Minimizing Multimodular Functions and Allocating Capacity in Bike-Sharing Systems

Abstract

Station-based bike-sharing systems have changed the urban landscape of major American cities including New York City, Boston, Washington DC, and Chicago. In these systems, stations are capacitated: a station’s capacity is given by the number of docks it consists of. Each dock can either be filled with a bike or empty with the number of bikes at the station fluctuating throughout the day. Interestingly, in these systems, stockouts can occur both when stations are empty (making rentals impossible) and when stations are full (making returns impossible). Avoiding stockouts of either type is the most pressing operational concern faced by these systems. Our work on capacity management in bike-sharing systems studies the strategic question of how to size stations in these systems in order to minimize stockouts of either kind. Our findings suggest that reallocating a small portion of the capacity within a system is a cost-efficient way to significantly improve service levels.