Dynamic programming formulation of the group interview problem with a general utility function

In many managerial decision situations such as buying an electronic appliance, 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 alternative, this optimal selection problem is known as the secretary problem, which has a long and rich history of research devoted to developing solution strategies. We propose a more generalized version of the secretary problem, called the group interview problem, in which each group contains more than one alternative and each group is presented and evaluated sequentially over time. Using a dynamic programming approach, we derive a backward recursive equation for solving the group interview problem in which a decision maker's utility of selecting a certain choice is expressed as a general function. Depending on the specific form of this function, we derive optimal selection strategies for various types of group interview problems such as minimum rank, maximum utility, best choice, and one out of the p best choice problems.