Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-23T22:02:55.706Z Has data issue: false hasContentIssue false
  • English
  • Français

A Multiple Stopping Problem

Published online by Cambridge University Press:  27 July 2009

J. Preater
J. Preater
Affiliation:
Department of Mathematics, University of Keele, Keele, Staffordshire, ST5 5BG, United Kingdom
Get access Rights & Permissions [Opens in a new window]

Abstract

In the context of team recruitment, we discuss an optimal multiple stopping problem for an infinite independent and identically distributed sequence, with general reward function and constant observation cost. We establish the existence and nature of an optimal stopping rule. For the particular case where team quality is governed by the fitness of the weakest member, we show that the recruiter should be more discriminating with either a better, or a larger, group of appointees in hand.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 8 , Issue 2 , April 1994 , pp. 169 - 177
Copyright
Copyright © Cambridge University Press 1994

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Chen, R.W., Nair, V.N., Odlyzko, A.M., Shepp, L.A., & Vardi, Y. (1984). Optimal sequential selection of N random variables under a sum constraint. Journal of Applied Probability 21: 537–547.CrossRefGoogle Scholar
2.Chow, Y.S., Robbins, H., & Seigmund, D. (1971). Great expectations: The theory of optimal stopping. Boston: Houghton Mifflin.Google Scholar
3.Coffman, E.G., Flatto, L., & Weber, R.R. (1987). Optimal selection of stochastic intervals under a sum constraint. Advances in Applied Probability 19: 454–473.CrossRefGoogle Scholar
4.Ferguson, T.S. (1989). Who solved the secretary problem? Statistical Science 4: 282–296.Google Scholar
5.Gilbert, J. & Mosteller, F. (1966). Recognising the maximum of a sequence. Journal of the American Statistical Association 61: 35–73.CrossRefGoogle Scholar
6.Haggstrom, G. (1967). Optimal sequential procedures when more than one stop is required. Annals of Mathematical Statistics 38: 1618–1626.CrossRefGoogle Scholar
7.Hardy, G.H. (1952). Pure mathematics, 10th ed.Cambridge: Cambridge University Press.Google Scholar
8.Nakai, T. (1986). An optimal selection problem for a sequence with a random number of applicants per period. Operations Research 34: 478–485.CrossRefGoogle Scholar
9.Preater, J. (1991). Sequential multiple selection problems. Ph.D. thesis, University of Keele, Keele, UK.Google Scholar
10.Preater, J. (1993). A note on monotonicity in optimal multiple stopping problems. Statistics and Probability Letters 16: 407–410.CrossRefGoogle Scholar
11.Stadje, W. (1985). On multiple stopping rules. Optimization 16: 401–418.CrossRefGoogle Scholar
12.Whittle, P. (1982). Optimization over time. Vol. 1. Chichester: Wiley.Google Scholar