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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
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    References listed on IDEAS

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    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.
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