IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v38y2019i1d10.1007_s10878-018-0367-6.html
   My bibliography  Save this article

The Best-or-Worst and the Postdoc problems with random number of candidates

Author

Listed:
  • L. Bayón

    (Universidad de Oviedo)

  • P. Fortuny

    (Universidad de Oviedo)

  • J. Grau

    (Universidad de Oviedo)

  • A. M. Oller-Marcén

    (Centro Universitario de la Defensa de Zaragoza - IUMA)

  • M. M. Ruiz

    (Universidad de Oviedo)

Abstract

In this paper we consider two variants of the Secretary problem: The Best-or-Worst and the Postdoc problems. We extend previous work by considering that the number of objects is not known and follows either a discrete Uniform distribution $${\mathcal {U}}[1,n]$$ U [ 1 , n ] or a Poisson distribution $${\mathcal {P}} (\lambda )$$ P ( λ ) . We show that in any case the optimal strategy is a threshold strategy, we provide the optimal cutoff values and the asymptotic probabilities of success. We also put our results in relation with closely related work.

Suggested Citation

  • L. Bayón & P. Fortuny & J. Grau & A. M. Oller-Marcén & M. M. Ruiz, 2019. "The Best-or-Worst and the Postdoc problems with random number of candidates," Journal of Combinatorial Optimization, Springer, vol. 38(1), pages 86-110, July.
    • Handle: RePEc:spr:jcomop:v:38:y:2019:i:1:d:10.1007_s10878-018-0367-6
    DOI: 10.1007/s10878-018-0367-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-018-0367-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10878-018-0367-6?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. L. Bayón & P. Fortuny Ayuso & J. M. Grau & A. M. Oller-Marcén & M. M. Ruiz, 2018. "The Best-or-Worst and the Postdoc problems," Journal of Combinatorial Optimization, Springer, vol. 35(3), pages 703-723, April.
    2. D. V. Lindley, 1961. "Dynamic Programming and Decision Theory," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 10(1), pages 39-51, March.
    3. Szajowski, Krzysztof, 2007. "A game version of the Cowan-Zabczyk-Bruss' problem," Statistics & Probability Letters, Elsevier, vol. 77(17), pages 1683-1689, November.
    4. John S. Rose, 1982. "A Problem of Optimal Choice and Assignment," Operations Research, INFORMS, vol. 30(1), pages 172-181, February.
    Full references (including those not matched with items on IDEAS)

    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. Fouad Ben Abdelaziz & Ray Saadaoui Mallek, 2018. "Multi-criteria optimal stopping methods applied to the portfolio optimisation problem," Annals of Operations Research, Springer, vol. 267(1), pages 29-46, August.
    2. L. Bayón & P. Fortuny Ayuso & J. M. Grau & A. M. Oller-Marcén & M. M. Ruiz, 2018. "The Best-or-Worst and the Postdoc problems," Journal of Combinatorial Optimization, Springer, vol. 35(3), pages 703-723, April.
    3. F. Thomas Bruss, 2021. "Combined Games with Randomly Delayed Beginnings," Mathematics, MDPI, vol. 9(5), pages 1-16, March.
    4. Chun, Young H. & Plante, Robert D. & Schneider, Helmut, 2002. "Buying and selling an asset over the finite time horizon: A non-parametric approach," European Journal of Operational Research, Elsevier, vol. 136(1), pages 106-120, January.
    5. Ravi Jagannathan & Iwan Meier, 2002. "Do We Need CAPM for Capital Budgeting?," Financial Management, Financial Management Association, vol. 31(4), Winter.
    6. Bruss, F. Thomas & Paindaveine, Davy, 2000. "Selecting a sequence of last successes in independent trials," MPRA Paper 21166, University Library of Munich, Germany.
    7. Kimmo Eriksson & Jonas Sjöstrand & Pontus Strimling, 2007. "Optimal Expected Rank in a Two-Sided Secretary Problem," Operations Research, INFORMS, vol. 55(5), pages 921-931, October.
    8. Schaffner, Florian, 2016. "Information transmission in high dimensional choice problems: The value of online ratings in the restaurant market," VfS Annual Conference 2016 (Augsburg): Demographic Change 145585, Verein für Socialpolitik / German Economic Association.
    9. José A. Soto & Abner Turkieltaub & Victor Verdugo, 2021. "Strong Algorithms for the Ordinal Matroid Secretary Problem," Mathematics of Operations Research, INFORMS, vol. 46(2), pages 642-673, May.
    10. Stein, William E. & Seale, Darryl A. & Rapoport, Amnon, 2003. "Analysis of heuristic solutions to the best choice problem," European Journal of Operational Research, Elsevier, vol. 151(1), pages 140-152, November.
    11. Wojciech Kaźmierczak, 2016. "The best choice problem for posets; colored complete binary trees," Journal of Combinatorial Optimization, Springer, vol. 31(1), pages 13-28, January.
    12. Yaakov Malinovsky & Gregory Haber & Paul S. Albert, 2020. "An optimal design for hierarchical generalized group testing," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(3), pages 607-621, June.
    13. Sadoghi, Amirhossein & Vecer, Jan, 2022. "Optimal liquidation problem in illiquid markets," European Journal of Operational Research, Elsevier, vol. 296(3), pages 1050-1066.
    14. Werner Guth & Torsten Weiland, 2011. "Aspiration formation and satisficing in search with(out) competition," New Zealand Economic Papers, Taylor & Francis Journals, vol. 45(1-2), pages 23-45.
    15. Hsiao, Yu-Chin & Kemp, Simon & Servátka, Maroš & Ward, Matt & Zhang, Le, 2021. "Time Costs and Search Behavior," MPRA Paper 105412, University Library of Munich, Germany.
    16. Martin Meier & Leopold Sögner, 2023. "Hunting for superstars," Mathematics and Financial Economics, Springer, volume 17, number 1, March.
    17. Daniel Cownden & David Steinsaltz, 2014. "Effects of Competition in a Secretary Problem," Operations Research, INFORMS, vol. 62(1), pages 104-113, February.
    18. Yu‐Chin Hsiao & Simon Kemp & Maroš Servátka, 2020. "On the Importance of Context in Sequential Search," Southern Economic Journal, John Wiley & Sons, vol. 86(4), pages 1510-1530, April.
    19. Ben Abdelaziz, F. & Krichen, S., 2005. "An interactive method for the optimal selection problem with two decision makers," European Journal of Operational Research, Elsevier, vol. 162(3), pages 602-609, May.
    20. Demers, Simon, 2021. "Expected duration of the no-information minimum rank problem," Statistics & Probability Letters, Elsevier, vol. 168(C).

    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:jcomop:v:38:y:2019:i:1:d:10.1007_s10878-018-0367-6. 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.