# Minimizing Multimodular Functions and Allocating Capacity in Bike-Sharing Systems

arXiv: https://arxiv.org/abs/1611.09304 · HTML: https://mlsanity.com/paper/1611.09304/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Nov 2016.

## Built on by (most cited first, 3 of 3)

- [A Fair OR-ML Framework for Resource Substitution in Large-Scale Networks](https://mlsanity.com/paper/2511.18269/) (2025)
- [A* search algorithm for an optimal investment problem in vehicle-sharing systems](https://mlsanity.com/paper/2311.08834/) (2023)
- [Online Lnatural-Convex Minimization](https://mlsanity.com/paper/2404.17158/) (2024)

## Abstract (arXiv)

The growing popularity of bike-sharing systems around the world has motivated recent attention to models and algorithms for their effective operation. Most of this literature focuses on their daily operation for managing asymmetric demand. In this work, we consider the more strategic question of how to (re-)allocate dock-capacity in such systems. We develop mathematical formulations for variations of this problem (either for service performance over the course of one day or for a long-run-average) and exhibit discrete convex properties in associated optimization problems. This allows us to design a practically fast polynomial-time allocation algorithm to compute an optimal solution for this problem, which can also handle practically motivated constraints, such as a limit on the number of docks moved in the system. We apply our algorithm to data sets from Boston, New York City, and Chicago to investigate how different dock allocations can yield better service in these systems. Recommendations based on our analysis have led to changes in the system design in Chicago and New York City. Beyond optimizing for improved quality of service through better allocations, our results also provide a metric to compare the impact of strategically reallocating docks and the rebalancing of bikes.