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

TL;DR

This work tackles the efficiency–equity tension created by library holds systems, focusing on how to preserve system-wide usage while maintaining in-person browser quality. It develops a theoretical server-fulfillment model with a $\frac{1}{2}$-optimal policy via a value-function approximation, and couples it with a simulation-optimization framework to balance browser experience through browser reserves. Calibrated to NYPL data, the approach reveals a meaningful usage–browser-experience trade-off but identifies a Pareto-frontier of implementable policies that improve browser experience—especially in low-income branches—with minimal loss to overall usage, thereby enhancing equity. The framework offers a practical path for public-interest operations to jointly optimize throughput and user experience, with potential applicability to other urban library systems and similar networked-resource settings.

Abstract

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%.

Figures (11)

• Figure 1: (a) The median income of patrons served by each library branch differs substantially across the boroughs of Manhattan (center), the Bronx (upper right), and Staten Island (left). (b) Substantial differences in patrons' tendency to use the holds system among branches, correlated with neighborhood income levels, as shown in liu2024identifying. For example, branches in Manhattan tend to serve higher-income patrons, who also use the holds system more, compared to branches in the Bronx. (c) Hold usage disproportionately pulls books from low-hold-usage and lower-income branches and thus worsens browser experience there. This effect is measured through the net desirability inflow of each branch, calculated as the difference between the number of books taken from other branches to fulfill holds at this branch and the number of books taken from this branch to fulfill holds at all other branches, weighted by the desirability of each book title. Book desirability, as measured by liu2024identifying, is a score between 0 and 1 assigned to each book title, with higher scores indicating a higher probability of getting checked out conditional on availability. We note that, once a book is returned by the holds user, it is returned to the source library.
• Figure 2: (Left) Pareto curve of the usage and browser experience objectives, based on 1,600 policies evaluated through the Bayesian optimization procedure. For each of the policies on the Pareto frontier, we additionally evaluate their implementable version. Historical data and a simulation of a policy approximating the historical policy achieve similar objective values. Crucially, we find many policies that Pareto dominate historical data. (Right) Examining one policy (denoted Balanced) in detail, we find that it achieves higher browser experience generally across branches and more overall usage in branches in lower-income neighborhoods, at the cost of some usage at higher-income branches. These patterns reflect the balanced policy reserving some book copies for in-person browsers, who are disproportionately patrons of branches in lower-income neighborhoods.
• Figure 3: Map of the usage and browser experience objectives at each branch, for each of the historical data and under the Balanced policy (ratios between the usage and browser experience values for the respective policy and the 'optimal' benchmark for that objective). We find that (1) the Balanced policy preserves usage for most branches compared to the Historical policy, except for some branches in lower Manhattan (lower tip of the center part of the map); (2) the balanced policy improves browser experience generally across branches, and especially branches in the Bronx (upper right), which are predominantly serving lower-income neighborhoods, who rely on browsing more (have lower hold usage). This is consistent with the Pareto curve in \ref{['fig:pareto']}, which shows that the historical policy relatively prioritized overall usage, at the expense of the browser experience.
• Figure 4: We study the impact of the balanced policy on one branch in particular: High Bridge Library in the Bronx, which serves an area highlighted in blue in subfigure (a). In the calendar year 2022, this moderately sized branch was among the lowest hold usage branches, and incurred the 6th highest net desirability outflow, as shown in \ref{['fig:1c']}. As illustrated in (a), historically, books from this branch are used to fulfill hold requests from branches predominantly in midtown and downtown Manhattan, and the Upper West and Upper East Sides (dark red areas in the middle of the plot); in contrast, under the Balanced policy, it incurs much less overall outflow, with an evenly distributed net outflow pattern. We further study the total inventory levels of 60 of the most popular book titles (roughly 2% of the total number of book titles simulated) at this branch. In subfigure (b), we compare the inventory levels over 30 simulation runs under the Balanced policy and approximate historical policy. The Balanced policy achieves higher inventory levels at equilibrium, providing a better browser experience at this branch.
• Figure 5: Latent demand sizes of each branch and latent desirability of each book title are used in conjunction with hold usage fraction of each branch (\ref{['fig:1b']}) to calculate arrival probability of each type of patron. The calculation is presented in \ref{['eq:browserarrival']}, and further adjustments are made for better calibration.

Theorems & Definitions (6)

• Proposition 1
• Proposition 2
• Lemma 1
• proof
• Proposition 2
• proof