Hiring Under Uncertainty: Stochastic Optimization through Dynamic Programming

Abstract

Making decisions under uncertainty is one of the most challenging problems faced by individuals in society today. When a company decides to hire candidates, it must make a decision before observing future candidates. Making the wrong decision will be very costly, leading to inefficiencies through either missing out on high-quality candidates, or hiring under-performing candidates.

This paper extends the Secretary Problem and builds on previous models to analyze the case where we have to hire k out of n candidates, each arriving sequentially. Several different approaches will be examined, with a focus on dynamic programming and optimizing for the sum of the values of the accepted candidates rather than the probability of selecting the best candidate. We will also discuss how feasible it is to implement each approach in real life, with an emphasis on interpretability, time and space considerations, and also ease of implementation.

Next, we will look at decision making from a candidate's perspective, and how each candidate's choice of applying early or late can impact their chance of being accepted. We will show whether each approach from above can be exploited, and possible steps taken to mitigate any detrimental effects.

Furthermore, we will look at extensions to the above problem to concepts in finance, specifically auctions in which a series of bids are made for multiple copies of the same item. We will consider storage costs, interest rates, depreciation and also mean-variance utility.

Lastly, we will look at how our approach can be adapted to fit models such as changing candidate distributions over time, the probability of candidates rejecting, dynamic rejections over time, the possibility of firing previously accepted candidates and more.