Optimal selection problem with three stops

Optimal selection problems with multiple choices, like secretary, dowry or marriage problems have attracted attention of many applied mathematicians and are also of great significance for those who are looking for ‘the best partner’. This paper considers a variation of the optimal selection problem with three stops allowed, which is often referred to as the secretary problem with multiple choices where the objective is to find an optimal stopping rule so as to maximize the probability of selecting three absolute bests. It also presents a set of dynamic programming equations for the problems both of selecting the best object with three stops and of selecting two absolute bests with three stops. For these problems the optimal stopping rules are numerically calculated by the aid of computer programming.