IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v34y1987i3p319-335.html
   My bibliography  Save this article

Evaluating the effects of machine breakdowns in stochastic scheduling problems

Author

Listed:
  • Kevin D. Glazebrook

Abstract

In most of the stochastic resource‐allocation problems discussed in the literature it is supposed that the key resource, herein called the machine, is continuously available until all tasks are completed. Plainly, this will often be an unrealistic assumption. This paper supposes that intermittent availability of the machine is due to a breakdown proces, and describes various approaches to the evaluation of the effect of breakdowns. Firstly, for the case of geometric up times, conditions are given under which breakdowns have no effect on optimal allocation strategies. Secondly, two different procedures are given which yield an upper bound on the loss incurred when a processing strategy is adopted under the assumption of no breakdowns, when in fact breakdowns do occur. The first of these is based on Gittins's indices and is described for the case of geometric up times, and the second uses a bounding argument on the breakdown process.

Suggested Citation

  • Kevin D. Glazebrook, 1987. "Evaluating the effects of machine breakdowns in stochastic scheduling problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(3), pages 319-335, June.
    • Handle: RePEc:wly:navres:v:34:y:1987:i:3:p:319-335
    DOI: 10.1002/1520-6750(198706)34:33.0.CO;2-5
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/1520-6750(198706)34:33.0.CO;2-5
    Download Restriction: no
    File URL: https://libkey.io/10.1002/1520-6750(198706)34:33.0.CO;2-5?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. K. D. Glazebrook & J. C. Gittins, 1981. "On Single-Machine Scheduling with Precedence Relations and Linear or Discounted Costs," Operations Research, INFORMS, vol. 29(1), pages 161-173, February.
    2. Jeffrey B. Sidney, 1975. "Decomposition Algorithms for Single-Machine Sequencing with Precedence Relations and Deferral Costs," Operations Research, INFORMS, vol. 23(2), pages 283-298, April.
    3. K. D. Glazebrook, 1984. "Scheduling stochastic jobs on a single machine subject to breakdowns," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 31(2), pages 251-264, 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. Yarlin Kuo & Zi‐Ann Chang, 2007. "Integrated production scheduling and preventive maintenance planning for a single machine under a cumulative damage failure process," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(6), pages 602-614, September.
    2. Li, Wei & Glazebrook, Kevin D., 1998. "On stochastic machine scheduling with general distributional assumptions," European Journal of Operational Research, Elsevier, vol. 105(3), pages 525-536, March.
    3. Charles Du & Michael Pinedo, 1995. "A note on minimizing the expected makespan in flowshops subject to breakdowns," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(8), pages 1251-1262, December.
    4. S. E. Pilnick & K. D. Glazebrook & D. P. Gaver, 1991. "Optimal sequential replenishment of ships during combat," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(5), pages 637-668, October.
    5. Sid Browne & Kevin D. Glazebrook, 1996. "Scheduling jobs that are subject to failure propagation," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(2), pages 265-288, March.
    6. K. D. Glazebrook, 1992. "Single‐machine scheduling of stochastic jobs subject to deterioration or delay," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(5), pages 613-633, August.
    7. J. Birge & J. B. G. Frenk & J. Mittenthal & A. H. G. Rinnooy Kan, 1990. "Single‐machine scheduling subject to stochastic breakdowns," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(5), pages 661-677, October.
    8. Lee, Chung-Yee & Lin, Chen-Sin, 2001. "Single-machine scheduling with maintenance and repair rate-modifying activities," European Journal of Operational Research, Elsevier, vol. 135(3), pages 493-513, December.

