Approximate results for a generalized secretary problem

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Abstract

A version of the classical secretary problem is studied, in which one is interested in selecting one of the b best out of a group of n differently ranked persons who are presented one by one in a random order. It is assumed that b ≥1 is a preassigned number. It is known, already for a long time, that for the optimal policy, one needs to compute b position thresholds (for instance, via backward induction). In this article we study approximate policies that use just a single or a double position threshold, albeit in conjunction with a level rank. We give exact and asymptotic (as n → ∞) results, which show that the double-level policy is an extremely accurate approximation. © 2011 Cambridge University Press.
Original languageEnglish
Pages (from-to)157-169
JournalProbability in the Engineering and Informational Sciences
Volume25
Issue number2
DOIs
Publication statusPublished - 2011

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