306-1314.
    16. Borjas, George J. & Cassidy, Hugh, 2019. "The wage penalty to undocumented immigration," Labour Economics, Elsevier, vol. 61(C).
    17. Birol, Fatih & Okogu, Bright E., 1997. "Purchasing-Power-Parity (PPP) approach to energy-efficiency measurement: Implications for energy and environmental policy," Energy, Elsevier, vol. 22(1), pages 7-16.
    18. 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.
    19. Sen, Parongama, 2020. "Scaling and crossover behaviour in a truncated long range quantum walk," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    20. Gargiulo, Nicola & Peluso, Antonio & Aprea, Paolo & Marino, Ottavio & Cioffi, Raffaele & Jannelli, Elio & Cimino, Stefano & Lisi, Luciana & Caputo, Domenico, 2019. "Chromium-based MIL-101 metal organic framework as a fully regenerable D4 adsorbent for biogas purification," Renewable Energy, Elsevier, vol. 138(C), pages 230-235.

    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:eee:ejores:v:284:y:2020:i:1:p:67-74. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.