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Optimal selection based on relative ranks with a random number of individuals

Published online by Cambridge University Press:  01 July 2016

Jacqueline Gianini-Pettitt
Jacqueline Gianini-Pettitt*
Affiliation:
University of Ottawa
*
∗Postal address: Faculty of Administration, Management Science, University of Ottawa, Ottawa, Ont., Canada K1N 9B5.
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Abstract

In one version of the familiar ‘secretary problem’, n rankable individuals appear sequentially in random order, and a selection procedure (stopping rule) is found to minimize the expected rank of the individual selected. It is assumed here that, instead of being a fixed integer n, the total number of individuals present is a bounded random variable N, of known distribution. The form of the optimal stopping rule is given, and for N belonging to a certain class of distributions, depending on n, and such that E(N) → ∞ as n → ∞, some asymptotic results concerning the minimal expected rank are given.

Keywords

OPTIMAL STOPPING RULESRELATIVE RANKSEXPECTED ABSOLUTE RANKS
Type
Research Article
Information
Advances in Applied Probability , Volume 11 , Issue 4 , December 1979 , pp. 720 - 736
Copyright
Copyright © Applied Probability Trust 1979 

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References

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