The group interview problem: Optimal selection and ordering strategies with sequentially presented groups of choices

Young Hak Chun, Purdue University

Abstract

In the so-called secretary problem and its extensions, we must make an irrevocable choice from a number of opportunities whose values or relative ranks are revealed only one after another. In the group interview problem however, we assume that groups of alternatives are presented one after another. This thesis deals with the group interview problem and its variations. After an introductory statement in Chapter I, Chapter II gives a historical development outlining the past variations and generalizations of the classical secretary problem which most likely relate to our own work. All published work to date on the secretary problem and its extensions is briefly reviewed. Chapter III and Chapter IV are devoted entirely to the no information group interview problem and its variations, in which no information is available except on the number of groups and the size of each group. Our decision is solely based on the relative ranks of the choices. In particular, Chapter III treats the minimum rank and the maximum utility group interview problems, while Chapter IV deals with the best choice, second-best choice, and one out of the p best choice group interview problems. The full information and the partial information group interview problems are discussed in Chapter V. We propose several selection strategies in the full information case; some of them maximize the probability of selecting the best choice, while others maximize the expected value of the selected choice. The partial information best choice problem is based on Bayesian statistics, because in this case the values are drawn from an incompletely known distribution whose parameters are unknown a priori. Unlike the classical secretary problem, the group interview problem gives rise to another interesting decision problem when we are permitted to determine the sequence in which groups are interviewed. This problem is called the optimal ordering strategy and discussed in Chapter VI. For the optimal ordering in the no information best choice problem, we propose an efficient heuristic algorithm and conduct a simulation experiment to analyze its performance in obtaining an optimal ordering of groups. The exact solution in the optimal ordering strategy in the full information case is also investigated.

Degree

Ph.D.

Advisors

Plante, Purdue University.

Subject Area

Management|Operations research

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