Minimizing Multimodular Functions and Allocating Capacity in Bike-Sharing Systems

TL;DR

This paper presents a novel polynomial-time algorithm for optimal dock-capacity allocation in bike-sharing systems, improving service quality and informing system design through data-driven analysis.

Contribution

It introduces a mathematical formulation with discrete convex properties and a fast algorithm for capacity reallocation, addressing a strategic planning problem in bike-sharing systems.

Findings

Algorithm successfully applied to real city data sets.

Optimal allocations improve service performance.

System design changes implemented based on analysis.

Abstract

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.