Optimizing Multiple Selections with a Random Number of Objects

The optimal stopping rules with multiple selections of m 1 objects with the objective of maximizing the probability of obtaining the best object are studied for two problems with an unknown number of objects:the problem with a random number of objects, and the problem where the objects arrive according to a homogeneous Poisson process with unknown intensity . These two problems are variation of the socalled secretary problem. This article introduces an easier method based on the one-stage look-ahead function (de ned herein) depending on m and its recursive relation to the number m, to nd the optimal stopping rule for all m, without a direct solution of equations suggested by a common dynamic programming approach. SECRETARY PROBLEM; OPTIMAL STOPPING; MULTIPLE CHOICES; PASCAL PROCESS AMS 1991 SUBJECT CLASSIFICATION: 60G40