Motivated by hiring pipelines, we study three selection and ordering problems in which applicants for a finite set of positions must be 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, non-adaptive 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 PTAS. 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 must be 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 due to 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 into when a firm should favor each one.

翻译：受招聘流程启发，我们研究了三个涉及有限职位申请者必须进行面试或收到录用通知的筛选与排序问题。面试/发出录用通知存在有限时间预算，每次面试/发出录用通知后，会随机发现申请者能力或接受意愿，这导致了计算上的挑战性问题。在第一个问题中，我们研究了顺序面试，并证明了一种计算上可行、非自适应的策略在假设录用通知总是被接受的情况下，可以在面试后立即发出录用通知且接近最优。我们进一步展示了如何将该策略作为子程序来获得多项式时间近似方案（PTAS）。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；我们开发了一种计算上可行的策略，可并行地向不同职位发出录用通知，即使职位具有异质性也能使用，且相对于能逐一发出相同总数录用通知的策略而言接近最优。在第三个问题中，我们引入了一个简洁的超额预订模型，其中所有录用通知必须同时发出，且每超出职位数量一个接受行为将产生线性惩罚；我们为实际中具有动机的价值排序策略提供了几乎紧的性能界。总体而言，本文基于线性规划对三种不同的招聘问题采用了统一方法。我们在前两个问题中的结果将Purohit等人（2019）现有保证的1/8至1/2泛化并改进为至少1-1/e的新保证。我们还对向候选者发出录用通知的三种不同设置（顺序、并行或同时）进行了数值比较，为企业在何种情况下应偏好每种方式提供了见解。