IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v295y2021i3p823-837.html
   My bibliography  Save this article

Solution methods for scheduling problems with sequence-dependent deterioration and maintenance events

Author

Listed:
  • Delorme, Maxence
  • Iori, Manuel
  • Mendes, Nilson F.M.

Abstract

In this work, we study the problem of scheduling jobs and maintenance activities on a set of unrelated parallel machines, by considering that the processing time of a job increases according to a deterioration factor that depends both on the machine and on the set of jobs the machine has processed since its last maintenance. The objective we consider is to minimize the makespan. We introduce four mixed integer linear programming models, two of which using big-M constraints and the other two using an exponential number of variables. We also propose an iterated local search metaheuristic to tackle large size instances and we provide empirical evidence of the performance of the proposed approaches by means of extensive computational experiments.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:295:y:2021:i:3:p:823-837
    DOI: 10.1016/j.ejor.2021.03.067
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221721003726
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2021.03.067?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. 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.
    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. Alex J. Ruiz-Torres & Giuseppe Paletta & Rym M’Hallah, 2017. "Makespan minimisation with sequence-dependent machine deterioration and maintenance events," International Journal of Production Research, Taylor & Francis Journals, vol. 55(2), pages 462-479, January.
    4. Nesello, Vitor & Subramanian, Anand & Battarra, Maria & Laporte, Gilbert, 2018. "Exact solution of the single-machine scheduling problem with periodic maintenances and sequence-dependent setup times," European Journal of Operational Research, Elsevier, vol. 266(2), pages 498-507.
    5. Maxence Delorme, 2018. "Mathematical models and decomposition algorithms for cutting and packing problems," 4OR, Springer, vol. 16(2), pages 229-230, June.
    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. Gur Mosheiov, 1991. "V-Shaped Policies for Scheduling Deteriorating Jobs," Operations Research, INFORMS, vol. 39(6), pages 979-991, December.
    8. Kunnathur, Anand S. & Gupta, Sushil K., 1990. "Minimizing the makespan with late start penalties added to processing times in a single facility scheduling problem," European Journal of Operational Research, Elsevier, vol. 47(1), pages 56-64, July.
    9. Lee, C. -Y. & Leon, V. J., 2001. "Machine scheduling with a rate-modifying activity," European Journal of Operational Research, Elsevier, vol. 128(1), pages 119-128, January.
    10. 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.
    11. Dell’Amico, Mauro & Delorme, Maxence & Iori, Manuel & Martello, Silvano, 2019. "Mathematical models and decomposition methods for the multiple knapsack problem," European Journal of Operational Research, Elsevier, vol. 274(3), pages 886-899.
    12. 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.
    13. 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.
    14. Vitaly A. Strusevich & Kabir Rustogi, 2017. "Scheduling with Rate-Modifying Activities," International Series in Operations Research & Management Science, in: Scheduling with Time-Changing Effects and Rate-Modifying Activities, chapter 0, pages 317-331, Springer.
    15. Vitor Nesello & Maxence Delorme & Manuel Iori & Anand Subramanian, 2018. "Mathematical models and decomposition algorithms for makespan minimization in plastic rolls production," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 69(3), pages 326-339, March.
    16. Sid Browne & Uri Yechiali, 1990. "Scheduling Deteriorating Jobs on a Single Processor," Operations Research, INFORMS, vol. 38(3), pages 495-498, June.
    17. Wieslaw Kubiak & Steef van de Velde, 1998. "Scheduling deteriorating jobs to minimize makespan," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(5), pages 511-523, August.
    18. P. C. Gilmore & R. E. Gomory, 1961. "A Linear Programming Approach to the Cutting-Stock Problem," Operations Research, INFORMS, vol. 9(6), pages 849-859, December.
    19. Kramer, Arthur & Dell’Amico, Mauro & Iori, Manuel, 2019. "Enhanced arc-flow formulations to minimize weighted completion time on identical parallel machines," European Journal of Operational Research, Elsevier, vol. 275(1), pages 67-79.
    20. Clautiaux, François & Hanafi, Saïd & Macedo, Rita & Voge, Marie-Émilie & Alves, Cláudio, 2017. "Iterative aggregation and disaggregation algorithm for pseudo-polynomial network flow models with side constraints," European Journal of Operational Research, Elsevier, vol. 258(2), pages 467-477.
    21. Ji, Min & Cheng, T.C.E., 2008. "Parallel-machine scheduling with simple linear deterioration to minimize total completion time," European Journal of Operational Research, Elsevier, vol. 188(2), pages 342-347, July.
    22. P. C. Gilmore & R. E. Gomory, 1963. "A Linear Programming Approach to the Cutting Stock Problem---Part II," Operations Research, INFORMS, vol. 11(6), pages 863-888, December.
    23. Vitaly A. Strusevich & Kabir Rustogi, 2017. "Scheduling with Time-Changing Effects and Rate-Modifying Activities," International Series in Operations Research and Management Science, Springer, number 978-3-319-39574-6, April.
    24. Maxence Delorme & Manuel Iori, 2020. "Enhanced Pseudo-polynomial Formulations for Bin Packing and Cutting Stock Problems," INFORMS Journal on Computing, INFORMS, vol. 32(1), pages 101-119, January.
    25. 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.
    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. Pawnrat Thumrongvut & Kanchana Sethanan & Thitipong Jamrus & Chuleeporn Wongloucha & Rapeepan Pitakaso & Paulina Golinska-Dawson, 2022. "Metaheuristics in Business Model Development for Local Tourism Sustainability Enhancement," Mathematics, MDPI, vol. 10(24), pages 1-21, December.
    2. Mathijs Barkel & Maxence Delorme, 2023. "Arcflow Formulations and Constraint Generation Frameworks for the Two Bar Charts Packing Problem," INFORMS Journal on Computing, INFORMS, vol. 35(2), pages 475-494, March.
    3. Shen, Yilan & Zhang, Xi & Shi, Leyuan, 2022. "Joint optimization of production and maintenance for a serial–parallel hybrid two-stage production system," Reliability Engineering and System Safety, Elsevier, vol. 226(C).

