Motivated by hiring pipelines, we study three selection and ordering problems in which applicants for a finite set of positions must be interviewed or made offers to. 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 can be used even if positions are heterogeneous and is approximately optimal relative to a policy that can make the same amount of offers not in parallel. In the third problem, we introduce a model where the hiring firm is tightly time constrained and must send all offers simultaneously in a single time step, with the possibility of hiring over capacity at a cost; we provide nearly-tight bounds for 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 guarantees from Purohit et al. (2019) that were between 1/8 and 1/2 to new guarantees that are at least 1-1/e. We also numerically compare three different settings of making offers to candidates (sequentially, in parallel, or simultaneously), providing insight on when a firm should favor each one.

翻译：受招聘流程的启发，我们研究了三个有关筛选与排序的问题，其中有限数量职位的申请者必须接受面试或获得录用通知。面试或发放录用通知均有有限的时间预算，且每次决策后会出现随机结果，导致问题在计算上具有挑战性。在第一个问题中，我们研究了顺序面试，并证明在假设被录用者始终接受录用通知的条件下，一种计算上可行、非自适应的策略（要求面试后立即发放录用通知）近似最优。在第二个问题中，我们假设申请者已完成面试，但仅以一定概率接受录用通知；我们提出了一种计算上可行的策略，可并行地向不同职位发放录用通知，该策略即使面对异质性职位也适用，且相较于非并行发放同等数量录用通知的策略，近似最优。在第三个问题中，我们引入了一个模型，其中招聘公司时间紧迫，必须在单个时间步内同时发送所有录用通知，并允许以一定成本超员招聘；我们为实际中受启发的价值排序策略的性能提供了近乎紧的边界。总体而言，我们的论文基于线性规划，采用统一方法处理了三个不同的招聘问题。在前两个问题中，我们将Purohit等人(2019)的保证（介于1/8和1/2之间）改进并推广为至少1-1/e的新保证。我们还通过数值比较了三种不同的录用发放方式（顺序、并行或同时），为企业在何种情况下应优先选择哪种方式提供了见解。