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

L. Bayón (), P. Fortuny (), J. Grau (), A. M. Oller-Marcén () and M. M. Ruiz ()
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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

Journal of Combinatorial Optimization, 2019, vol. 38, issue 1, No 5, 86-110

Abstract: 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.

Keywords: Secretary problem; Best-or-Worst problem; Postdoc problem; Combinatorial optimization; 60G40; 62L15 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10878-018-0367-6

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