A secretary problem is an optimal stopping problem based on relative ranks. To the usual formulation of the secretary problem we add a cumulative interview cost function $h(\cdot)$, no longer obtaining "cutoff point" rules. For an appealing form of $h(\cdot)$ we examine the limiting results using the infinite secretary problem. It is shown that the other appealing form of $h(\cdot)$ leads to trivial limiting results. A large class of problems is considered and recursive equations leading to the limiting solution are given. In particular we solve the problem of minimizing expected rank with a linear interview cost function. An approximation to the rank problem with fixed cost $c$ per interview is obtained (for all values of $c$) through the solution of a single differential equation.
Publié le : 1981-02-14
Classification:
Optimal stopping rules,
relative ranks,
loss function sampling cost,
60G40
@article{1176994519,
author = {Lorenzen, Thomas J.},
title = {Optimal Stopping with Sampling Cost: The Secretary Problem},
journal = {Ann. Probab.},
volume = {9},
number = {6},
year = {1981},
pages = { 167-172},
language = {en},
url = {http://dml.mathdoc.fr/item/1176994519}
}
Lorenzen, Thomas J. Optimal Stopping with Sampling Cost: The Secretary Problem. Ann. Probab., Tome 9 (1981) no. 6, pp. 167-172. http://gdmltest.u-ga.fr/item/1176994519/