IDEAS home Printed from https://ideas.repec.org/a/spr/snopef/v2y2021i4d10.1007_s43069-021-00096-7.html
   My bibliography  Save this article

Scheduling Piecewise Linear Deteriorating Jobs to Minimize Makespan in a Two-Machine Flowshop

Author

Listed:
  • Abbasali Jafari-Nodoushan

    (Meybod University)

  • Hassan Khademi Zare

    (Yazd University)

  • M. M. Lotfi

    (Yazd University)

  • R. Tavakkoli-Moghaddam

    (University of Tehran)

Abstract

A job processed later may consume more time in many realistic machine scheduling situations than the same job when processed earlier. This phenomenon is known as the deterioration of jobs. In this paper, two-machine flowshop scheduling problem under piecewise linear deteriorating jobs is investigated where the objective is to minimize the makespan. Deteriorating jobs may increase the makespan and it is important to obtain the optimal or near-optimal solution. Tab;At first, a Mixed Integer Non-Linear Programming (MINLP) model is presented for the problem and linearization of it is performed. After that, a branch and bound algorithm with dominance rules and lower bounds is established to solve the problem optimally. Several simple heuristics are also proposed to derive near-optimal solutions. The computational experiments are conducted through randomly generated examples to evaluate the performance of the proposed algorithms. The results demonstrate that the branch and bound algorithm can solve most medium-sized problems within a reasonable time. The heuristic algorithm is relatively accurate, with an average error percentage of less than 1.6%.

Suggested Citation

  • Abbasali Jafari-Nodoushan & Hassan Khademi Zare & M. M. Lotfi & R. Tavakkoli-Moghaddam, 2021. "Scheduling Piecewise Linear Deteriorating Jobs to Minimize Makespan in a Two-Machine Flowshop," SN Operations Research Forum, Springer, vol. 2(4), pages 1-29, December.
    • Handle: RePEc:spr:snopef:v:2:y:2021:i:4:d:10.1007_s43069-021-00096-7
    DOI: 10.1007/s43069-021-00096-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s43069-021-00096-7
    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/s43069-021-00096-7?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. Wang, Ling & Sun, Lin-Yan & Sun, Lin-Hui & Wang, Ji-Bo, 2010. "On three-machine flow shop scheduling with deteriorating jobs," International Journal of Production Economics, Elsevier, vol. 125(1), pages 185-189, May.
    2. Jun Pei & Bayi Cheng & Xinbao Liu & Panos M. Pardalos & Min Kong, 2019. "Single-machine and parallel-machine serial-batching scheduling problems with position-based learning effect and linear setup time," Annals of Operations Research, Springer, vol. 272(1), pages 217-241, January.
    3. Cheng, T. C. E. & Ding, Q. & Lin, B. M. T., 2004. "A concise survey of scheduling with time-dependent processing times," European Journal of Operational Research, Elsevier, vol. 152(1), pages 1-13, January.
    4. Abbasali Jafari & Ghasem Moslehi, 2012. "Scheduling linear deteriorating jobs to minimize the number of tardy jobs," Journal of Global Optimization, Springer, vol. 54(2), pages 389-404, October.
    5. Sid Browne & Uri Yechiali, 1990. "Scheduling Deteriorating Jobs on a Single Processor," Operations Research, INFORMS, vol. 38(3), pages 495-498, June.
    6. 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.
    Full references (including those not matched with items on IDEAS)

