Optimal Partitioning Of Groups In Selecting The Best Or The Second Best Choice

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^*.