Optimal selection of thek best of a sequence withk stops

6533b862fe1ef96bd12c6be6

RESEARCH PRODUCT

Optimal selection of thek best of a sequence withk stops

subject

Sequence Selection (relational algebra)General Mathematics General problem Value (computer science)Management Science and Operations Research Approx Combinatorics Optimal stopping rule Optimal stopping Algorithm Software Secretary problem Mathematics

description

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 eN, the maximum asymptotic value of the probability of the best choice being limN→∝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 valuesPk of the form $$P_k \approx \frac{1}{{(e - 1)k + 1}}$$ for any k eN.

year	journal	country	edition	language
1997-06-01	Mathematical Methods of Operations Research

https://doi.org/10.1007/bf01217694

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