Minimizing Multimodular Functions and Allocating Capacity in Bike-Sharing Systems

Daniel Freund (), Shane G. Henderson () and David B. Shmoys ()
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Daniel Freund: Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02142
Shane G. Henderson: School of Operations Research and Information Engineering, Cornell University, Ithaca, New York 14853
David B. Shmoys: School of Operations Research and Information Engineering, Cornell University, Ithaca, New York 14853

Operations Research, 2022, vol. 70, issue 5, 2715-2731

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 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.

Keywords: Transportation; discrete convexity; transportation; sharing economy (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:70:y:2022:i:5:p:2715-2731

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