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Optimal selection of thek best of a sequence withk stops

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  • Aarni Lehtinen

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 ε N, 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 values P k of the form $$P_k \approx \frac{1}{{(e - 1)k + 1}}$$ for any k ε N. Copyright Physica-Verlag 1997

Suggested Citation

  • Aarni Lehtinen, 1997. "Optimal selection of thek best of a sequence withk stops," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 46(2), pages 251-261, June.
    • Handle: RePEc:spr:mathme:v:46:y:1997:i:2:p:251-261
    DOI: 10.1007/BF01217694
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    References listed on IDEAS

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    1. R. J. Vanderbei, 1980. "The Optimal Choice of a Subset of a Population," Mathematics of Operations Research, INFORMS, vol. 5(4), pages 481-486, November.
    2. Wilson, John G., 1991. "Optimal choice and assignment of the best m of n randomly arriving items," Stochastic Processes and their Applications, Elsevier, vol. 39(2), pages 325-343, December.
    3. J. Preater, 1994. "On Multiple Choice Secretary Problems," Mathematics of Operations Research, INFORMS, vol. 19(3), pages 597-602, August.
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