Minimizing Multimodular Functions and Allocating Capacity in Bike-Sharing Systems

• 成果类型: Article; Early Access
• 署名作者: Freund, Daniel; Henderson, Shane G.; Shmoys, David B.
• 署名单位: Massachusetts Institute of Technology (MIT); Cornell University
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2022.2320
• 发表日期: 2022
• 页码: 1-17
• 关键词: static repositioning problem; rebalancing problem; optimization; convexity; algorithm; models

摘要

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 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 daily rebalancing of bikes.