The Secretary Problem With Multiple Job Vacancies And Batch Candidate Arrivals

We extend the secretary problem with multiple vacancies to allow batch arrival of candidates. We establish structural properties of the optimal policies. We show that the optimal reward is convex and submodular in the values of candidates, which means that there is benefit for having a candidate pool with more variable or less interdependent values. Similar properties continue to hold when there are multiple classes of vacancies. Our model is applicable to recruitment, dynamic auctions and sequential investment. (C) 2021 Elsevier B.V. All rights reserved.