Title: Decision-making analysis for a new variant of the classical secretary problem

Authors: Yu Wu

Addresses: School of Transportation and Logistics, Southwest Jiaotong University, Chengdu, Sichuan, 611756, China

Abstract: In this paper, a new variant of the classic secretary problem is studied, in which the interviewer has a look-ahead privilege to observe partial future candidates before making a decision each time. Different from the classic problem, a decision can be deferred till some subsequent candidates are interviewed in this variant. We define the degree of look-ahead privilege on one candidate as how many candidates are sequentially interviewed from when this candidate is interviewed to when its decision is made. We first propose a general optimal decision strategy framework that can maximise the probability of successfully selecting the best candidate. Then, focusing on one specially structured look-ahead privilege, we apply the proposed strategy framework and obtain the probability of success in a closed function, to which an explicit solution will give the concrete optimal strategy; and further, through computational experiments, we study relationships between related parameters.

Keywords: secretary problem; look-ahead privilege; optimal strategy.

DOI: 10.1504/IJMOR.2024.138054

International Journal of Mathematics in Operational Research, 2024 Vol.27 No.3, pp.305 - 316

Received: 06 Jan 2023
Accepted: 14 Jan 2023
Published online: 18 Apr 2024 *

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