Selection and Ordering Policies for Hiring Pipelines via Linear Programming

Hiring the right person for the job is crucial for the success of any organization. In “Selection and Ordering Policies for Hiring Pipelines via Linear Programming,” Epstein and Ma study several problems motivated by a firm that is carrying out a recruitment process. Restricted to a finite time budget, the firm must decide who will be interviewed out of a pool of applicants and who will receive offers among the interviewed applicants. They develop approximation algorithms with constant factor guarantees that approach optimality when the number of vacant positions grows large. The algorithms they develop are nonadaptive: they fix a subset of candidates and an order to conduct the interviews and the order remains unchanged, independent of the outcomes of other interviews. Thus, they establish bounds on the adaptivity gap: a worst-case measure of how poorly non-adaptive algorithms can perform with respect to their adaptive counterparts.

Motivated by hiring pipelines, we study three selection and ordering problems in which applicants for a finite set of positions are interviewed or sent offers. There is a finite time budget for interviewing/sending offers, and every interview/offer is followed by a stochastic realization of discovering the applicant’s quality or acceptance decision, leading to computationally challenging problems. In the first problem, we study sequential interviewing and show that a computationally tractable, nonadaptive policy that must make offers immediately after interviewing is near optimal, assuming offers are always accepted. We further show how to use this policy as a subroutine for obtaining a polynomial-time approximation scheme. 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 can be used even if positions are heterogeneous, and is near optimal relative to a policy that can make the same total number of offers one by one. In the third problem, we introduce a parsimonious model of overbooking where all offers are sent simultaneously, and a linear penalty is incurred for each acceptance beyond the number of positions; we provide nearly tight bounds on the performance of practically motivated value-ordered policies. All in all, our paper takes a unified approach to three different hiring problems based on linear programming. Our results in the first two problems generalize and improve the existing guarantees in the literature that were between 1/8 and 1/2 to new guarantees that are at least 1−1/e≈63.2%. We also numerically compare three different settings of making offers to candidates (sequentially, in parallel, or simultaneously), providing insight into when a firm should favor each one.

Supplemental Material: The online appendices are available at https://doi.org/10.1287/opre.2023.0061.