A Rolling Recruitment Process Under Applicant Stochastic Departures

Problem definition: We study a rolling recruitment process in which applicants leave the system stochastically. Applicants arrive randomly over time, and each applicant is available for a random amount of time after they arrive. In each period, the recruiter must decide whether to stop or to wait. If the recruiter stops, he or she needs to determine how many offers to make and whom to make offers to, and the applicants who do not receive an offer will leave the system. If the recruiter waits, more applicants will be available in the next period, whereas some who arrived earlier will leave. Methodology/results: We model the process as a large-scale optimal stopping problem and show how the applicant qualifications, measured by scores, affect the recruiter’s optimal policy. Managerial implications: We find that the optimal stopping rule for each applicant’s score is a two-threshold policy. If the score exceeds the higher threshold, then the recruiter stops and makes an offer to the applicant and possibly to others. If the score falls below the lower threshold, then the recruiter also stops but makes no offer to the applicant. If the score is in between the two thresholds, the recruiter waits. We further explore the impact on an applicant’s likelihood of receiving an offer if his or her competitors become more qualified. When the score of another applicant increases, the recruiter may change from making an offer to an applicant to waiting or to instead making an offer to the other applicant whose score has increased. In other words, an applicant may be disadvantaged if he or she faces stronger competitors, which is expected. However, an applicant may also benefit from having stronger competitors. When the score of another applicant increases, the recruiter may change from not making an offer to an applicant to making an offer to both applicants. Overall, we provide valuable insights into the role of applicant qualifications in stopping decisions, propose methods for computing the optimal policy, and quantify the benefits of endogenously determining the stopping rule. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2024.1456 .