Optimizing Library Usage and Browser Experience: Application to the New York Public Library

We tackle the challenge brought to urban library systems by the {holds system} -- which allows users to request books available at other branches to be transferred for local pickup. The holds system increases usage of the entire collection, at the expense of an in-person browser's experience at the source branch. We study the optimization of usage and browser experience, where the library has two levers: where a book should come from when a hold request is placed, and how many book copies at each branch should be available through the holds system versus reserved for browsers. We first show that the problem of maximizing usage can be viewed through the lens of revenue management, for which near-optimal fulfillment policies exist. We then develop a simulation framework that further optimizes for browser experience, through book reservations. We empirically apply our methods to data from the New York Public Library to design implementable policies. We find that though a substantial trade-off exists between these two desiderata, a balanced policy can improve browser experience over the historical policy without significantly sacrificing usage. Because browser usage is more prevalent among branches in low-income areas, this policy further increases system-wide equity: notably, for branches in the 25% lowest-income neighborhoods, it improves both usage and browser experience by about 15%.