IDEAS home Printed from https://ideas.repec.org/a/pal/jorsoc/v58y2007i3d10.1057_palgrave.jors.2602141.html
   My bibliography  Save this article

Minimizing total tardiness in an unrelated parallel-machine scheduling problem

Author

Listed:
  • S-O Shim

    (Korea Advanced Institute of Science and Technology, Yusong-gu)

  • Y-D Kim

    (Korea Advanced Institute of Science and Technology, Yusong-gu)

Abstract

We consider a problem of scheduling n independent jobs on m unrelated parallel machines with the objective of minimizing total tardiness. Processing times of a job on different machines may be different on unrelated parallel-machine scheduling problems. We develop several dominance properties and lower bounds for the problem, and suggest a branch and bound algorithm using them. Results of computational experiments show that the suggested algorithm gives optimal solutions for problems with up to five machines and 20 jobs in a reasonable amount of CPU time.

Suggested Citation

  • S-O Shim & Y-D Kim, 2007. "Minimizing total tardiness in an unrelated parallel-machine scheduling problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(3), pages 346-354, March.
    • Handle: RePEc:pal:jorsoc:v:58:y:2007:i:3:d:10.1057_palgrave.jors.2602141
    DOI: 10.1057/palgrave.jors.2602141
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1057/palgrave.jors.2602141
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1057/palgrave.jors.2602141?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. Panwalkar, S. S. & Smith, M. L. & Koulamas, C. P., 1993. "A heuristic for the single machine tardiness problem," European Journal of Operational Research, Elsevier, vol. 70(3), pages 304-310, November.
    2. Kondakci, Suna & Kirca, Omer & Azizoglu, Meral, 1994. "An efficient algorithm for the single machine tardiness problem," International Journal of Production Economics, Elsevier, vol. 36(2), pages 213-219, September.
    3. Ari P. J. Vepsalainen & Thomas E. Morton, 1987. "Priority Rules for Job Shops with Weighted Tardiness Costs," Management Science, INFORMS, vol. 33(8), pages 1035-1047, August.
    4. Azizoglu, Meral & Kirca, Omer, 1998. "Tardiness minimization on parallel machines," International Journal of Production Economics, Elsevier, vol. 55(2), pages 163-168, July.
    5. Yalaoui, Farouk & Chu, Chengbin, 2002. "Parallel machine scheduling to minimize total tardiness," International Journal of Production Economics, Elsevier, vol. 76(3), pages 265-279, April.
    6. J N D Gupta & A J Ruiz-torres & S Webster, 2003. "Minimizing maximum tardiness and number of tardy jobs on parallel machines subject to minimum flow-time," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(12), pages 1263-1274, December.
    7. Lee, Young Hoon & Pinedo, Michael, 1997. "Scheduling jobs on parallel machines with sequence-dependent setup times," European Journal of Operational Research, Elsevier, vol. 100(3), pages 464-474, August.
    8. Ali Dogramaci & Julius Surkis, 1979. "Evaluation of a Heuristic for Scheduling Independent Jobs on Parallel Identical Processors," Management Science, INFORMS, vol. 25(12), pages 1208-1216, December.
    9. Chris N. Potts & Luk N. Van Wassenhove, 1985. "A Branch and Bound Algorithm for the Total Weighted Tardiness Problem," Operations Research, INFORMS, vol. 33(2), pages 363-377, April.
    10. Hamilton Emmons, 1969. "One-Machine Sequencing to Minimize Certain Functions of Job Tardiness," Operations Research, INFORMS, vol. 17(4), pages 701-715, August.
    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. Chung-Ho Su & Jen-Ya Wang, 2022. "A Branch-and-Bound Algorithm for Minimizing the Total Tardiness of Multiple Developers," Mathematics, MDPI, vol. 10(7), pages 1-24, April.
    2. Hongliang Zhang & Yujuan Wu & Ruilin Pan & Gongjie Xu, 2021. "Two-stage parallel speed-scaling machine scheduling under time-of-use tariffs," Journal of Intelligent Manufacturing, Springer, vol. 32(1), pages 91-112, January.
    3. Wang, Haibo & Alidaee, Bahram, 2019. "Effective heuristic for large-scale unrelated parallel machines scheduling problems," Omega, Elsevier, vol. 83(C), pages 261-274.
    4. Kerem Bülbül & Halil Şen, 2017. "An exact extended formulation for the unrelated parallel machine total weighted completion time problem," Journal of Scheduling, Springer, vol. 20(4), pages 373-389, August.

