IDEAS home Printed from https://ideas.repec.org/a/pal/jorsoc/v62y2011i4d10.1057_jors.2010.26.html
   My bibliography  Save this article

Single-machine scheduling to minimize total absolute differences in waiting times with deteriorating jobs

Author

Listed:
  • L-H Sun

    (School of Business Administration, Xi’an University of Technology
    Knowledge Management & Innovation Research Centre, Xi’an Jiaotong University
    The State Key Laboratory on Mechanic Manufacturing, Xi’an Jiaotong University)

  • L-Y Sun

    (The State Key Laboratory on Mechanic Manufacturing, Xi’an Jiaotong University
    Management School, Xi'an Jiaotong University
    The Key Laboratory of the Ministry of Education on Process Control and Efficiency, Xi’an Jiaotong University)

  • J-B Wang

    (Knowledge Management & Innovation Research Centre, Xi’an Jiaotong University
    Operations Research and Cybernetics Institute, School of Science, Shenyang Institute of Aeronautical Engineering)

Abstract

In this paper we consider a single-machine scheduling problem with simple linear deterioration. By simple linear deterioration, we mean that the processing time of a job is a simple linear function of its execution starting time and its deterioration rate. The objective is to find a schedule that minimizes total absolute differences in waiting times. We show that the optimal schedule is V-shaped: jobs are arranged in descending order of their deterioration rates if they are placed before the job with the smallest deterioration rate, but in ascending order of their deterioration rates if placed after it. We prove other several properties of an optimal schedule, and introduce two efficient heuristic algorithms that are tested against a lower bound. We also provide computational results to evaluate the performance of the heuristic algorithms.

Suggested Citation

  • L-H Sun & L-Y Sun & J-B Wang, 2011. "Single-machine scheduling to minimize total absolute differences in waiting times with deteriorating jobs," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(4), pages 768-775, April.
    • Handle: RePEc:pal:jorsoc:v:62:y:2011:i:4:d:10.1057_jors.2010.26
    DOI: 10.1057/jors.2010.26
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1057/jors.2010.26
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1057/jors.2010.26?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. B Alidaee & N K Womer, 1999. "Scheduling with time dependent processing times: Review and extensions," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(7), pages 711-720, July.
    2. 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.
    3. T C E Cheng & L Y Kang & C T Ng, 2007. "Due-date assignment and parallel-machine scheduling with deteriorating jobs," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(8), pages 1103-1108, August.
    4. Uttarayan Bagchi, 1989. "Simultaneous Minimization of Mean and Variation of Flow Time and Waiting Time in Single Machine Systems," Operations Research, INFORMS, vol. 37(1), pages 118-125, February.
    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. Yurong Zhang & Xi Wang & Li-Han Zhang & Xue Jia & Ji-Bo Wang, 2024. "Different due-window assignment scheduling with deterioration effects," Journal of Combinatorial Optimization, Springer, vol. 48(5), pages 1-21, December.

    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. Min Ji & Chou-Jung Hsu & Dar-Li Yang, 2013. "Single-machine scheduling with deteriorating jobs and aging effects under an optional maintenance activity consideration," Journal of Combinatorial Optimization, Springer, vol. 26(3), pages 437-447, October.
    2. Zhao, Chuanli & Tang, Hengyong, 2012. "Two-machine flow shop scheduling with deteriorating jobs and chain precedence constraints," International Journal of Production Economics, Elsevier, vol. 136(1), pages 131-136.
    3. Jin, Xianfei & Li, Kunpeng & Sivakumar, Appa Iyer, 2013. "Scheduling and optimal delivery time quotation for customers with time sensitive demand," International Journal of Production Economics, Elsevier, vol. 145(1), pages 349-358.
    4. Li, Shisheng & Ng, C.T. & Yuan, Jinjiang, 2011. "Scheduling deteriorating jobs with CON/SLK due date assignment on a single machine," International Journal of Production Economics, Elsevier, vol. 131(2), pages 747-751, June.
    5. 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.
    6. 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.
    7. Mosheiov, Gur, 2005. "Minimizing total completion time and total deviation of job completion times from a restrictive due-date," European Journal of Operational Research, Elsevier, vol. 165(1), pages 20-33, August.
    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. Wen-Hung Wu & Yunqiang Yin & T C E Cheng & Win-Chin Lin & Juei-Chao Chen & Shin-Yi Luo & Chin-Chia Wu, 2017. "A combined approach for two-agent scheduling with sum-of-processing-times-based learning effect," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(2), pages 111-120, February.
    11. 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.
    12. T C E Cheng & L Kang & C T Ng, 2004. "Due-date assignment and single machine scheduling with deteriorating jobs," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(2), pages 198-203, February.
    13. Radosław Rudek, 2012. "Scheduling problems with position dependent job processing times: computational complexity results," Annals of Operations Research, Springer, vol. 196(1), pages 491-516, July.
    14. Li, Shisheng & Ng, C.T. & Cheng, T.C.E. & Yuan, Jinjiang, 2011. "Parallel-batch scheduling of deteriorating jobs with release dates to minimize the makespan," European Journal of Operational Research, Elsevier, vol. 210(3), pages 482-488, May.
    15. Lodree Jr., Emmett J. & Geiger, Christopher D., 2010. "A note on the optimal sequence position for a rate-modifying activity under simple linear deterioration," European Journal of Operational Research, Elsevier, vol. 201(2), pages 644-648, March.
    16. W-H Kuo & D-L Yang, 2008. "Minimizing the makespan in a single-machine scheduling problem with the cyclic process of an aging effect," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(3), pages 416-420, March.
    17. Kai-biao Sun & Hong-xing Li, 2009. "Some single-machine scheduling problems with actual time and position dependent learning effects," Fuzzy Information and Engineering, Springer, vol. 1(2), pages 161-177, June.
    18. Shakeri, Shakib & Logendran, Rasaratnam, 2007. "A mathematical programming-based scheduling framework for multitasking environments," European Journal of Operational Research, Elsevier, vol. 176(1), pages 193-209, January.
    19. Cai, X. & Lum, V. Y. S. & Chan, J. M. T., 1997. "Scheduling about a common due date with kob-dependent asymmetric earliness and tardiness penalties," European Journal of Operational Research, Elsevier, vol. 98(1), pages 154-168, April.
    20. Dirk Briskorn & Konrad Stephan & Nils Boysen, 2022. "Minimizing the makespan on a single machine subject to modular setups," Journal of Scheduling, Springer, vol. 25(1), pages 125-137, February.

    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:pal:jorsoc:v:62:y:2011:i:4:d:10.1057_jors.2010.26. 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.palgrave-journals.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.