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Selection and Ordering Policies for Hiring Pipelines via Linear Programming

Author

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  • Boris Epstein

    (Graduate School of Business, Columbia University, New York, New York 10027)

  • Will Ma

    (Graduate School of Business, Columbia University, New York, New York 10027)

Abstract

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 .

Suggested Citation

  • Boris Epstein & Will Ma, 2024. "Selection and Ordering Policies for Hiring Pipelines via Linear Programming," Operations Research, INFORMS, vol. 72(5), pages 2000-2013, September.
    • Handle: RePEc:inm:oropre:v:72:y:2024:i:5:p:2000-2013
    DOI: 10.1287/opre.2023.0061
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    References listed on IDEAS

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    1. Hedyeh Beyhaghi & Negin Golrezaei & Renato Paes Leme & Martin Pál & Balasubramanian Sivan, 2021. "Improved Revenue Bounds for Posted-Price and Second-Price Mechanisms," Operations Research, INFORMS, vol. 69(6), pages 1805-1822, November.
    2. Guillermo Gallego & Huseyin Topaloglu, 2019. "Revenue Management and Pricing Analytics," International Series in Operations Research and Management Science, Springer, number 978-1-4939-9606-3, May.
    3. Nick Arnosti & Will Ma, 2023. "Tight Guarantees for Static Threshold Policies in the Prophet Secretary Problem," Operations Research, INFORMS, vol. 71(5), pages 1777-1788, September.
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    Cited by:

    1. Chenyin Gong & Qing Li, 2026. "A Rolling Recruitment Process Under Applicant Stochastic Departures," Manufacturing & Service Operations Management, INFORMS, vol. 28(1), pages 290-307, January.
    2. Sebastian Perez-Salazar & Mohit Singh & Alejandro Toriello, 2025. "Robust Online Selection with Uncertain Offer Acceptance," Mathematics of Operations Research, INFORMS, vol. 50(3), pages 2226-2260, August.

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