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. 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.
    2. 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.
    3. 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.
    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. 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.
    5. Roy, Bernard, 2010. "Robustness in operational research and decision aiding: A multi-faceted issue," European Journal of Operational Research, Elsevier, vol. 200(3), pages 629-638, February.
    6. 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.
    7. 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.
    8. Lee, Zu-Hsu & Deng, Shiming & Lin, Beixin & Yang, James G.S., 2010. "Decision model and analysis for investment interest expense deduction and allocation," European Journal of Operational Research, Elsevier, vol. 200(1), pages 268-280, January.
    9. Kalaı¨, Rim & Lamboray, Claude & Vanderpooten, Daniel, 2012. "Lexicographic α-robustness: An alternative to min–max criteria," European Journal of Operational Research, Elsevier, vol. 220(3), pages 722-728.
    10. Andjel, Enrique & López, F. Javier & Sanz, Gerardo, 2002. "Ergodicity of one-dimensional resource sharing systems," Stochastic Processes and their Applications, Elsevier, vol. 98(1), pages 1-22, March.
    11. Khaled Elbassioni & Areg Karapetyan & Trung Thanh Nguyen, 2019. "Approximation schemes for r-weighted Minimization Knapsack problems," Annals of Operations Research, Springer, vol. 279(1), pages 367-386, August.
    12. 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.
    13. Harwin De Vries & Lisa E. Swinkels & Luk N. Van Wassenhove, 2021. "Site Visit Frequency Policies for Mobile Family Planning Services," Production and Operations Management, Production and Operations Management Society, vol. 30(12), pages 4522-4540, December.
    14. 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.
    15. Renato de Matta & Vernon Ning Hsu & Timothy J. Lowe, 1999. "The selection allocation problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(6), pages 707-725, September.
    16. 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.
    17. Botte, Marco & Schöbel, Anita, 2019. "Dominance for multi-objective robust optimization concepts," European Journal of Operational Research, Elsevier, vol. 273(2), pages 430-440.
    18. Thekra Al-douri & Mhand Hifi & Vassilis Zissimopoulos, 2021. "An iterative algorithm for the Max-Min knapsack problem with multiple scenarios," Operational Research, Springer, vol. 21(2), pages 1355-1392, June.
    19. Frédéric Ouimet, 2023. "A refined continuity correction for the negative binomial distribution and asymptotics of the median," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(7), pages 827-849, October.
    20. Fabio Furini & Manuel Iori & Silvano Martello & Mutsunori Yagiura, 2015. "Heuristic and Exact Algorithms for the Interval Min–Max Regret Knapsack Problem," INFORMS Journal on Computing, INFORMS, vol. 27(2), pages 392-405, May.

    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.