IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v47y2000i8p657-668.html
   My bibliography  Save this article

Minimizing mean absolute deviation of job completion times from the mean completion time

Author

Listed:
  • Gur Mosheiov

Abstract

In many scheduling environments it is recommended to control the balance of the performance of individual jobs, e.g., the variability of the job completion or waiting times. In service systems, for example, it may be important to provide customers with an identical or similar service quality, as measured by their time in system or waiting time. Several measures of variation have been studied in scheduling literature in this context; our paper considers the measure of Mean Absolute Deviation of job completion times from the Mean Completion time (MADMC). Recently, Aneja et al. (1998) proved that minimizing MADMC on a single‐machine is NP‐hard. We introduce a simple heuristic and an easily obtained lower bound on the optimal MADMC value. We prove that the worst case optimality gap of the heuristic is bounded by the constant 2, and that this bound is tight. Better worst case bounds can be achieved in special cases. Both the heuristic and the lower bound are shown to be asymptotically accurate under very general conditions. Both the heuristic and lower bound are extended to parallel identical machines. In our extensive numerical study we show that the heuristic produces, both in the single‐machine and in the multi‐machine case, extremely close‐to‐optimal schedules. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 657–668, 2000

Suggested Citation

  • Gur Mosheiov, 2000. "Minimizing mean absolute deviation of job completion times from the mean completion time," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(8), pages 657-668, December.
    • Handle: RePEc:wly:navres:v:47:y:2000:i:8:p:657-668
    DOI: 10.1002/1520-6750(200012)47:83.0.CO;2-1
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/1520-6750(200012)47:83.0.CO;2-1
    Download Restriction: no
    File URL: https://libkey.io/10.1002/1520-6750(200012)47:83.0.CO;2-1?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. Uttarayan Bagchi & Robert S. Sullivan & Y. L. Chang, 1986. "Minimizing mean absolute deviation of completion times about a common due date," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 33(2), pages 227-240, May.
    2. Alan G. Merten & Mervin E. Muller, 1972. "Variance Minimization in Single Machine Sequencing Problems," Management Science, INFORMS, vol. 18(9), pages 518-528, May.
    3. P. S. Sundararaghavan & Mesbah U. Ahmed, 1984. "Minimizing the sum of absolute lateness in single‐machine and multimachine scheduling," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 31(2), pages 325-333, June.
    4. Samuel Eilon & I. G. Chowdhury, 1977. "Minimising Waiting Time Variance in the Single Machine Problem," Management Science, INFORMS, vol. 23(6), pages 567-575, February.
    5. Awi Federgruen & Gur Mosheiov, 1997. "Heuristics for multimachine minmax scheduling problems with general earliness and tardiness costs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 44(3), pages 287-299, April.
    6. John J. Kanet, 1981. "Minimizing Variation of Flow Time in Single Machine Systems," Management Science, INFORMS, vol. 27(12), pages 1453-1459, December.
    7. Michael X. Weng & Jose A. Ventura, 1994. "Scheduling about a large common due date with tolerance to minimize mean absolute deviation of completion times," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(6), pages 843-851, October.
    8. Nicholas G. Hall, 1986. "Single‐ and multiple‐processor models for minimizing completion time variance," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 33(1), pages 49-54, February.
    9. 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.
    10. Uttarayan Bagchi, 1989. "Simultaneous Minimization of Mean and Variation of Flow Time and Waiting Time in Single Machine Systems," Operations Research, INFORMS, vol. 37(1), pages 118-125, February.
    11. 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.
    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. J. Steve Davis & John J. Kanet, 1993. "Single‐machine scheduling with early and tardy completion costs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(1), pages 85-101, February.
    2. Cai, X., 1995. "Minimization of agreeably weighted variance in single machine systems," European Journal of Operational Research, Elsevier, vol. 85(3), pages 576-592, September.
    3. 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.
    4. C.T. Ng & X. Cai & T.C.E. Cheng, 1999. "Probabilistic analysis of an asymptotically optimal solution for the completion time variance problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(4), pages 373-398, June.
    5. Koulamas, Christos & Kyparisis, George J., 2023. "Two-stage no-wait proportionate flow shop scheduling with minimal service time variation and optional job rejection," European Journal of Operational Research, Elsevier, vol. 305(2), pages 608-616.
    6. 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.
    7. Uttarayan Bagchi & Yih‐Long Chang & Robert S. Sullivan, 1987. "Minimizing absolute and squared deviations of completion times with different earliness and tardiness penalties and a common due date," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(5), pages 739-751, October.
    8. Cai, X., 1996. "V-shape property for job sequences that minimize the expected completion time variance," European Journal of Operational Research, Elsevier, vol. 91(1), pages 118-123, May.
    9. Wlodzimierz Szwarc, 1989. "Single‐machine scheduling to minimize absolute deviation of completion times from a common due date," Naval Research Logistics (NRL), John Wiley & Sons, vol. 36(5), pages 663-673, October.
    10. Nasini, Stefano & Nessah, Rabia, 2024. "Time-flexible min completion time variance in a single machine by quadratic programming," European Journal of Operational Research, Elsevier, vol. 312(2), pages 427-444.
    11. Srirangacharyulu, B. & Srinivasan, G., 2013. "An exact algorithm to minimize mean squared deviation of job completion times about a common due date," European Journal of Operational Research, Elsevier, vol. 231(3), pages 547-556.
    12. Kerem Bülbül & Safia Kedad-Sidhoum & Halil Şen, 2019. "Single-machine common due date total earliness/tardiness scheduling with machine unavailability," Journal of Scheduling, Springer, vol. 22(5), pages 543-565, October.
    13. G Mosheiov, 2008. "Minimizing total absolute deviation of job completion times: extensions to position-dependent processing times and parallel identical machines," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(10), pages 1422-1424, October.
    14. Enrique Gerstl & Gur Mosheiov, 2014. "Single machine just‐in‐time scheduling problems with two competing agents," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(1), pages 1-16, February.
    15. Nasini, Stefano & Nessah, Rabia, 2021. "An almost exact solution to the min completion time variance in a single machine," European Journal of Operational Research, Elsevier, vol. 294(2), pages 427-441.
    16. Weng, Xiaohua & Ventura, Jose A., 1996. "Scheduling about a given common due date to minimize mean squared deviation of completion times," European Journal of Operational Research, Elsevier, vol. 88(2), pages 328-335, January.
    17. Seo, Jong Hwa & Kim, Chae-Bogk & Lee, Dong Hoon, 2001. "Minimizing mean squared deviation of completion times with maximum tardiness constraint," European Journal of Operational Research, Elsevier, vol. 129(1), pages 95-104, February.
    18. Kubiak, Wieslaw & Cheng, Jinliang & Kovalyov, Mikhail Y., 2002. "Fast fully polynomial approximation schemes for minimizing completion time variance," European Journal of Operational Research, Elsevier, vol. 137(2), pages 303-309, March.
    19. Hamilton Emmons, 1987. "Scheduling to a common due date on parallel uniform processors," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(6), pages 803-810, December.
    20. Ganesan, Viswanath Kumar & Sivakumar, Appa Iyer, 2006. "Scheduling in static jobshops for minimizing mean flowtime subject to minimum total deviation of job completion times," International Journal of Production Economics, Elsevier, vol. 103(2), pages 633-647, October.

    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:47:y:2000:i:8:p:657-668. 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.