IDEAS home Printed from https://ideas.repec.org/a/eee/proeco/v119y2009i2p298-307.html
   My bibliography  Save this article

A bicriteria approach to minimize number of tardy jobs and resource consumption in scheduling a single machine

Author

Listed:
  • Yedidsion, Liron
  • Shabtay, Dvir
  • Korach, Ephraim
  • Kaspi, Moshe

Abstract

We extend the classical scheduling problem of minimizing the number of tardy jobs in a single-machine to the case where the job processing times are controllable by allocating a continuous and non-renewable resource to the processing operations. Our aim is to construct an efficient trade-off curve between the number of tardy jobs and total resource consumption using a bicriteria approach. Most of the research on scheduling with controllable resource-dependent processing times is done either to a linear resource consumption function or to a specific type of convex resource consumption function. We, in contrast, analyze the problem for a more general type of convex decreasing resource consumption function, which guarantees a very robust analysis that can be applied to a wide range of problems. We present four different variations of the problem and prove them to be -hard. We then present a polynomial time algorithm to solve an important special case of the problem and also suggest and compare the performances of three different heuristic algorithms.

Suggested Citation

  • Yedidsion, Liron & Shabtay, Dvir & Korach, Ephraim & Kaspi, Moshe, 2009. "A bicriteria approach to minimize number of tardy jobs and resource consumption in scheduling a single machine," International Journal of Production Economics, Elsevier, vol. 119(2), pages 298-307, June.
    • Handle: RePEc:eee:proeco:v:119:y:2009:i:2:p:298-307
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0925-5273(09)00078-4
    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. In-Soo Lee, 1991. "Single machine scheduling with controllable processing times: a parametric study," International Journal of Production Economics, Elsevier, vol. 22(2), pages 105-110, November.
    2. Van Wassenhove, Luk N. & Baker, Kenneth R., 1982. "A bicriterion approach to time/cost trade-offs in sequencing," European Journal of Operational Research, Elsevier, vol. 11(1), pages 48-54, September.
    3. 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.
    4. Chung-Yee Lee & Lei Lei, 2001. "Multiple-Project Scheduling with Controllable Project Duration and Hard Resource Constraint: Some Solvable Cases," Annals of Operations Research, Springer, vol. 102(1), pages 287-307, February.
    5. 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.
    6. 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.
    7. J. Michael Moore, 1968. "An n Job, One Machine Sequencing Algorithm for Minimizing the Number of Late Jobs," Management Science, INFORMS, vol. 15(1), pages 102-109, September.
    8. Biskup, Dirk & Jahnke, Hermann, 2001. "Common due date assignment for scheduling on a single machine with jointly reducible processing times," International Journal of Production Economics, Elsevier, vol. 69(3), pages 317-322, 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.
    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. Vinod, V. & Sridharan, R., 2011. "Simulation modeling and analysis of due-date assignment methods and scheduling decision rules in a dynamic job shop production system," International Journal of Production Economics, Elsevier, vol. 129(1), pages 127-146, January.
    2. 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.

    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. Dvir Shabtay & George Steiner, 2008. "The single-machine earliness-tardiness scheduling problem with due date assignment and resource-dependent processing times," Annals of Operations Research, Springer, vol. 159(1), pages 25-40, March.
    2. Yaron Leyvand & Dvir Shabtay & George Steiner & Liron Yedidsion, 2010. "Just-in-time scheduling with controllable processing times on parallel machines," Journal of Combinatorial Optimization, Springer, vol. 19(3), pages 347-368, April.
    3. 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.
    4. Koulamas, Christos & Gupta, Sushil & Kyparisis, George J., 2010. "A unified analysis for the single-machine scheduling problem with controllable and non-controllable variable job processing times," European Journal of Operational Research, Elsevier, vol. 205(2), pages 479-482, September.
    5. Daniel Ng, C. T. & Cheng, T. C. Edwin & Kovalyov, Mikhail Y., 2004. "Single machine batch scheduling with jointly compressible setup and processing times," European Journal of Operational Research, Elsevier, vol. 153(1), pages 211-219, February.
    6. 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.
    7. 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.
    8. J-G Kim & D-H Lee, 2009. "Algorithms for common due-date assignment and sequencing on a single machine with sequence-dependent setup times," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(9), pages 1264-1272, September.
    9. Janiak, Adam & Kovalyov, Mikhail Y. & Portmann, Marie-Claude, 2005. "Single machine group scheduling with resource dependent setup and processing times," European Journal of Operational Research, Elsevier, vol. 162(1), pages 112-121, April.
    10. 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.
    11. Gordon, Valery & Proth, Jean-Marie & Chu, Chengbin, 2002. "A survey of the state-of-the-art of common due date assignment and scheduling research," European Journal of Operational Research, Elsevier, vol. 139(1), pages 1-25, May.
    12. Du-Juan Wang & Yunqiang Yin & Shuenn-Ren Cheng & T.C.E. Cheng & Chin-Chia Wu, 2016. "Due date assignment and scheduling on a single machine with two competing agents," International Journal of Production Research, Taylor & Francis Journals, vol. 54(4), pages 1152-1169, February.
    13. 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.
    14. Dvir Shabtay & Moshe Kaspi, 2006. "Minimizing the makespan in open‐shop scheduling problems with a convex resource consumption function," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(3), pages 204-216, April.
    15. 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.
    16. Biskup, Dirk, 1999. "Single-machine scheduling with learning considerations," European Journal of Operational Research, Elsevier, vol. 115(1), pages 173-178, May.
    17. Oron, Daniel, 2016. "Scheduling controllable processing time jobs with position-dependent workloads," International Journal of Production Economics, Elsevier, vol. 173(C), pages 153-160.
    18. Cheng, T. C. E. & Ng, C. T. & Yuan, J. J. & Liu, Z. H., 2005. "Single machine scheduling to minimize total weighted tardiness," European Journal of Operational Research, Elsevier, vol. 165(2), pages 423-443, September.
    19. Min Ji & Sai Liu & Xiaolin Zhang & Keke Cao & T. C. E. Cheng, 2017. "Sequencing Games with Slack Due Windows and Group Technology Considerations," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(2), pages 121-133, February.
    20. Mor, Baruch & Mosheiov, Gur, 2012. "Scheduling a maintenance activity and due-window assignment based on common flow allowance," International Journal of Production Economics, Elsevier, vol. 135(1), pages 222-230.

    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:proeco:v:119:y:2009:i:2:p:298-307. 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/ijpe .

    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.