IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v38y1991i5p715-720.html
   My bibliography  Save this article

A proof for the longest‐job‐first policy in one‐machine scheduling

Author

Listed:
  • T. C. E. Cheng
  • H. G. Kahlbacher

Abstract

We consider a one‐machine scheduling problem with earliness and tardiness penalties. All jobs are assigned a common due date and the objective is to minimize the total penalty due to job earliness and tardiness. We are interested in finding the optimal combination of the common due‐date value and the job sequence. Despite the fact that this problem in general is very hard to solve, we prove that there exists at least a common property for all optimal solutions: The first job in an optimal sequence is one of the longest jobs. We also prove that this property holds for a general class of unimodal penalty functions.

Suggested Citation

  • T. C. E. Cheng & H. G. Kahlbacher, 1991. "A proof for the longest‐job‐first policy in one‐machine scheduling," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(5), pages 715-720, October.
    • Handle: RePEc:wly:navres:v:38:y:1991:i:5:p:715-720
    DOI: 10.1002/1520-6750(199110)38:53.0.CO;2-6
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/1520-6750(199110)38:53.0.CO;2-6
    Download Restriction: no
    File URL: https://libkey.io/10.1002/1520-6750(199110)38:53.0.CO;2-6?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
    ---><---

    References listed on IDEAS

    as
    1. S. S. Panwalkar & M. L. Smith & A. Seidmann, 1982. "Common Due Date Assignment to Minimize Total Penalty for the One Machine Scheduling Problem," Operations Research, INFORMS, vol. 30(2), pages 391-399, April.
    2. John J. Kanet, 1981. "Minimizing the average deviation of job completion times about a common due date," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 28(4), pages 643-651, December.
    3. Kenneth R. Baker & Gary D. Scudder, 1990. "Sequencing with Earliness and Tardiness Penalties: A Review," Operations Research, INFORMS, vol. 38(1), pages 22-36, February.
    4. Cheng, T. C. E. & Gupta, M. C., 1989. "Survey of scheduling research involving due date determination decisions," European Journal of Operational Research, Elsevier, vol. 38(2), pages 156-166, January.
    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. Chung‐Lun Li & T. C. E. Cheng, 1994. "The parallel machine min‐max weighted absolute lateness scheduling problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(1), pages 33-46, February.
    2. Bernard Dickman & Yonah Wilamowsky & Sheldon Epstein, 2001. "Multiple common due dates," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(4), pages 293-298, June.
    3. Zhi-Long Chen, 1997. "Scheduling with batch setup times and earliness-tardiness penalties," European Journal of Operational Research, Elsevier, vol. 96(3), pages 518-537, February.
    4. Lin, Shih-Wei & Chou, Shuo-Yan & Ying, Kuo-Ching, 2007. "A sequential exchange approach for minimizing earliness-tardiness penalties of single-machine scheduling with a common due date," European Journal of Operational Research, Elsevier, vol. 177(2), pages 1294-1301, March.
    5. Andreas C. Nearchou & Sotiris L. Omirou, 2024. "Self-Adaptive Biased Differential Evolution for Scheduling Against Common Due Dates," SN Operations Research Forum, Springer, vol. 5(2), pages 1-29, June.
    6. Umar M. Al‐Turki & John Mittenthal & M. Raghavachari, 1996. "The single‐machine absolute‐deviation early‐tardy problem with random completion times," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(4), pages 573-587, June.
    7. 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.
    8. Adamopoulos, G. I. & Pappis, C. P., 1995. "The CON due-date determination method with processing time-dependent lateness penalties," International Journal of Production Economics, Elsevier, vol. 40(1), pages 29-36, June.
    9. S.S. Panwalkar & Christos Koulamas, 2015. "On equivalence between the proportionate flow shop and single‐machine scheduling problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(7), pages 595-603, October.
    10. Soroush, H. M., 1999. "Sequencing and due-date determination in the stochastic single machine problem with earliness and tardiness costs," European Journal of Operational Research, Elsevier, vol. 113(2), pages 450-468, March.
    11. Prabuddha De & Jay B. Ghosh & Charles E. Wells, 1994. "Due‐date assignment and early/tardy scheduling on identical parallel machines," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(1), pages 17-32, February.
    12. Li, Shisheng & Ng, C.T. & Yuan, Jinjiang, 2011. "Group scheduling and due date assignment on a single machine," International Journal of Production Economics, Elsevier, vol. 130(2), pages 230-235, April.
    13. Chen, Zhi-Long, 1996. "Scheduling and common due date assignment with earliness-tardiness penalties and batch delivery costs," European Journal of Operational Research, Elsevier, vol. 93(1), pages 49-60, August.
    14. Adamopoulos, G. I. & Pappis, C. P., 1996. "Scheduling jobs with different, job-dependent earliness and tardiness penalties using the SLK method," European Journal of Operational Research, Elsevier, vol. 88(2), pages 336-344, January.
    15. Oğuzhan Ahmet Arik, 2023. "A heuristic for single machine common due date assignment problem with different earliness/tardiness weights," OPSEARCH, Springer;Operational Research Society of India, vol. 60(3), pages 1561-1574, September.
    16. Philip Kaminsky & Onur Kaya, 2008. "Scheduling and due‐date quotation in a make‐to‐order supply chain," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(5), pages 444-458, August.
    17. Kolahan, F. & Liang, M., 1998. "An adaptive TS approach to JIT sequencing with variable processing times and sequence-dependent setups," European Journal of Operational Research, Elsevier, vol. 109(1), pages 142-159, August.
    18. Y. P. Aneja & S. N. Kabadi & A. Nagar, 1998. "Minimizing weighted mean absolute deviation of flow times in single machine systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(3), pages 297-311, April.
    19. Xia, Yu & Chen, Bintong & Yue, Jinfeng, 2008. "Job sequencing and due date assignment in a single machine shop with uncertain processing times," European Journal of Operational Research, Elsevier, vol. 184(1), pages 63-75, January.
    20. Awi Federgruen & Gur Mosheiov, 1993. "Simultaneous optimization of efficiency and performance balance measures in single‐machine scheduling problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(7), pages 951-970, December.

    More about this item

    Statistics

    Access and download statistics

    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:wly:navres:v:38:y:1991:i:5:p:715-720. 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    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.