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

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  • 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
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    References listed on IDEAS

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    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.
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    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. 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.
    3. 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.
    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.

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