【作者】 刘欣；

【导师】 孙平；

【作者基本信息】 东北大学 ， 应用数学， 2006， 硕士

【摘要】 秘书问题研究的是报酬函数仅与所选项的秩相关而与其实际值无关的序贯观察和选择问题。它属于概率论与最优化理论的一个交叉研究领域，是最优停止理论中的一个著名问题。本文主要讨论秘书问题的变形——“组面试问题”在目标是选择最优或次优时的最佳选择策略(停止规则)，采用的主要方法是后退归纳法和边界阶段方法。在通过边界阶段方法得到的最优组面试问题的最佳选择策略基础上，第二章给出了允许重排序时获得最佳排序的定理。第三章重点讨论最优或次优组面试问题的最佳划分选择策略，并得到了确定两个边界阶段的最优不等式。更多还原

【Abstract】 Secretary problems refer to the sequential observations and selection problems in which the payoff depends on the observations only through their relative ranks and not otherwise on their actual values. As a famous problem of optimal stopping theory, it constitutes a field of study within probability-optimization. This article deals with a natural variation of the classical secretary problem called the group interview problem, in which each group contains several alternatives and each group of alternatives is presented and evaluated sequentially over time. In the second chapter we develop a simple heuristic procedure to the ordering problem of the group interview problem in selecting the best choice. In the third chapter we derive the optimal selection rule called the optimal partitioning strategy for the group interview problem in selecting the best or the second best choice by backward induction and boundary stage method. We obtain the optimal inequalities of the two boundary stage k₁^* and k₂^*.更多还原