IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v205y2010i2p325-331.html
   My bibliography  Save this article

A search method for optimal control of a flow shop system of traditional machines

Author

Listed:
  • Selvi, Omer
  • Gokbayrak, Kagan

Abstract

We consider a convex and nondifferentiable optimization problem for deterministic flow shop systems in which the arrival times of the jobs are known and jobs are processed in the order they arrive. The decision variables are the service times that are to be set only once before processing the first job, and cannot be altered between processes. The cost objective is the sum of regular costs on job completion times and service costs inversely proportional to the controllable service times. A finite set of subproblems, which can be solved by trust-region methods, are defined and their solutions are related to the optimal solution of the optimization problem under consideration. Exploiting these relationships, we introduce a two-phase search method which converges in a finite number of iterations. A numerical study is held to demonstrate the solution performance of the search method compared to a subgradient method proposed in earlier work.

Suggested Citation

  • Selvi, Omer & Gokbayrak, Kagan, 2010. "A search method for optimal control of a flow shop system of traditional machines," European Journal of Operational Research, Elsevier, vol. 205(2), pages 325-331, September.
    • Handle: RePEc:eee:ejores:v:205:y:2010:i:2:p:325-331
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(10)00009-3
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Hoogeveen, Han, 2005. "Multicriteria scheduling," European Journal of Operational Research, Elsevier, vol. 167(3), pages 592-623, December.
    2. Clyde L. Monma & Alexander Schrijver & Michael J. Todd & Victor K. Wei, 1990. "Convex Resource Allocation Problems on Directed Acyclic Graphs: Duality, Complexity, Special Cases, and Extensions," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 736-748, November.
    3. Nowicki, Eugeniusz & Zdrzalka, Stanislaw, 1988. "A two-machine flow shop scheduling problem with controllable job processing times," European Journal of Operational Research, Elsevier, vol. 34(2), pages 208-220, March.
    4. Nowicki, Eugeniusz, 1993. "An approximation algorithm for the m-machine permutation flow shop scheduling problem with controllable processing times," European Journal of Operational Research, Elsevier, vol. 70(3), pages 342-349, November.
    5. Gurel, Sinan & Akturk, M. Selim, 2007. "Considering manufacturing cost and scheduling performance on a CNC turning machine," European Journal of Operational Research, Elsevier, vol. 177(1), pages 325-343, February.
    6. R. G. Vickson, 1980. "Choosing the Job Sequence and Processing Times to Minimize Total Processing Plus Flow Cost on a Single Machine," Operations Research, INFORMS, vol. 28(5), pages 1155-1167, October.
    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. Jansen, Klaus & Mastrolilli, Monaldo & Solis-Oba, Roberto, 2005. "Approximation schemes for job shop scheduling problems with controllable processing times," European Journal of Operational Research, Elsevier, vol. 167(2), pages 297-319, December.
    2. Cheng, T. C. E. & Oguz, C. & Qi, X. D., 1996. "Due-date assignment and single machine scheduling with compressible processing times," International Journal of Production Economics, Elsevier, vol. 43(1), pages 29-35, May.
    3. Gurel, Sinan & Akturk, M. Selim, 2007. "Considering manufacturing cost and scheduling performance on a CNC turning machine," European Journal of Operational Research, Elsevier, vol. 177(1), pages 325-343, February.
    4. Wang, Ji-Bo & Xia, Zun-Quan, 2007. "Single machine scheduling problems with controllable processing times and total absolute differences penalties," European Journal of Operational Research, Elsevier, vol. 177(1), pages 638-645, February.
    5. T.C.E. Cheng & Zhi‐Long Chen & Chung‐Lun Li & B.M.‐T. Lin, 1998. "Scheduling to minimize the total compression and late costs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(1), pages 67-82, February.
    6. Hoogeveen, Han, 2005. "Multicriteria scheduling," European Journal of Operational Research, Elsevier, vol. 167(3), pages 592-623, December.
    7. Shabtay, Dvir, 2022. "Single-machine scheduling with machine unavailability periods and resource dependent processing times," European Journal of Operational Research, Elsevier, vol. 296(2), pages 423-439.
    8. Lu Liu & Jian-Jun Wang & Xiao-Yuan Wang, 2016. "Single machine due-window assignment scheduling with resource-dependent processing times to minimise total resource consumption cost," International Journal of Production Research, Taylor & Francis Journals, vol. 54(4), pages 1186-1195, February.
    9. Cheng, T. C. E. & Oguz, C. & Qi, X. D., 1996. "Due-date assignment and single machine scheduling with compressible processing times," International Journal of Production Economics, Elsevier, vol. 43(2-3), pages 107-113, June.
    10. Lee, Kangbok & Choi, Byung-Cheon, 2011. "Two-stage production scheduling with an outsourcing option," European Journal of Operational Research, Elsevier, vol. 213(3), pages 489-497, September.
    11. Carrasco, Rodrigo A. & Iyengar, Garud & Stein, Cliff, 2018. "Resource cost aware scheduling," European Journal of Operational Research, Elsevier, vol. 269(2), pages 621-632.
    12. Byung-Cheon Choi & Myoung-Ju Park, 2022. "Single-machine scheduling with resource-dependent processing times and multiple unavailability periods," Journal of Scheduling, Springer, vol. 25(2), pages 191-202, April.
    13. Kailiang Xu & Zuren Feng & Liangjun Ke, 2011. "Single machine scheduling with total tardiness criterion and convex controllable processing times," Annals of Operations Research, Springer, vol. 186(1), pages 383-391, June.
    14. Liu Guiqing & Li Kai & Cheng Bayi, 2015. "Preemptive Scheduling with Controllable Processing Times on Parallel Machines," Journal of Systems Science and Information, De Gruyter, vol. 3(1), pages 68-76, February.
    15. David Fischer & Péter Györgyi, 2023. "Approximation algorithms for coupled task scheduling minimizing the sum of completion times," Annals of Operations Research, Springer, vol. 328(2), pages 1387-1408, September.
    16. Chen, Bo & Zhang, Xiandong, 2019. "Scheduling with time-of-use costs," European Journal of Operational Research, Elsevier, vol. 274(3), pages 900-908.
    17. Ali Kordmostafapour & Javad Rezaeian & Iraj Mahdavi & Mahdi Yar Farjad, 2022. "Scheduling unrelated parallel machine problem with multi-mode processing times and batch delivery cost," OPSEARCH, Springer;Operational Research Society of India, vol. 59(4), pages 1438-1470, December.
    18. Yazdani Sabouni, M.T. & Logendran, Rasaratnam, 2013. "Carryover sequence-dependent group scheduling with the integration of internal and external setup times," European Journal of Operational Research, Elsevier, vol. 224(1), pages 8-22.
    19. Balasubramanian, Hari & Fowler, John & Keha, Ahmet & Pfund, Michele, 2009. "Scheduling interfering job sets on parallel machines," European Journal of Operational Research, Elsevier, vol. 199(1), pages 55-67, November.
    20. Yepes-Borrero, Juan C. & Perea, Federico & Ruiz, Rubén & Villa, Fulgencia, 2021. "Bi-objective parallel machine scheduling with additional resources during setups," European Journal of Operational Research, Elsevier, vol. 292(2), pages 443-455.

    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:205:y:2010:i:2:p:325-331. 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.