DYNAMIC-PROGRAMMING FORMULATION OF THE GROUP INTERVIEW PROBLEM WITH AGENERAL UTILITY FUNCTION

In many managerial decision situations such as buying an electronic ap pliance, several groups of alternatives are presented sequentially and an accept-or-reject decision is made immediately after evaluating the alternatives in each group. If each group contains only one alternati ve, this optimal selection problem is known as the secretary problem w hich has a long and rich history of research devoted to developing sol ution strategies. We propose a more generalized version of the secreta ry problem, called the group interview problem, in which each group co ntains more than one alternative and each group is presented and evalu ated sequentially over time. Using a dynamic programming approach, we derive a backward recursive equation for solving the group interview p roblem in which a decision maker's utility of selecting a certain choi ce is expressed as a general function. Depending on the specific form of this function, we derive optimal selection strategies for various t ypes of group interview problems such as minimum rank, maximum utility , best choice, and one out of the p best choice problems.