The best-choice secretary problem with random freeze on jobs

Ester Samuel-Cahn

Stochastic Processes and their Applications, 1995, vol. 55, issue 2, 315-327

Abstract: We consider the best-choice secretary problem, with a known number, n, of applicants, and a random, independent "freeze" variable M, with known distribution. No hiring is possible after time M. The goal is to choose the best among the n applicants, where the decisions must be made depending only on the relative ranks of the applicants observed so far. A necessary and sufficient condition is given for the optimal rule to have the "simple" structure: let k* -- 1 applicants pass, and stop with the first applicant (if any) from the k*th onward, who is better than all previous observed candidates. For uniform, geometric and Poisson freeze variables the optimal rules are simple. Some asymptotic results (as n --> [infinity]), and minimax results are also discussed.

Keywords: Optimal stopping Random horizon Secretary problem Best choice; Job-freeze (search for similar items in EconPapers)
Date: 1995
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