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Submodular Returns and Greedy Heuristics for Queueing Scheduling Problems

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  • R. Garbe

    (Newcastle University, Newcastle upon Tyne, United Kingdom)

  • K. D. Glazebrook

    (Newcastle University, Newcastle upon Tyne, United Kingdom)

Abstract

We consider a range of controlled stochastic systems satisfying conservation laws together with a reducibility property that says that appropriate laws continue to hold when access to the system is restricted to a subset of all possible demand (job, customer) types. We show that for linear objectives, the optimum system-wide performance is a nondecreasing submodular (or supermodular) function of the subset chosen and that these properties are inherited from the geometry of the performance space concerned. These results are of considerable interest in their own right, but they also motivate the use of greedy heuristics for the solution of a range of job selection and scheduling problems which have hitherto seemed intractable. Computational experience suggests that such heuristics perform very well.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:46:y:1998:i:3:p:336-346
    DOI: 10.1287/opre.46.3.336
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    References listed on IDEAS

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    Cited by:

    1. Marcus Dacre & Kevin Glazebrook & José Niño-Mora, 1998. "The achievable region approach to the optimal control of stochastic systems," Economics Working Papers 306, Department of Economics and Business, Universitat Pompeu Fabra.
    2. Simai He & Jiawei Zhang & Shuzhong Zhang, 2012. "Polymatroid Optimization, Submodularity, and Joint Replenishment Games," Operations Research, INFORMS, vol. 60(1), pages 128-137, February.

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