Skip to main content
SpringerLink
Log in

Optimal selection of thek best of a sequence withk stops

  • Published:
Mathematical Methods of Operations Research Aims and scope Submit manuscript

Abstract

We first consider the situation in which the decision-maker is allowed to have five choices with purpose to choose exactly the five absolute best candidates fromN applicants. The optimal stopping rule and the maximum probability of making the right five-choice are given for largeN εN, the maximum asymptotic value of the probability of the best choice being lim N→∝ P (win) ≈ 0.104305. Then, we study the general problem of selecting thek best of a sequence withk stops, constructing first a rough solution for this problem. Using this suboptimal solution, we find an approximation for the optimal probability valuesP k of the form

$$P_k \approx \frac{1}{{(e - 1)k + 1}}$$

for any k εN.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Ano K (1989) Optimal selection problem with three stops. J. Oper. Res. Soc. Japan 32:491–504

    Google Scholar 

  • Ano K (1992) Doctor thesis, University of Osaka, Japan

    Google Scholar 

  • Ferguson T (1989) Who solved the secretary problem? Statistical Science 4:282–296

    Google Scholar 

  • Freeman P (1983) The secretary problem and its extensions: A review. Internat. Statist. Rev. 51:189–206

    Google Scholar 

  • Lehtinen A (1992) Recognizing the three best of a sequence. Ann. Acad. Sci. Fenn. 17:73–79

    Google Scholar 

  • Lehtinen A (1993) The best choice problem with an unknown number of objects. Z. für Oper. Res. 37:97–106

    Google Scholar 

  • Lehtinen A (1993) Optimal selection of the four best of a sequence. Z. für Oper. Res. 38:309–315

    Google Scholar 

  • Nikolaev M (1977) On a generalization of the best choice problem. Theory Prob. Appl. 22:187–190

    Google Scholar 

  • Preater J (1994) On multiple choice secretary problems. Math. Oper. Res. 19:597–602

    Google Scholar 

  • Samuels SM (1991) Secretary problems. In: Ghosh BK, Sen PK (eds.) Handbook of Sequential Analysis, Marcel Dekker, Boston, pp. 381–405

    Google Scholar 

  • Tamaki M (1979) Recognizing both the maximum and the second maximum of a sequence. J. Appl. Prob. 16:803–812

    Google Scholar 

  • Vanderbei RJ (1980) The optimal choice of a subset of a population. Math. Oper. Res. 5:481–486

    Google Scholar 

  • Wilson JG (1991) Optimal choice and assignment of the best m of n randomly arriving items. Stoch. Proc. Appl. 39:325–343

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Jyväskylä, P.O. Box 35, SF-40351, Jyväskylä, Finland

    Aarni Lehtinen

Authors
  1. Aarni Lehtinen
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lehtinen, A. Optimal selection of thek best of a sequence withk stops. Mathematical Methods of Operations Research 46, 251–261 (1997). https://doi.org/10.1007/BF01217694

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01217694

Key words

Search

Navigation