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Approximate Results for a Generalized Secretary Problem

Author

Listed:
  • Chris Dietz

    (VU University Amsterdam)

  • Dinard van der Laan

    (VU University Amsterdam)

  • Ad Ridder

    (VU University Amsterdam)

Abstract
This discussion paper resulted in a publication in 'Probability in the Engineering and Informational Sciences' , 2011, 25(2), 157-69. A version of the classical secretary problem is studied, in which one is interested in selecting one of the b best out of a group of n differently ranked persons who are presented one by one in a random order. It is assumed that b is bigger than or equal to 1 is a preassigned number. It is known, already for a long time, that for the optimal policy one needs to compute b position thresholds, for instance via backwards induction. In this paper we study approximate policies, that use just a single or a double position threshold, albeit in conjunction with a level rank. We give exact and asymptotic (as n goes to infinity) results, which show that the double-level policy is an extremely accurate approximation.

Suggested Citation

  • Chris Dietz & Dinard van der Laan & Ad Ridder, 2010. "Approximate Results for a Generalized Secretary Problem," Tinbergen Institute Discussion Papers 10-092/4, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20100092
    as

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    File URL: https://papers.tinbergen.nl/10092.pdf
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    References listed on IDEAS

    as
    1. Frank, Arthur Q. & Samuels, Stephen M., 1980. "On an optimal stopping problem of Gusein-Zade," Stochastic Processes and their Applications, Elsevier, vol. 10(3), pages 299-311, October.
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    More about this item

    Keywords

    Secretary Problem; Dynamic Programming; Approximate Policies;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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