IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v46y1998i3p336-346.html
   My bibliography  Save this article

Submodular Returns and Greedy Heuristics for Queueing Scheduling Problems

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.46.3.336
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.46.3.336?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. G. L. Nemhauser & L. A. Wolsey, 1978. "Best Algorithms for Approximating the Maximum of a Submodular Set Function," Mathematics of Operations Research, INFORMS, vol. 3(3), pages 177-188, August.
    2. A. Federgruen & H. Groenevelt, 1988. "M/G/c Queueing Systems with Multiple Customer Classes: Characterization and Control of Achievable Performance Under Nonpreemptive Priority Rules," Management Science, INFORMS, vol. 34(9), pages 1121-1138, September.
    3. De, Prabuddha & Ghosh, Jay B. & Wells, Charles E., 1993. "Job selection and sequencing on a single machine in a random environment," European Journal of Operational Research, Elsevier, vol. 70(3), pages 425-431, November.
    4. Nemhauser, G.L. & Wolsey, L.A., 1978. "Best algorithms for approximating the maximum of a submodular set function," LIDAM Reprints CORE 343, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. J. George Shanthikumar & David D. Yao, 1992. "Multiclass Queueing Systems: Polymatroidal Structure and Optimal Scheduling Control," Operations Research, INFORMS, vol. 40(3-supplem), pages 293-299, June.
    6. Nemhauser, G.L. & Wolsey, L.A., 1981. "Maximizing submodular set functions: formulations and analysis of algorithms," LIDAM Reprints CORE 455, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Glazebrook, K. D., 1982. "On the evaluation of fixed permutations as strategies in stochastic scheduling," Stochastic Processes and their Applications, Elsevier, vol. 13(2), pages 171-187, August.
    8. 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. 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.

    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. Ivan Contreras & Elena Fernández, 2014. "Hub Location as the Minimization of a Supermodular Set Function," Operations Research, INFORMS, vol. 62(3), pages 557-570, June.
    2. 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.
    3. Chuangen Gao & Shuyang Gu & Jiguo Yu & Hai Du & Weili Wu, 2022. "Adaptive seeding for profit maximization in social networks," Journal of Global Optimization, Springer, vol. 82(2), pages 413-432, February.
    4. Bertsimas, Dimitris., 1995. "The achievable region method in the optimal control of queueing systems : formulations, bounds and policies," Working papers 3837-95., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    5. Suning Gong & Qingqin Nong & Jiazhu Fang & Ding-Zhu Du, 2024. "Algorithms for Cardinality-Constrained Monotone DR-Submodular Maximization with Low Adaptivity and Query Complexity," Journal of Optimization Theory and Applications, Springer, vol. 200(1), pages 194-214, January.
    6. Bin Liu & Miaomiao Hu, 2022. "Fast algorithms for maximizing monotone nonsubmodular functions," Journal of Combinatorial Optimization, Springer, vol. 43(5), pages 1655-1670, July.
    7. Veeraruna Kavitha & Jayakrishnan Nair & Raman Kumar Sinha, 2019. "Pseudo conservation for partially fluid, partially lossy queueing systems," Annals of Operations Research, Springer, vol. 277(2), pages 255-292, June.
    8. Santiago R. Balseiro & Ozan Candogan, 2017. "Optimal Contracts for Intermediaries in Online Advertising," Operations Research, INFORMS, vol. 65(4), pages 878-896, August.
    9. Zhenning Zhang & Donglei Du & Yanjun Jiang & Chenchen Wu, 2021. "Maximizing DR-submodular+supermodular functions on the integer lattice subject to a cardinality constraint," Journal of Global Optimization, Springer, vol. 80(3), pages 595-616, July.
    10. Awi Federgruen & Nan Yang, 2008. "Selecting a Portfolio of Suppliers Under Demand and Supply Risks," Operations Research, INFORMS, vol. 56(4), pages 916-936, August.
    11. Dimitris Bertsimas & Velibor V. Mišić, 2016. "Decomposable Markov Decision Processes: A Fluid Optimization Approach," Operations Research, INFORMS, vol. 64(6), pages 1537-1555, December.
    12. Simon Bruggmann & Rico Zenklusen, 2019. "Submodular Maximization Through the Lens of Linear Programming," Management Science, INFORMS, vol. 44(4), pages 1221-1244, November.
    13. Xin Sun & Tiande Guo & Congying Han & Hongyang Zhang, 2025. "Greedy algorithms for stochastic monotone k-submodular maximization under full-bandit feedback," Journal of Combinatorial Optimization, Springer, vol. 49(1), pages 1-25, January.
    14. Jon Lee & Maxim Sviridenko & Jan Vondrák, 2010. "Submodular Maximization over Multiple Matroids via Generalized Exchange Properties," Mathematics of Operations Research, INFORMS, vol. 35(4), pages 795-806, November.
    15. Cheng Lu & Wenguo Yang & Ruiqi Yang & Suixiang Gao, 2022. "Maximizing a non-decreasing non-submodular function subject to various types of constraints," Journal of Global Optimization, Springer, vol. 83(4), pages 727-751, August.
    16. Maxim Sviridenko & Jan Vondrák & Justin Ward, 2017. "Optimal Approximation for Submodular and Supermodular Optimization with Bounded Curvature," Mathematics of Operations Research, INFORMS, vol. 42(4), pages 1197-1218, November.
    17. Bertsimas, Dimitris. & Niño-Mora, Jose., 1994. "Restless bandit, linear programming relaxations and a primal-dual heuristic," Working papers 3727-94., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    18. Niv Buchbinder & Moran Feldman & Roy Schwartz, 2017. "Comparing Apples and Oranges: Query Trade-off in Submodular Maximization," Mathematics of Operations Research, INFORMS, vol. 42(2), pages 308-329, May.
    19. Goldengorin, Boris, 2009. "Maximization of submodular functions: Theory and enumeration algorithms," European Journal of Operational Research, Elsevier, vol. 198(1), pages 102-112, October.
    20. Sundarraj, R. P., 2002. "An optimization approach to plan for reusable software components," European Journal of Operational Research, Elsevier, vol. 142(1), pages 128-137, October.

    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:inm:oropre:v:46:y:1998:i:3:p:336-346. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.