IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/vyid10.1007_s10878-020-00607-y.html
   My bibliography  Save this article

A multi-objective simulated annealing to solve an identical parallel machine scheduling problem with deterioration effect and resources consumption constraints

Author

Listed:
  • Norelhouda Sekkal

    (University of Tlemcen)

  • Fayçal Belkaid

    (University of Tlemcen)

Abstract

Production systems are subject to machine deterioration and resource consumption constraints. The deterioration increases the processing time which leads to an increase in resource consumption. In this study, we investigate and model the behavior of a parallel machine scheduling problem with respect to the processing time. The machine is subject to deterioration and includes two resource consumption constraints. The first resource R1 controls the processing time so that additional amounts of R1 decrease the processing time. The second R2 is controlled by the actual processing time so that R2 consumption is a linear function of the actual processing time. The increment of R1 consumption leads to processing time and so R2 decrement. Solving this problem consists in finding the optimal schedule that will minimize both makespan and resources cost. This paper provides a mathematical programming model. In fact, due to the deterioration effect and the two resource consumptions, solving such a problem may be very difficult and requires a large computational time. In this paper, we introduce a multi objective simulated annealing (MOSA) in order to solve the combinatorial optimization problem related to finding the best combination (machine, job, position, R1). Literally the best jobs assignment and resources allocation so that makespan and resources cost are minimized. In order to improve the quality of the results we also developed a 2-steps algorithm by decomposing the original problem into two sub problems: an assignment problem and a resources allocation problem. Some simulations were performed to analyze the performances of the two algorithms. The results show that the 2-steps algorithm is very efficient and outperforms MOSA.

