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A Random Arrival Time Best-Choice Problem with Uniform Prior on the Number of Arrivals

In: Optimization and Optimal Control

Author

Listed:
  • Mitsushi Tamaki

    (Aichi University)

  • Qi Wang

    (Aichi University)

Abstract

Summary Suppose that a random number N of rankable applicants appear and their arrival times are i.i.d. random variables having a known distribution function. A method of choosing the best applicant is investigated when a prior on N is uniform on $$\{1,2,\ldots ,n\}$$ . An exact form of the optimal selection rule is derived. Stewart first studied this problem, but examined only the case of the non-informative prior, i.e., the limiting case of $$n\to \infty$$ , so our result can be considered as a generalization of Stewart’s result.

Suggested Citation

  • Mitsushi Tamaki & Qi Wang, 2010. "A Random Arrival Time Best-Choice Problem with Uniform Prior on the Number of Arrivals," Springer Optimization and Its Applications, in: Altannar Chinchuluun & Panos M. Pardalos & Rentsen Enkhbat & Ider Tseveendorj (ed.), Optimization and Optimal Control, pages 499-510, Springer.
    • Handle: RePEc:spr:spochp:978-0-387-89496-6_24
    DOI: 10.1007/978-0-387-89496-6_24
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    Cited by:

    1. Gnedin, Alexander, 2022. "The best choice problem with random arrivals: How to beat the 1/e-strategy," Stochastic Processes and their Applications, Elsevier, vol. 145(C), pages 226-240.
    2. Alexander Gnedin & Zakaria Derbazi, 2022. "Trapping the Ultimate Success," Mathematics, MDPI, vol. 10(1), pages 1-19, January.

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