Order Selection Problems in Hiring Pipelines
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Motivated by hiring pipelines, we study two order selection problems in which applicants for a finite set of positions must be interviewed or made offers sequentially. There is a finite time budget for interviewing or making offers, and a stochastic realization after each decision, leading to computationally-challenging problems. In the first problem we study sequential interviewing, and show that a computationally-tractable, non-adaptive policy that must make offers immediately after interviewing is approximately optimal, assuming offerees always accept their offers. In the second problem, we assume that applicants have already been interviewed but only accept offers with some probability; we develop a computationally-tractable policy that makes offers for the different positions in parallel, which is approximately optimal even relative to a policy that does not need to make parallel offers. Our two results both generalize and improve the guarantees in the work of Purohit et al. on hiring algorithms, from 1/2 and 1/4 to approximation factors that are at least 1-1/e.
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