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Generalizing the secretary problem

Published online by Cambridge University Press:  01 July 2016

Thomas J. Lorenzen
Thomas J. Lorenzen*
Affiliation:
General Motors Research Laboratories, Warren, Michigan
*
∗Postal address: Mathematics Department, General Motors Research Laboratories, Warren, Michigan 48090, U.S.A.
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Abstract

The secretary problem refers to a certain class of optimal stopping problems based on relative ranks. To allow a more realistic formulation of the problem, this paper considers an arbitrary loss function. A finite and an infinite problem are defined and the optimal solutions are obtained. The solution for the infinite problem is given by a differential equation while the finite problem is given by a difference equation. Under general conditions, the finite problem tends to the infinite problem. An example involving the secretary problem with interview cost is considered and illustrates the usefulness of the present paper.

Keywords

OPTIMAL STOPPING RULESRELATIVE RANKSLOSS FUNCTION
Type
Research Article
Information
Advances in Applied Probability , Volume 11 , Issue 2 , June 1979 , pp. 384 - 396
Copyright
Copyright © Applied Probability Trust 1979 

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Footnotes

Parts of this paper are taken from the author's doctoral thesis, written under the direction of Dr S. M. Samuels.

References

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