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A Full-Information Best-Choice Problem with Allowance

Published online by Cambridge University Press:  27 July 2009

Mitsushi Tamaki  and
J. George Shanthikumar
Mitsushi Tamaki
Affiliation:
Department of Business Administration, Aichi University, Nishikamo, Aichi, Japan, 470-02
J. George Shanthikumar
Affiliation:
School of Business Administration, University of California, Berkeley, California 94720
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Abstract

This paper considers a variation of the classical full-information best-choice problem. The problem allows success to be obtained even when the best item is not selected, provided the item that is selected is within the allowance of the best item. Under certain regularity conditions on the allowance function, the general nature of the optimal strategy is given as well as an algorithm to determine it exactly. It is also examined how the success probability depends on the allowance function and the underlying distribution of the observed values of the items.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 10 , Issue 1 , January 1996 , pp. 41 - 56
Copyright
Copyright © Cambridge University Press 1996

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References

1.Bruss, F.T. & Ferguson, T.S. (1993). Minimizing the expected rank with full information. Journal of Applied Probability 30: 616–626.CrossRefGoogle Scholar
2.Enns, E.G. (1975). Selecting the maximum of a sequence with imperfect information. Journal of the American Statistical Association 70: 640–643.Google Scholar
3.Ferguson, T.S. (1989). Who solved the secretary problem? Statistical Science 4: 282–296.Google Scholar
4.Frank, A.Q. & Samuels, S.M. (1980). On an optimal stopping problem of Gusein-Zade. Stochastic Processes and Their Applications 10: 299–311.CrossRefGoogle Scholar
5.Gilbert, J.P. & Mosteller, F. (1966). Recognizing the maximum of a sequence. Journal of the American Statistical Association 61: 35–73.CrossRefGoogle Scholar
6.Gusein-Zade, S.M. (1966). The problem of choice and the optimal stopping rule for a sequence of independent trials. Theory of Probability Applications 11: 472–476.CrossRefGoogle Scholar
7.Petruccelli, J.D. (1982). Full-information best-choice problems with recall of observations and uncertainty of selection depending on the observation. Advances of Applied Probability 14: 340–358.CrossRefGoogle Scholar
8.Sakaguchi, M. (1973). A note on the dowry problem. Rep. Statist. Appl. Res. JUSE 20: 11–17.Google Scholar
9.Samuels, S.M. (1980). Exact solutions for the full information best choice problem. Purdue University Statistics Department Mimeograph Series, pp. 82–87.Google Scholar
10.Samuels, S.M. (1991). Secretary problems. In Ghosh, B.K. & Sen, P.K. (eds.). Handbook of sequential analysis. New York: Marcel Dekker, pp. 381–405.Google Scholar
11.Tamaki, M. (1980). Optimal selection with two choices — Full information case. Mathematica Japonica 25: 359–368.Google Scholar
12.Tamaki, M. (1986). A full-information best-choice problem with finite memory. Journal of Applied Probability 23: 718–735.CrossRefGoogle Scholar