IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v172y2009i1p221-23010.1007-s10479-009-0564-x.html
   My bibliography  Save this article

A randomized algorithm for the min-max selecting items problem with uncertain weights

Author

Listed:
  • Adam Kasperski
  • Paweł Zieliński

Abstract

This paper deals with the min-max version of the problem of selecting p items of the minimum total weight out of a set of n items, where the item weights are uncertain. The discrete scenario representation of uncertainty is considered. The computational complexity of the problem is explored. A randomized algorithm for the problem is then proposed, which returns an O(ln K)-approximate solution with a high probability, where K is the number of scenarios. This is the first approximation algorithm with better than K worst case ratio for the class of min-max combinatorial optimization problems with unbounded scenario set. Copyright Springer Science+Business Media, LLC 2009

Suggested Citation

  • Adam Kasperski & Paweł Zieliński, 2009. "A randomized algorithm for the min-max selecting items problem with uncertain weights," Annals of Operations Research, Springer, vol. 172(1), pages 221-230, November.
    • Handle: RePEc:spr:annopr:v:172:y:2009:i:1:p:221-230:10.1007/s10479-009-0564-x
    DOI: 10.1007/s10479-009-0564-x
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-009-0564-x
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-009-0564-x?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Hamza, Kais, 1995. "The smallest uniform upper bound on the distance between the mean and the median of the binomial and Poisson distributions," Statistics & Probability Letters, Elsevier, vol. 23(1), pages 21-25, April.
    2. Gang Yu, 1996. "On the Max-Min 0-1 Knapsack Problem with Robust Optimization Applications," Operations Research, INFORMS, vol. 44(2), pages 407-415, April.
    3. Satoru Fujishige & Naoki Katoh & Tetsuo Ichimori, 1988. "The Fair Resource Allocation Problem with Submodular Constraints," Mathematics of Operations Research, INFORMS, vol. 13(1), pages 164-173, February.
    4. Aissi, Hassene & Bazgan, Cristina & Vanderpooten, Daniel, 2007. "Approximation of min-max and min-max regret versions of some combinatorial optimization problems," European Journal of Operational Research, Elsevier, vol. 179(2), pages 281-290, 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. repec:wut:journl:v:2:y:2012:id:1022 is not listed on IDEAS
    2. Bogusz Przybysławski & Adam Kasperski, 2012. "A computational study of approximation algorithms for a minmax resource allocation problem," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 22(2), pages 35-43.

    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. Alireza Amirteimoori & Simin Masrouri, 2021. "DEA-based competition strategy in the presence of undesirable products: An application to paper mills," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 31(2), pages 5-21.
    2. Fabrice Talla Nobibon & Roel Leus, 2014. "Complexity Results and Exact Algorithms for Robust Knapsack Problems," Journal of Optimization Theory and Applications, Springer, vol. 161(2), pages 533-552, May.
    3. Aissi, Hassene & Bazgan, Cristina & Vanderpooten, Daniel, 2009. "Min-max and min-max regret versions of combinatorial optimization problems: A survey," European Journal of Operational Research, Elsevier, vol. 197(2), pages 427-438, September.
    4. Alexandre Belloni & Mitchell J. Lovett & William Boulding & Richard Staelin, 2012. "Optimal Admission and Scholarship Decisions: Choosing Customized Marketing Offers to Attract a Desirable Mix of Customers," Marketing Science, INFORMS, vol. 31(4), pages 621-636, July.
    5. Sbihi, Abdelkader, 2010. "A cooperative local search-based algorithm for the Multiple-Scenario Max-Min Knapsack Problem," European Journal of Operational Research, Elsevier, vol. 202(2), pages 339-346, April.
    6. Klamroth, Kathrin & Köbis, Elisabeth & Schöbel, Anita & Tammer, Christiane, 2017. "A unified approach to uncertain optimization," European Journal of Operational Research, Elsevier, vol. 260(2), pages 403-420.
    7. J. Puerto & A. M. Rodríguez-Chía & A. Tamir, 2009. "Minimax Regret Single-Facility Ordered Median Location Problems on Networks," INFORMS Journal on Computing, INFORMS, vol. 21(1), pages 77-87, February.
    8. Baldo, Alessandro & Boffa, Matteo & Cascioli, Lorenzo & Fadda, Edoardo & Lanza, Chiara & Ravera, Arianna, 2023. "The polynomial robust knapsack problem," European Journal of Operational Research, Elsevier, vol. 305(3), pages 1424-1434.
    9. Botte, Marco & Schöbel, Anita, 2019. "Dominance for multi-objective robust optimization concepts," European Journal of Operational Research, Elsevier, vol. 273(2), pages 430-440.
    10. Dmitriev, Daniil & Zhukovskii, Maksim, 2021. "On monotonicity of Ramanujan function for binomial random variables," Statistics & Probability Letters, Elsevier, vol. 177(C).
    11. Florian Biermann & Victor Naroditskiy & Maria Polukarov & Alex Rogers & Nicholas Jennings, 2011. "Task Assignment with Autonomous and Controlled Agents," Working Papers 004-11, International School of Economics at TSU, Tbilisi, Republic of Georgia.
    12. S Das & D Ghosh, 2003. "Binary knapsack problems with random budgets," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(9), pages 970-983, September.
    13. Choi, Byung-Cheon & Chung, Kwanghun, 2016. "Min–max regret version of a scheduling problem with outsourcing decisions under processing time uncertainty," European Journal of Operational Research, Elsevier, vol. 252(2), pages 367-375.
    14. Nikulin, Yury, 2006. "Robustness in combinatorial optimization and scheduling theory: An extended annotated bibliography," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 606, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    15. Iida, Hiroshi, 2007. "Comments on knapsack problems with a penalty," ビジネス創造センターディスカッション・ペーパー (Discussion papers of the Center for Business Creation) 10252/910, Otaru University of Commerce.
    16. Hanan Luss, 1999. "On Equitable Resource Allocation Problems: A Lexicographic Minimax Approach," Operations Research, INFORMS, vol. 47(3), pages 361-378, June.
    17. Onno Boxma & Offer Kella & Uri Yechiali, 2016. "An ASIP model with general gate opening intervals," Queueing Systems: Theory and Applications, Springer, vol. 84(1), pages 1-20, October.
    18. G. Yu, 1998. "Min-Max Optimization of Several Classical Discrete Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 98(1), pages 221-242, July.
    19. Mikita Hradovich & Adam Kasperski & Paweł Zieliński, 2017. "Recoverable robust spanning tree problem under interval uncertainty representations," Journal of Combinatorial Optimization, Springer, vol. 34(2), pages 554-573, August.
    20. Büsing, Christina & Goetzmann, Kai-Simon & Matuschke, Jannik & Stiller, Sebastian, 2017. "Reference points and approximation algorithms in multicriteria discrete optimization," European Journal of Operational Research, Elsevier, vol. 260(3), pages 829-840.

    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:spr:annopr:v:172:y:2009:i:1:p:221-230:10.1007/s10479-009-0564-x. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.