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The Best-or-Worst and the Postdoc problems

Author

Listed:
  • L. Bayón

    (Universidad de Oviedo)

  • P. Fortuny Ayuso

    (Universidad de Oviedo)

  • J. M. Grau

    (Universidad de Oviedo)

  • A. M. Oller-Marcén

    (Centro Universitario de la Defensa de Zaragoza)

  • M. M. Ruiz

    (Universidad de Oviedo)

Abstract

We consider two variants of the secretary problem, the Best-or-Worst and the Postdoc problems, which are closely related. First, we prove that both variants, in their standard form with binary payoff 1 or 0, share the same optimal stopping rule. We also consider additional cost/perquisites depending on the number of interviewed candidates. In these situations the optimal strategies are very different. Finally, we also focus on the Best-or-Worst variant with different payments depending on whether the selected candidate is the best or the worst.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:35:y:2018:i:3:d:10.1007_s10878-017-0203-4
    DOI: 10.1007/s10878-017-0203-4
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    References listed on IDEAS

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    1. 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.
    2. 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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    Cited by:

    1. 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.
    2. F. Thomas Bruss, 2021. "Combined Games with Randomly Delayed Beginnings," Mathematics, MDPI, vol. 9(5), pages 1-16, March.

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