    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. Jun Pei & Xinbao Liu & Panos M. Pardalos & Athanasios Migdalas & Shanlin Yang, 2017. "Serial-batching scheduling with time-dependent setup time and effects of deterioration and learning on a single-machine," Journal of Global Optimization, Springer, vol. 67(1), pages 251-262, January.
    2. Stanisław Gawiejnowicz, 2020. "A review of four decades of time-dependent scheduling: main results, new topics, and open problems," Journal of Scheduling, Springer, vol. 23(1), pages 3-47, February.
    3. Wu, Chin-Chia & Lee, Wen-Chiung, 2008. "Single-machine group-scheduling problems with deteriorating setup times and job-processing times," International Journal of Production Economics, Elsevier, vol. 115(1), pages 128-133, September.
    4. Hongfeng Wang & Min Huang & Junwei Wang, 2019. "An effective metaheuristic algorithm for flowshop scheduling with deteriorating jobs," Journal of Intelligent Manufacturing, Springer, vol. 30(7), pages 2733-2742, October.
    5. Sun, Lin-Hui & Sun, Lin-Yan & Wang, Ming-Zheng & Wang, Ji-Bo, 2012. "Flow shop makespan minimization scheduling with deteriorating jobs under dominating machines," International Journal of Production Economics, Elsevier, vol. 138(1), pages 195-200.
    6. Lee, Wen-Chiung & Shiau, Yau-Ren & Chen, Shiuan-Kang & Wu, Chin-Chia, 2010. "A two-machine flowshop scheduling problem with deteriorating jobs and blocking," International Journal of Production Economics, Elsevier, vol. 124(1), pages 188-197, March.
    7. C-C He & C-C Wu & W-C Lee, 2009. "Branch-and-bound and weight-combination search algorithms for the total completion time problem with step-deteriorating jobs," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(12), pages 1759-1766, December.
    8. Jun Pei & Xinbao Liu & Panos M. Pardalos & Wenjuan Fan & Shanlin Yang, 2017. "Scheduling deteriorating jobs on a single serial-batching machine with multiple job types and sequence-dependent setup times," Annals of Operations Research, Springer, vol. 249(1), pages 175-195, February.
    9. Wang, Ling & Sun, Lin-Yan & Sun, Lin-Hui & Wang, Ji-Bo, 2010. "On three-machine flow shop scheduling with deteriorating jobs," International Journal of Production Economics, Elsevier, vol. 125(1), pages 185-189, May.
    10. 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.
    11. Li, Yongqiang & Li, Gang & Sun, Linyan & Xu, Zhiyong, 2009. "Single machine scheduling of deteriorating jobs to minimize total absolute differences in completion times," International Journal of Production Economics, Elsevier, vol. 118(2), pages 424-429, April.
    12. Zhao, Chuan-Li & Tang, Heng-Yong, 2010. "Scheduling deteriorating jobs under disruption," International Journal of Production Economics, Elsevier, vol. 125(2), pages 294-299, June.
    13. C. Ng & Q. Ding & T. Cheng & S. Lam, 2012. "Preemptive repayment policy for multiple loans," Annals of Operations Research, Springer, vol. 192(1), pages 141-150, January.
    14. Ma, Ran & Tao, Jiping & Yuan, Jinjiang, 2016. "Online scheduling with linear deteriorating jobs to minimize the total weighted completion time," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 570-583.
    15. Wang, Xiuli & Edwin Cheng, T.C., 2007. "Single-machine scheduling with deteriorating jobs and learning effects to minimize the makespan," European Journal of Operational Research, Elsevier, vol. 178(1), pages 57-70, April.
    16. Delorme, Maxence & Iori, Manuel & Mendes, Nilson F.M., 2021. "Solution methods for scheduling problems with sequence-dependent deterioration and maintenance events," European Journal of Operational Research, Elsevier, vol. 295(3), pages 823-837.
    17. Xing Chai & Wenhua Li & Hang Yuan & Libo Wang, 2022. "Online scheduling on a single machine with linear deteriorating processing times and delivery times," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 1900-1912, October.
    18. J-B Wang & Z-Q Xia, 2006. "Flow shop scheduling problems with deteriorating jobs under dominating machines," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(2), pages 220-226, February.
    19. Cheng, Yushao & Sun, Shijie, 2009. "Scheduling linear deteriorating jobs with rejection on a single machine," European Journal of Operational Research, Elsevier, vol. 194(1), pages 18-27, April.
    20. Abbasali Jafari & Ghasem Moslehi, 2012. "Scheduling linear deteriorating jobs to minimize the number of tardy jobs," Journal of Global Optimization, Springer, vol. 54(2), pages 389-404, October.

    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:snopef:v:2:y:2021:i:4:d:10.1007_s43069-021-00096-7. 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.