Selecting the best choice in the weighted secretary problem

In the sequential evaluation and selection problem with n applicants, we assume that a decision maker has some prior information about each applicant so that unequal weights may be assigned to each applicant according to his or her likelihood of being the best among all applicants. Assuming that the pre-assigned weights are available in advance, we derive the optimal selection strategy that maximizes the probability of selecting the best among all applicants. For the case where the decision maker is permitted to rearrange the sequence in which applicants are evaluated, we further propose a simple heuristic procedure to the problem of optimally ordering the sequence of evaluations. Based on a pairwise comparison matrix and a goal programming procedure, we also propose a method that easily computes the weights in a practical situation.