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Motivated by hiring pipelines, we study three selection and ordering problemsin which applicants for a finite set of positions must be interviewed or sentoffers. There is a finite time budget for interviewing/sending offers, andevery interview/offer is followed by a stochastic realization of discoveringthe applicant's quality or acceptance decision, leading to computationallychallenging problems. In the first problem, we study sequential interviewingand show that a computationally tractable, non-adaptive policy that must makeoffers immediately after interviewing is near-optimal, assuming offers arealways accepted. We further show how to use this policy as a subroutine forobtaining a PTAS. In the second problem, we assume that applicants have alreadybeen interviewed but only accept offers with some probability; we develop acomputationally tractable policy that makes offers for the different positionsin parallel, which can be used even if positions are heterogeneous, and isnear-optimal relative to a policy that can make the same total number of offersone by one. In the third problem, we introduce a parsimonious model ofoverbooking where all offers must be sent simultaneously and a linear penaltyis incurred for each acceptance beyond the number of positions; we providenearly tight bounds on the performance of practically motivated value-orderedpolicies.  All in all, our paper takes a unified approach to three different hiringproblems, based on linear programming. Our results in the first two problemsgeneralize and improve the existing guarantees due to Purohit et al. (2019)that were between 1/8 and 1/2 to new guarantees that are at least 1-1/e. Wealso numerically compare three different settings of making offers tocandidates (sequentially, in parallel, or simultaneously), providing insightinto when a firm should favor each one.

Selection and Ordering Policies for Hiring Pipelines via Linear Programming