IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v75y2020i1d10.1007_s10589-019-00142-5.html
   My bibliography  Save this article

Heuristics for the single machine weighted sum of completion times scheduling problem with periodic maintenance

Author

Listed:
  • Hanane Krim

    (Polytechnic University of Hauts-de-France)

  • Rachid Benmansour

    (Polytechnic University of Hauts-de-France
    INSEA)

  • David Duvivier

    (Polytechnic University of Hauts-de-France)

  • Daoud Aït-Kadi

    (University of Laval)

  • Said Hanafi

    (Polytechnic University of Hauts-de-France)

Abstract

This paper tackles the single machine scheduling problem with periodic preventive maintenance in order to minimize the weighted sum of completion times. This criterion is certainly less studied than the makespan but it remains nonetheless interesting on the theoretical and practical levels. Indeed, the weights can quantify the holding cost per unit of time of the products to transform. Thus, this criterion can represent the global holding cost. This problem is proved to be NP-hard and a mixed integer linear programming formulation is proposed to solve small size instances of the problem. To solve large instances, we proposed three properties for this problem which generalize already existing works. These properties have been of great use in designing efficient heuristics capable of solving instances with up to 1000 jobs. To evaluate the performances of the proposed heuristics, lower bounds based on special cases of the problem are provided. Computational experiments show that the average percentage error of the best heuristic is less than 10%.

Suggested Citation

  • Hanane Krim & Rachid Benmansour & David Duvivier & Daoud Aït-Kadi & Said Hanafi, 2020. "Heuristics for the single machine weighted sum of completion times scheduling problem with periodic maintenance," Computational Optimization and Applications, Springer, vol. 75(1), pages 291-320, January.
  • Handle: RePEc:spr:coopap:v:75:y:2020:i:1:d:10.1007_s10589-019-00142-5
    DOI: 10.1007/s10589-019-00142-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-019-00142-5
    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/s10589-019-00142-5?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. Kacem, Imed & Chu, Chengbin, 2008. "Worst-case analysis of the WSPT and MWSPT rules for single machine scheduling with one planned setup period," European Journal of Operational Research, Elsevier, vol. 187(3), pages 1080-1089, June.
    2. Guoqing Wang & Hongyi Sun & Chengbin Chu, 2005. "Preemptive Scheduling with Availability Constraints to Minimize Total Weighted Completion Times," Annals of Operations Research, Springer, vol. 133(1), pages 183-192, January.
    3. Roux, O. & Duvivier, D. & Quesnel, G. & Ramat, E., 2013. "Optimization of preventive maintenance through a combined maintenance-production simulation model," International Journal of Production Economics, Elsevier, vol. 143(1), pages 3-12.
    4. Li, Guo & Liu, Mengqi & Sethi, Suresh P. & Xu, Dehua, 2017. "Parallel-machine scheduling with machine-dependent maintenance periodic recycles," International Journal of Production Economics, Elsevier, vol. 186(C), pages 1-7.
    5. W J Chen, 2006. "Minimizing total flow time in the single-machine scheduling problem with periodic maintenance," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(4), pages 410-415, April.
    6. Wayne E. Smith, 1956. "Various optimizers for single‐stage production," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 3(1‐2), pages 59-66, March.
    7. X Qi & T Chen & F Tu, 1999. "Scheduling the maintenance on a single machine," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(10), pages 1071-1078, October.
    8. Sadfi, Cherif & Penz, Bernard & Rapine, Christophe & Blazewicz, Jacek & Formanowicz, Piotr, 2005. "An improved approximation algorithm for the single machine total completion time scheduling problem with availability constraints," European Journal of Operational Research, Elsevier, vol. 161(1), pages 3-10, 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. Abdelhak Elidrissi & Rachid Benmansour & Nicolas Zufferey & Mohammed Benbrahim & David Duvivier, 2024. "Minimization of maximum lateness on parallel machines with a single server and job release dates," 4OR, Springer, vol. 22(3), pages 351-385, September.