Suggested Citation

  • Norelhouda Sekkal & Fayçal Belkaid, 0. "A multi-objective simulated annealing to solve an identical parallel machine scheduling problem with deterioration effect and resources consumption constraints," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-37.
  • Handle: RePEc:spr:jcomop:v::y::i::d:10.1007_s10878-020-00607-y
    DOI: 10.1007/s10878-020-00607-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-020-00607-y
    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/s10878-020-00607-y?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. Rustogi, Kabir & Strusevich, Vitaly A., 2012. "Single machine scheduling with general positional deterioration and rate-modifying maintenance," Omega, Elsevier, vol. 40(6), pages 791-804.
    2. Yang, Suh-Jenq & Yang, Dar-Li, 2010. "Minimizing the makespan on single-machine scheduling with aging effect and variable maintenance activities," Omega, Elsevier, vol. 38(6), pages 528-533, December.
    3. Sid Browne & Uri Yechiali, 1990. "Scheduling Deteriorating Jobs on a Single Processor," Operations Research, INFORMS, vol. 38(3), pages 495-498, June.
    4. Su, Ling-Huey & Lien, Chun-Yuan, 2009. "Scheduling parallel machines with resource-dependent processing times," International Journal of Production Economics, Elsevier, vol. 117(2), pages 256-266, February.
    5. Ji-Bo Wang & Jian-Jun Wang, 2015. "Research on scheduling with job-dependent learning effect and convex resource-dependent processing times," International Journal of Production Research, Taylor & Francis Journals, vol. 53(19), pages 5826-5836, October.
    6. Gara-Ali, Ahmed & Finke, Gerd & Espinouse, Marie-Laure, 2016. "Parallel-machine scheduling with maintenance: Praising the assignment problem," European Journal of Operational Research, Elsevier, vol. 252(1), pages 90-97.
    7. Fanjul-Peyro, Luis & Perea, Federico & Ruiz, Rubén, 2017. "Models and matheuristics for the unrelated parallel machine scheduling problem with additional resources," European Journal of Operational Research, Elsevier, vol. 260(2), pages 482-493.
    8. Shih-Wei Lin & Kuo-Ching Ying, 2015. "A multi-point simulated annealing heuristic for solving multiple objective unrelated parallel machine scheduling problems," International Journal of Production Research, Taylor & Francis Journals, vol. 53(4), pages 1065-1076, February.
    9. Dvir Shabtay & George Steiner, 2007. "Optimal Due Date Assignment and Resource Allocation to Minimize the Weighted Number of Tardy Jobs on a Single Machine," Manufacturing & Service Operations Management, INFORMS, vol. 9(3), pages 332-350, March.
    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. Janiak, Adam & Kovalyov, Mikhail Y., 1996. "Single machine scheduling subject to deadlines and resource dependent processing times," European Journal of Operational Research, Elsevier, vol. 94(2), pages 284-291, October.
    12. Kabir Rustogi & Vitaly A. Strusevich, 2017. "Single machine scheduling with a generalized job-dependent cumulative effect," Journal of Scheduling, Springer, vol. 20(6), pages 583-592, December.
    13. Janiak, Adam, 1998. "Minimization of the makespan in a two-machine problem under given resource constraints," European Journal of Operational Research, Elsevier, vol. 107(2), pages 325-337, June.
    14. Richard L. Daniels & Barbara J. Hoopes & Joseph B. Mazzola, 1996. "Scheduling Parallel Manufacturing Cells with Resource Flexibility," Management Science, INFORMS, vol. 42(9), pages 1260-1276, September.
    15. Zhi-Long Chen, 2004. "Simultaneous Job Scheduling and Resource Allocation on Parallel Machines," Annals of Operations Research, Springer, vol. 129(1), pages 135-153, July.
    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. Norelhouda Sekkal & Fayçal Belkaid, 2020. "A multi-objective simulated annealing to solve an identical parallel machine scheduling problem with deterioration effect and resources consumption constraints," Journal of Combinatorial Optimization, Springer, vol. 40(3), pages 660-696, October.
    2. Geurtsen, M. & Didden, Jeroen B.H.C. & Adan, J. & Atan, Z. & Adan, I., 2023. "Production, maintenance and resource scheduling: A review," European Journal of Operational Research, Elsevier, vol. 305(2), pages 501-529.
    3. Du-Juan Wang & Yunqiang Yin & Mengqi Liu, 2016. "Bicriteria scheduling problems involving job rejection, controllable processing times and rate-modifying activity," International Journal of Production Research, Taylor & Francis Journals, vol. 54(12), pages 3691-3705, June.
    4. Finke, Gerd & Gara-Ali, Ahmed & Espinouse, Marie-Laure & Jost, Vincent & Moncel, Julien, 2017. "Unified matrix approach to solve production-maintenance problems on a single machine," Omega, Elsevier, vol. 66(PA), pages 140-146.
    5. Anna Arigliano & Gianpaolo Ghiani & Antonio Grieco & Emanuela Guerriero, 2017. "Single-machine time-dependent scheduling problems with fixed rate-modifying activities and resumable jobs," 4OR, Springer, vol. 15(2), pages 201-215, 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. 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.
    8. Shabtay, Dvir & Bensoussan, Yaron & Kaspi, Moshe, 2012. "A bicriteria approach to maximize the weighted number of just-in-time jobs and to minimize the total resource consumption cost in a two-machine flow-shop scheduling system," International Journal of Production Economics, Elsevier, vol. 136(1), pages 67-74.
    9. Liliana Grigoriu & Dirk Briskorn, 2017. "Scheduling jobs and maintenance activities subject to job-dependent machine deteriorations," Journal of Scheduling, Springer, vol. 20(2), pages 183-197, April.
    10. Dujuan Wang & Yugang Yu & Huaxin Qiu & Yunqiang Yin & T. C. E. Cheng, 2020. "Two‐agent scheduling with linear resource‐dependent processing times," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(7), pages 573-591, October.
    11. Shabtay, Dvir & Steiner, George & Zhang, Rui, 2016. "Optimal coordination of resource allocation, due date assignment and scheduling decisions," Omega, Elsevier, vol. 65(C), pages 41-54.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. Xu, Dehua & Wan, Long & Liu, Aihua & Yang, Dar-Li, 2015. "Single machine total completion time scheduling problem with workload-dependent maintenance duration," Omega, Elsevier, vol. 52(C), pages 101-106.
    19. 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.
    20. Leyvand, Yaron & Shabtay, Dvir & Steiner, George, 2010. "A unified approach for scheduling with convex resource consumption functions using positional penalties," European Journal of Operational Research, Elsevier, vol. 206(2), pages 301-312, 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:jcomop:v::y::i::d:10.1007_s10878-020-00607-y. 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.