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A markov chain version of the secretary problem

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  • S. Christian Albright

Abstract

This paper deals with the Secretary Problem where n secretaries are interviewed sequentially and the best k must be hired. The values of the secretaries are observed as they are interviewed, but beforehand only the distributions of these values are known. Furthermore, the distributions of two successive secretaries' values are governed by a Markov chain. Optimal hiring policies for finite n and limiting optimal policies as k and n approach infinity are obtained.

Suggested Citation

  • S. Christian Albright, 1976. "A markov chain version of the secretary problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 23(1), pages 151-159, March.
    • Handle: RePEc:wly:navlog:v:23:y:1976:i:1:p:151-159
    DOI: 10.1002/nav.3800230114
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    Cited by:

    1. Meghan Shanks & Ge Yu & Sheldon H. Jacobson, 2023. "Approximation algorithms for stochastic online matching with reusable resources," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 98(1), pages 43-56, August.
    2. Golshid Baharian & Sheldon H. Jacobson, 2013. "Limiting behavior of the stochastic sequential assignment problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(4), pages 321-330, June.

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