IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v255y2016i1p21-33.html
   My bibliography  Save this article

Modeling the Parallel Machine Scheduling Problem with Step Deteriorating Jobs

Author

Listed:
  • Lalla-Ruiz, Eduardo
  • Voß, Stefan

Abstract

This paper addresses the Parallel Machine Scheduling Problem with Step Deteriorating Jobs. This problem arises from real environments in which processing a job later than at a specific time may require an extra processing time. This time-dependent variation is known in the literature as step deterioration and has several practical applications (production planning, computer programming, medicine treatment, equipment maintenance, etc.). In the problem tackled in this work we aim to minimize the total completion time on identical parallel machines where each job has a deteriorating date and observes a step function for the processing time. For solving it, we propose two novel mathematical models based on the Set Partitioning Problem (SPP) that improve the unique model proposed in the literature. The computational performance of these models implemented in a general purpose solver allows to compete with the best algorithms proposed in the literature. Finally, we provide some insights for managing similar SPP formulations when large-sized instances have to be addressed.

Suggested Citation

  • Lalla-Ruiz, Eduardo & Voß, Stefan, 2016. "Modeling the Parallel Machine Scheduling Problem with Step Deteriorating Jobs," European Journal of Operational Research, Elsevier, vol. 255(1), pages 21-33.
  • Handle: RePEc:eee:ejores:v:255:y:2016:i:1:p:21-33
    DOI: 10.1016/j.ejor.2016.04.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221716302296
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.ejor.2016.04.010?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. Cheng, T. C. E. & Ding, Q., 2001. "Single machine scheduling with step-deteriorating processing times," European Journal of Operational Research, Elsevier, vol. 134(3), pages 623-630, November.
    2. Leung, Joseph Y.-T. & Ng, C.T. & Cheng, T.C. Edwin, 2008. "Minimizing sum of completion times for batch scheduling of jobs with deteriorating processing times," European Journal of Operational Research, Elsevier, vol. 187(3), pages 1090-1099, June.
    3. Cheng, T. C. E. & Sin, C. C. S., 1990. "A state-of-the-art review of parallel-machine scheduling research," European Journal of Operational Research, Elsevier, vol. 47(3), pages 271-292, August.
    4. Blazewicz, Jacek & Dror, Moshe & Weglarz, Jan, 1991. "Mathematical programming formulations for machine scheduling: A survey," European Journal of Operational Research, Elsevier, vol. 51(3), pages 283-300, April.
    5. 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.
    6. 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.
    7. Sundararaghavan, P. S. & Kunnathur, A. S., 1994. "Single machine scheduling with start time dependent processing times: Some solvable cases," European Journal of Operational Research, Elsevier, vol. 78(3), pages 394-403, November.
    8. Matteo Fischetti & Michele Monaci, 2014. "Exploiting Erraticism in Search," Operations Research, INFORMS, vol. 62(1), pages 114-122, February.
    9. A A K Jeng & B M T Lin, 2004. "Makespan minimization in single-machine scheduling with step-deterioration of processing times," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(3), pages 247-256, March.
    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, Qianqian & Lin, Ling & Tan, Zhiyi & Yan, Yujie, 2017. "Coordination mechanisms for scheduling games with proportional deterioration," European Journal of Operational Research, Elsevier, vol. 263(2), pages 380-389.
    2. Baruch Mor, 2023. "Single machine scheduling problems involving job-dependent step-deterioration dates and job rejection," Operational Research, Springer, vol. 23(1), pages 1-19, March.
    3. 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.

    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. 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.
    2. 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.
    3. A A K Jeng & B M T Lin, 2004. "Makespan minimization in single-machine scheduling with step-deterioration of processing times," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(3), pages 247-256, March.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Baruch Mor & Gur Mosheiov, 2012. "Batch scheduling with step‐deteriorating processing times to minimize flowtime," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(8), pages 587-600, December.
    9. 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.
    10. Biber Nurit & Mor Baruch & Schlissel Yitzhak & Shapira Dana, 2023. "Lot scheduling involving completion time problems on identical parallel machines," Operational Research, Springer, vol. 23(1), pages 1-29, March.
    11. 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.
    12. 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.
    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. S Gawiejnowicz & W-C Lee & C-L Lin & C-C Wu, 2011. "Single-machine scheduling of proportionally deteriorating jobs by two agents," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(11), pages 1983-1991, November.
    15. 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.
    16. Cheng, MingBao & Sun, ShiJie & He, LongMin, 2007. "Flow shop scheduling problems with deteriorating jobs on no-idle dominant machines," European Journal of Operational Research, Elsevier, vol. 183(1), pages 115-124, November.
    17. 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.
    18. Ji, Min & Cheng, T.C.E., 2010. "Batch scheduling of simple linear deteriorating jobs on a single machine to minimize makespan," European Journal of Operational Research, Elsevier, vol. 202(1), pages 90-98, April.
    19. Wang, Ji-Bo, 2007. "Single-machine scheduling problems with the effects of learning and deterioration," Omega, Elsevier, vol. 35(4), pages 397-402, August.
    20. Lotte Berghman & Roel Leus & Frits Spieksma, 2014. "Optimal solutions for a dock assignment problem with trailer transportation," Annals of Operations Research, Springer, vol. 213(1), pages 3-25, 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:eee:ejores:v:255:y:2016:i:1:p:21-33. 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.