Keywords: [ Stochastic Optimization ] [ decision making under uncertainty ] [ Approximation Algorithms ]
In academic recruitment settings, including faculty hiring and PhD admissions, committees aim to maximize the overall quality of recruited candidates, but there is uncertainty about whether a candidate would accept an offer if given one. Previous work has considered algorithms that make offers sequentially and are subject to a hard budget constraint. We argue that these modeling choices may be inconsistent with the practice of academic recruitment. Instead, we restrict ourselves to a single batch of offers, and we treat the target number of positions as a soft constraint, so we risk overshooting or undershooting the target. Specifically, our objective is to select a subset of candidates that maximizes the overall expected value associated with candidates who accept, minus an expected penalty for deviating from the target. We first analyze the guarantees provided by natural greedy heuristics, showing their desirable properties despite the simplicity. Depending on the structure of the penalty function, we further develop algorithms that provide fully polynomial-time approximation schemes and constant-factor approximations to this objective. Empirical evaluation of our algorithms corroborates these theoretical results.