    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. Shim, Sang-Oh & Kim, Yeong-Dae, 2007. "Scheduling on parallel identical machines to minimize total tardiness," European Journal of Operational Research, Elsevier, vol. 177(1), pages 135-146, February.
    2. Söhnke Maecker & Liji Shen, 2020. "Solving parallel machine problems with delivery times and tardiness objectives," Annals of Operations Research, Springer, vol. 285(1), pages 315-334, February.
    3. Biskup, Dirk & Herrmann, Jan & Gupta, Jatinder N.D., 2008. "Scheduling identical parallel machines to minimize total tardiness," International Journal of Production Economics, Elsevier, vol. 115(1), pages 134-142, September.
    4. Yalaoui, Farouk & Chu, Chengbin, 2002. "Parallel machine scheduling to minimize total tardiness," International Journal of Production Economics, Elsevier, vol. 76(3), pages 265-279, April.
    5. Chen, Jeng-Fung & Wu, Tai-Hsi, 2006. "Total tardiness minimization on unrelated parallel machine scheduling with auxiliary equipment constraints," Omega, Elsevier, vol. 34(1), pages 81-89, January.
    6. Alidaee, Bahram & Kochenberger, Gary A. & Amini, Mohammad M., 2001. "Greedy solutions of selection and ordering problems," European Journal of Operational Research, Elsevier, vol. 134(1), pages 203-215, October.
    7. Tanaka, Shunji & Araki, Mituhiko, 2008. "A branch-and-bound algorithm with Lagrangian relaxation to minimize total tardiness on identical parallel machines," International Journal of Production Economics, Elsevier, vol. 113(1), pages 446-458, May.
    8. Sen, Tapan & Sulek, Joanne M. & Dileepan, Parthasarati, 2003. "Static scheduling research to minimize weighted and unweighted tardiness: A state-of-the-art survey," International Journal of Production Economics, Elsevier, vol. 83(1), pages 1-12, January.
    9. Arthur Kramer & Anand Subramanian, 2019. "A unified heuristic and an annotated bibliography for a large class of earliness–tardiness scheduling problems," Journal of Scheduling, Springer, vol. 22(1), pages 21-57, February.
    10. J. J. Kanet, 2007. "New Precedence Theorems for One-Machine Weighted Tardiness," Mathematics of Operations Research, INFORMS, vol. 32(3), pages 579-588, August.
    11. Koulamas, Christos, 2010. "The single-machine total tardiness scheduling problem: Review and extensions," European Journal of Operational Research, Elsevier, vol. 202(1), pages 1-7, April.
    12. Su, Ling-Huey & Chen, Chung-Jung, 2008. "Minimizing total tardiness on a single machine with unequal release dates," European Journal of Operational Research, Elsevier, vol. 186(2), pages 496-503, April.
    13. Og[breve]uz, Ceyda & Sibel Salman, F. & Bilgintürk YalçIn, Zehra, 2010. "Order acceptance and scheduling decisions in make-to-order systems," International Journal of Production Economics, Elsevier, vol. 125(1), pages 200-211, May.
    14. S-W Lin & K-C Ying, 2008. "A hybrid approach for single-machine tardiness problems with sequence-dependent setup times," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(8), pages 1109-1119, August.
    15. Valente, Jorge M.S., 2007. "Improving the performance of the ATC dispatch rule by using workload data to determine the lookahead parameter value," International Journal of Production Economics, Elsevier, vol. 106(2), pages 563-573, April.
    16. Christos Koulamas, 1997. "Decomposition and hybrid simulated annealing heuristics for the parallel‐machine total tardiness problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 44(1), pages 109-125, February.
    17. Bilge, Umit & Kurtulan, Mujde & Kirac, Furkan, 2007. "A tabu search algorithm for the single machine total weighted tardiness problem," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1423-1435, February.
    18. Daniel Schubert & André Scholz & Gerhard Wäscher, 2017. "Integrated Order Picking and Vehicle Routing with Due Dates," FEMM Working Papers 170007, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.
    19. Donghun Lee & Hyeongwon Kang & Dongjin Lee & Jeonwoo Lee & Kwanho Kim, 2023. "Deep Reinforcement Learning-Based Scheduler on Parallel Dedicated Machine Scheduling Problem towards Minimizing Total Tardiness," Sustainability, MDPI, vol. 15(4), pages 1-14, February.
    20. Chengbin Chu, 1992. "A branch‐and‐bound algorithm to minimize total tardiness with different release dates," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(2), pages 265-283, March.

    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:pal:jorsoc:v:58:y:2007:i:3:d:10.1057_palgrave.jors.2602141. 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.palgrave-journals.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.