    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. K. D. Glazebrook, 1992. "Single‐machine scheduling of stochastic jobs subject to deterioration or delay," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(5), pages 613-633, August.
    2. S. E. Pilnick & K. D. Glazebrook & D. P. Gaver, 1991. "Optimal sequential replenishment of ships during combat," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(5), pages 637-668, October.
    3. Zhenpeng Li & Congdian Cheng, 2023. "The Expected Competitive Ratio on a Kind of Stochastic-Online Flowtime Scheduling with Machine Subject to an Uncertain Breakdown," Mathematics, MDPI, vol. 11(11), pages 1-12, May.
    4. Seyed M. R. Iravani & John A. Buzacott & Morton J. M. Posner, 2003. "Operations and Shipment Scheduling of a Batch on a Felxible Machine," Operations Research, INFORMS, vol. 51(4), pages 585-601, August.
    5. Herbert Hamers & Flip Klijn & Bas van Velzen, 2002. "On Games corresponding to Sequencing Situations with Precedence Relations," UFAE and IAE Working Papers 553.02, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    6. P. Detti & D. Pacciarelli, 2001. "A branch and bound algorithm for the minimum storage‐time sequencing problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(4), pages 313-331, June.
    7. Herbert Hamers & Flip Klijn & Bas Velzen, 2005. "On the Convexity of Precedence Sequencing Games," Annals of Operations Research, Springer, vol. 137(1), pages 161-175, July.
    8. Davila-Pena, Laura & Borm, Peter & Garcia-Jurado, Ignacio & Schouten, Jop, 2023. "An Allocation Rule for Graph Machine Scheduling Problems," Other publications TiSEM 17013f33-1d65-4294-802c-b, Tilburg University, School of Economics and Management.
    9. Robbert Fokkink & Thomas Lidbetter & László A. Végh, 2019. "On Submodular Search and Machine Scheduling," Management Science, INFORMS, vol. 44(4), pages 1431-1449, November.
    10. J. Birge & J. B. G. Frenk & J. Mittenthal & A. H. G. Rinnooy Kan, 1990. "Single‐machine scheduling subject to stochastic breakdowns," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(5), pages 661-677, October.
    11. Chung, Chia-Shin & Flynn, James & Kirca, Omer, 2002. "A branch and bound algorithm to minimize the total flow time for m-machine permutation flowshop problems," International Journal of Production Economics, Elsevier, vol. 79(3), pages 185-196, October.
    12. Christoph Ambühl & Monaldo Mastrolilli & Nikolaus Mutsanas & Ola Svensson, 2011. "On the Approximability of Single-Machine Scheduling with Precedence Constraints," Mathematics of Operations Research, INFORMS, vol. 36(4), pages 653-669, November.
    13. Tzafestas, Spyros & Triantafyllakis, Alekos, 1993. "Deterministic scheduling in computing and manufacturing systems: a survey of models and algorithms," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 35(5), pages 397-434.
    14. Yarlin Kuo & Zi‐Ann Chang, 2007. "Integrated production scheduling and preventive maintenance planning for a single machine under a cumulative damage failure process," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(6), pages 602-614, September.
    15. Rostami, Salim & Creemers, Stefan & Leus, Roel, 2019. "Precedence theorems and dynamic programming for the single-machine weighted tardiness problem," European Journal of Operational Research, Elsevier, vol. 272(1), pages 43-49.
    16. Agnetis, Alessandro & Hermans, Ben & Leus, Roel & Rostami, Salim, 2022. "Time-critical testing and search problems," European Journal of Operational Research, Elsevier, vol. 296(2), pages 440-452.
    17. Ben Hermans & Roel Leus & Jannik Matuschke, 2022. "Exact and Approximation Algorithms for the Expanding Search Problem," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 281-296, January.
    18. K. D. Glazebrook, 1995. "A suboptimality bound for permutation policies in single machine stochastic scheduling," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(6), pages 993-1005, September.
    19. Sid Browne & Kevin D. Glazebrook, 1996. "Scheduling jobs that are subject to failure propagation," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(2), pages 265-288, March.
    20. François Margot & Maurice Queyranne & Yaoguang Wang, 2003. "Decompositions, Network Flows, and a Precedence Constrained Single-Machine Scheduling Problem," Operations Research, INFORMS, vol. 51(6), pages 981-992, 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:34:y:1987:i:3:p:319-335. 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.