臺灣博碩士論文加值系統

本論文主要是研究秘書問題的三個推廣型問題。第一個問題是在標準秘書問題的條件下，探討使選中者的絕對名次不大s 的最佳策略，我們採用一個不同於Quine 和Law (1996)的方法來分析此問題，也給出一些極限的結果。接著我們探討兩個很自然的推廣型問題，其一稱為分組問題，另一稱為m位決策者的問題。在分組問題中假設有N組應徵者由一位經理逐個來面試，而m位決策者的問題中是有m位經理同時進行面試，其目標都是要找一個策略使選中最好的應徵者的機率最大。雖然這兩個問題比標準秘書問題複雜，但是我們仍可採用後退歸納法來找最佳策略而得到如同標準問題的最佳策略般美妙的結果。

We consider some variations of the secretary problem. Under the assumptions of the standard secretary problem, the optimal stopping rule which maximized the probability that the absolute rank of the selected one is not greater than s will be discussed in the first part of this article. We use a method which is different from that used in Quine and Law(1996). Some asymptotic results are also given. Besides this, we also consider two natural variations of the standard secretary problem. In the first variation, there are N groups of applicants interviewed sequentially by a manager; and in the second one, m managers go on with the interview at the same time. The goal for each variation is to find a strategy which maximizes the probability of selecting the best applicant. We use the usual backward induction method to find the optimal strategies, which are surprisingly as elegant as the one of the standard secretary problem.