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A secretary problem with backward solicitation and uncertain employment

  • K. I. Choe (a1) and D. S. Bai (a2)

Abstract

A secretary problem which allows the applicant to refuse an offer of employment with a fixed probability and admits backward solicitations of previous interviewees with known probability of successful solicitation is considered. The optimal strategy that maximizes the probability of employing the best applicant is derived. Two types of probability of successful solicitation, constant and geometric, are discussed in detail.

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Corresponding author

Postal Address: Department of Industrial Engineering, Ulsan Institute of Technology, Ulsan, Kyungnam, Korea.
∗∗ Postal Address: Department of Industrial Engineering, Korea Advanced Institute of Science and Technology, P.O. Box 150, Chongyangni, Seoul, Korea.

Footnotes

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Work done while this author was at Korea Advanced Institute of Science and Technology.

An earlier draft of the paper was presented at the Annual Meeting of the Korean Statistical Society held in Taegu, Korea, on May 16–17, 1981.

Footnotes

References

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Chow, Y. S., Moriguti, S., Robbins, H. and Samuels, S. M. (1964) Optimum selection based on relative rank (the ‘secretary problem’). Israel J. Math. 2, 8190.
Gilbert, J. P. and Mosteller, F. (1966) Recognizing the maximum of a sequence. J. Amer. Statist. Assoc. 61, 3573.
Lorenzen, T. J. (1981) Optimal stopping with sampling cost; the secretary problem. Ann. Prob. 9, 167172.
Smith, M. H. (1975) A secretary problem with uncertain employment. J. Appl. Prob. 12, 620624.
Yang, M. C. K. (1974) Recognizing the maximum of a random sequence based on relative rank with backward solicitation. J. Appl. Prob. 11, 504512.

Keywords

A secretary problem with backward solicitation and uncertain employment

  • K. I. Choe (a1) and D. S. Bai (a2)

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