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Best-choice problems involving recall and uncertainty of selection when the number of observations is random

Published online by Cambridge University Press:  01 July 2016

Joseph D. Petruccelli
Joseph D. Petruccelli*
Affiliation:
Worcester Polytechnic Institute
*
∗Postal address: Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA 01609, U.S.A.
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Abstract

From one point of view this paper adds to a previous formulation of the best-choice problem (Petruccelli (1981)) the possibility that the number of available observations, rather than being known, is a bounded random variable N with known distribution. From another perspective, it expands the formulations of Presman and Sonin (1972) and Rasmussen and Robbins (1975) to include recall and uncertainty of selection of observations. The behaviour of optimal stopping rules is examined under various assumptions on the general model. For optimal stopping rules and their probabilities of best choice relations are obtained between the bounded and unbounded N cases. Two particular classes of stopping rules which generalize the s(r) rules of Rasmussen and Robbins (1975) are considered in detail.

Keywords

OPTIMAL STOPPINGSECRETARY PROBLEMRELATIVE RANKS
Type
Research Article
Information
Advances in Applied Probability , Volume 16 , Issue 1 , March 1984 , pp. 111 - 130
Copyright
Copyright © Applied Probability Trust 1984 

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