    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. 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.
    2. de Lima, Vinícius L. & Alves, Cláudio & Clautiaux, François & Iori, Manuel & Valério de Carvalho, José M., 2022. "Arc flow formulations based on dynamic programming: Theoretical foundations and applications," European Journal of Operational Research, Elsevier, vol. 296(1), pages 3-21.
    3. Helmut A. Sedding, 2020. "Scheduling jobs with a V-shaped time-dependent processing time," Journal of Scheduling, Springer, vol. 23(6), pages 751-768, December.
    4. 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.
    5. Ming Liu & Feifeng Zheng & Chengbin Chu & Jiantong Zhang, 2012. "An FPTAS for uniform machine scheduling to minimize makespan with linear deterioration," Journal of Combinatorial Optimization, Springer, vol. 23(4), pages 483-492, May.
    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. 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.
    8. Stanisław Gawiejnowicz & Wiesław Kurc, 2020. "New results for an open time-dependent scheduling problem," Journal of Scheduling, Springer, vol. 23(6), pages 733-744, December.
    9. 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.
    10. Wang, Ji-Bo, 2007. "Single-machine scheduling problems with the effects of learning and deterioration," Omega, Elsevier, vol. 35(4), pages 397-402, August.
    11. Ocetkiewicz, Krzysztof M., 2010. "A FPTAS for minimizing total completion time in a single machine time-dependent scheduling problem," European Journal of Operational Research, Elsevier, vol. 203(2), pages 316-320, June.
    12. Dar-Li Yang & Wen-Hung Kuo, 2009. "Single-machine scheduling with both deterioration and learning effects," Annals of Operations Research, Springer, vol. 172(1), pages 315-327, November.
    13. Wang, Ting & Baldacci, Roberto & Lim, Andrew & Hu, Qian, 2018. "A branch-and-price algorithm for scheduling of deteriorating jobs and flexible periodic maintenance on a single machine," European Journal of Operational Research, Elsevier, vol. 271(3), pages 826-838.
    14. 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.
    15. Alan J. Soper & Vitaly A. Strusevich, 2020. "Refined conditions for V-shaped optimal sequencing on a single machine to minimize total completion time under combined effects," Journal of Scheduling, Springer, vol. 23(6), pages 665-680, December.
    16. Xinyu Sun & Tao Liu & Xin-Na Geng & Yang Hu & Jing-Xiao Xu, 2023. "Optimization of scheduling problems with deterioration effects and an optional maintenance activity," Journal of Scheduling, Springer, vol. 26(3), pages 251-266, June.
    17. 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.
    18. Wenhua Li & Libo Wang & Xing Chai & Hang Yuan, 2020. "Online Batch Scheduling of Simple Linear Deteriorating Jobs with Incompatible Families," Mathematics, MDPI, vol. 8(2), pages 1-12, February.
    19. 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.
    20. 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.

    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:295:y:2021:i:3:p:823-837. 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.