IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v49y2002i7p706-721.html
   My bibliography  Save this article

An index policy for a stochastic scheduling model with improving/deteriorating jobs

Author

Listed:
  • K.D. Glazebrook
  • H.M. Mitchell

Abstract

We consider stochastic scheduling models which have the natural character that jobs improve while being processed, but deteriorate (and may possibly leave the system altogether) while processing is diverted elsewhere. Such restless bandit problems are shown to be indexable in the sense of Whittle. A numerical study which elucidates the strong performance of the resulting index policy is complemented by a theoretical study which demonstrates the optimality of the index policy under given conditions and which develops performance guarantees for the index heuristic more generally. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 706–721, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10036

Suggested Citation

  • K.D. Glazebrook & H.M. Mitchell, 2002. "An index policy for a stochastic scheduling model with improving/deteriorating jobs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(7), pages 706-721, October.
    • Handle: RePEc:wly:navres:v:49:y:2002:i:7:p:706-721
    DOI: 10.1002/nav.10036
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/nav.10036
    Download Restriction: no
    File URL: https://libkey.io/10.1002/nav.10036?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, 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. Dimitris Bertsimas & José Niño-Mora, 1996. "Conservation Laws, Extended Polymatroids and Multiarmed Bandit Problems; A Polyhedral Approach to Indexable Systems," Mathematics of Operations Research, INFORMS, vol. 21(2), pages 257-306, May.
    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. K.D. Glazebrook & C. Kirkbride, 2004. "Index policies for the routing of background jobs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(6), pages 856-872, September.
    2. Nicolas Gast & Bruno Gaujal & Kimang Khun, 2023. "Testing indexability and computing Whittle and Gittins index in subcubic time," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 97(3), pages 391-436, June.
    3. Andrei Sleptchenko & M. Eric Johnson, 2015. "Maintaining Secure and Reliable Distributed Control Systems," INFORMS Journal on Computing, INFORMS, vol. 27(1), pages 103-117, February.
    4. Sheldon M. Ross, 2015. "A sequential scheduling problem with impatient jobs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(8), pages 659-663, 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. José Niño-Mora, 2006. "Restless Bandit Marginal Productivity Indices, Diminishing Returns, and Optimal Control of Make-to-Order/Make-to-Stock M/G/1 Queues," Mathematics of Operations Research, INFORMS, vol. 31(1), pages 50-84, February.
    2. José Niño-Mora, 2020. "Fast Two-Stage Computation of an Index Policy for Multi-Armed Bandits with Setup Delays," Mathematics, MDPI, vol. 9(1), pages 1-36, December.
    3. R. T. Dunn & K. D. Glazebrook, 2004. "Discounted Multiarmed Bandit Problems on a Collection of Machines with Varying Speeds," Mathematics of Operations Research, INFORMS, vol. 29(2), pages 266-279, May.
    4. R. Garbe & K. D. Glazebrook, 1998. "Submodular Returns and Greedy Heuristics for Queueing Scheduling Problems," Operations Research, INFORMS, vol. 46(3), pages 336-346, June.
    5. Vikram Krishnamurthy & Bo Wahlberg, 2009. "Partially Observed Markov Decision Process Multiarmed Bandits---Structural Results," Mathematics of Operations Research, INFORMS, vol. 34(2), pages 287-302, May.
    6. Dong Li & Li Ding & Stephen Connor, 2020. "When to Switch? Index Policies for Resource Scheduling in Emergency Response," Production and Operations Management, Production and Operations Management Society, vol. 29(2), pages 241-262, February.
    7. Santiago R. Balseiro & Ozan Candogan, 2017. "Optimal Contracts for Intermediaries in Online Advertising," Operations Research, INFORMS, vol. 65(4), pages 878-896, August.
    8. Anupam Gupta & Ravishankar Krishnaswamy & Viswanath Nagarajan & R. Ravi, 2015. "Running Errands in Time: Approximation Algorithms for Stochastic Orienteering," Mathematics of Operations Research, INFORMS, vol. 40(1), pages 56-79, February.
    9. Wieslaw Kubiak & Steef van de Velde, 1998. "Scheduling deteriorating jobs to minimize makespan," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(5), pages 511-523, August.
    10. Dimitris Bertsimas & Velibor V. Mišić, 2016. "Decomposable Markov Decision Processes: A Fluid Optimization Approach," Operations Research, INFORMS, vol. 64(6), pages 1537-1555, December.
    11. Lidbetter, Thomas, 2020. "Search and rescue in the face of uncertain threats," European Journal of Operational Research, Elsevier, vol. 285(3), pages 1153-1160.
    12. Kevin D. Glazebrook & José Niño-Mora, 2001. "Parallel Scheduling of Multiclass M/M/m Queues: Approximate and Heavy-Traffic Optimization of Achievable Performance," Operations Research, INFORMS, vol. 49(4), pages 609-623, August.
    13. Malekipirbazari, Milad & Çavuş, Özlem, 2024. "Index policy for multiarmed bandit problem with dynamic risk measures," European Journal of Operational Research, Elsevier, vol. 312(2), pages 627-640.
    14. K. D. Glazebrook & C. Kirkbride & H. M. Mitchell & D. P. Gaver & P. A. Jacobs, 2007. "Index Policies for Shooting Problems," Operations Research, INFORMS, vol. 55(4), pages 769-781, August.
    15. Louis Anthony (Tony)Cox, 2008. "What's Wrong with Risk Matrices?," Risk Analysis, John Wiley & Sons, vol. 28(2), pages 497-512, April.
    16. José R. Correa & Maurice Queyranne, 2012. "Efficiency of equilibria in restricted uniform machine scheduling with total weighted completion time as social cost," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(5), pages 384-395, August.
    17. Andrei Sleptchenko & M. Eric Johnson, 2015. "Maintaining Secure and Reliable Distributed Control Systems," INFORMS Journal on Computing, INFORMS, vol. 27(1), pages 103-117, February.
    18. José Niño-Mora, 2020. "A Verification Theorem for Threshold-Indexability of Real-State Discounted Restless Bandits," Mathematics of Operations Research, INFORMS, vol. 45(2), pages 465-496, May.
    19. Alfredo Torrico & Alejandro Toriello, 2022. "Dynamic Relaxations for Online Bipartite Matching," INFORMS Journal on Computing, INFORMS, vol. 34(4), pages 1871-1884, July.
    20. David M. Markowitz & Lawrence M. Wein, 2001. "Heavy Traffic Analysis of Dynamic Cyclic Policies: A Unified Treatment of the Single Machine Scheduling Problem," Operations Research, INFORMS, vol. 49(2), pages 246-270, April.

    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:49:y:2002:i:7:p:706-721. 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.