Decision-making analysis for a new variant of the classical secretary problem Online publication date: Thu, 18-Apr-2024
by Yu Wu
International Journal of Mathematics in Operational Research (IJMOR), Vol. 27, No. 3, 2024
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.
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