    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. Kacem, Imed & Chu, Chengbin, 2008. "Efficient branch-and-bound algorithm for minimizing the weighted sum of completion times on a single machine with one availability constraint," International Journal of Production Economics, Elsevier, vol. 112(1), pages 138-150, March.
    2. 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.
    3. Imed Kacem, 2009. "Approximation algorithms for the makespan minimization with positive tails on a single machine with a fixed non-availability interval," Journal of Combinatorial Optimization, Springer, vol. 17(2), pages 117-133, February.
    4. Zhenpeng Li & Congdian Cheng, 2023. "The Expected Competitive Ratio on a Kind of Stochastic-Online Flowtime Scheduling with Machine Subject to an Uncertain Breakdown," Mathematics, MDPI, vol. 11(11), pages 1-12, May.
    5. Hans Kellerer & Vitaly A. Strusevich, 2016. "Optimizing the half-product and related quadratic Boolean functions: approximation and scheduling applications," Annals of Operations Research, Springer, vol. 240(1), pages 39-94, May.
    6. Kellerer, Hans & Kubzin, Mikhail A. & Strusevich, Vitaly A., 2009. "Two simple constant ratio approximation algorithms for minimizing the total weighted completion time on a single machine with a fixed non-availability interval," European Journal of Operational Research, Elsevier, vol. 199(1), pages 111-116, November.
    7. Jing Fan & Xiwen Lu, 2015. "Supply chain scheduling problem in the hospital with periodic working time on a single machine," Journal of Combinatorial Optimization, Springer, vol. 30(4), pages 892-905, November.
    8. Kacem, Imed & Chu, Chengbin, 2008. "Worst-case analysis of the WSPT and MWSPT rules for single machine scheduling with one planned setup period," European Journal of Operational Research, Elsevier, vol. 187(3), pages 1080-1089, June.
    9. Shabtay, Dvir & Zofi, Moshe, 2018. "Single machine scheduling with controllable processing times and an unavailability period to minimize the makespan," International Journal of Production Economics, Elsevier, vol. 198(C), pages 191-200.
    10. Hanane Krim & Nicolas Zufferey & Jean-Yves Potvin & Rachid Benmansour & David Duvivier, 2022. "Tabu search for a parallel-machine scheduling problem with periodic maintenance, job rejection and weighted sum of completion times," Journal of Scheduling, Springer, vol. 25(1), pages 89-105, February.
    11. Chen, Wen-Jinn, 2009. "Minimizing number of tardy jobs on a single machine subject to periodic maintenance," Omega, Elsevier, vol. 37(3), pages 591-599, June.
    12. Baruch Mor & Dana Shapira, 2022. "Single machine scheduling with non-availability interval and optional job rejection," Journal of Combinatorial Optimization, Springer, vol. 44(1), pages 480-497, August.
    13. Sun, Kaibiao & Li, Hongxing, 2010. "Scheduling problems with multiple maintenance activities and non-preemptive jobs on two identical parallel machines," International Journal of Production Economics, Elsevier, vol. 124(1), pages 151-158, March.
    14. Sandeep Kumar & Bhupesh Kumar Lad, 2017. "Integrated production and maintenance planning for parallel machine system considering cost of rejection," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(7), pages 834-846, July.
    15. 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.
    16. Mellouli, Racem & Sadfi, Chrif & Chu, Chengbin & Kacem, Imed, 2009. "Identical parallel-machine scheduling under availability constraints to minimize the sum of completion times," European Journal of Operational Research, Elsevier, vol. 197(3), pages 1150-1165, September.
    17. Michael Geurtsen & Jelle Adan & Alp Akçay, 2024. "Integrated maintenance and production scheduling for unrelated parallel machines with setup times," Flexible Services and Manufacturing Journal, Springer, vol. 36(3), pages 1046-1079, September.
    18. Marieke Quant & Marc Meertens & Hans Reijnierse, 2008. "Processing games with shared interest," Annals of Operations Research, Springer, vol. 158(1), pages 219-228, February.
    19. José R. Correa & Maurice Queyranne, 2012. "Efficiency of equilibria in restricted uniform machine scheduling with total weighted completion time as social cost," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(5), pages 384-395, August.
    20. Ben Hermans & Roel Leus & Jannik Matuschke, 2022. "Exact and Approximation Algorithms for the Expanding Search Problem," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 281-296, January.

    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:coopap:v:75:y:2020:i:1:d:10.1007_s10589-019-00142-5. 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.