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APPROXIMATE RESULTS FOR A GENERALIZED SECRETARY PROBLEM

Published online by Cambridge University Press:  31 March 2011

Chris Dietz ,
Dinard van der Laan  and
Ad Ridder
Chris Dietz
Affiliation:
Vrije University Amsterdam, The Netherlands E-mail: cdietz@feweb.vu.nl; dalaan@feweb.vu.nl; aridder@feweb.vu.nl
Dinard van der Laan
Affiliation:
Vrije University Amsterdam, The Netherlands E-mail: cdietz@feweb.vu.nl; dalaan@feweb.vu.nl; aridder@feweb.vu.nl
Ad Ridder
Affiliation:
Vrije University Amsterdam, The Netherlands E-mail: cdietz@feweb.vu.nl; dalaan@feweb.vu.nl; aridder@feweb.vu.nl
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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.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 25 , Issue 2 , April 2011 , pp. 157 - 169
Copyright
Copyright © Cambridge University Press 2011

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