Analytics and Bikes: Riding Tandem with Motivate to Improve Mobility

Daniel Freund, S. G. Henderson, E. O’Mahony, and D. B. Shmoys, Analytics and Bikes: Riding Tandem with Motivate to Improve Mobility, INFORMS Journal on Applied Analytics, Vol. 49, No. 5, 2019, Pages 307-396. (First Prize: Wagner Prize for Excellence in Operations Research Practice)

Bike-sharing systems are now ubiquitous across the United States. We have worked with Motivate, the operator of the systems in, for example, New York, Chicago, and San Francisco, to both innovate a data-driven approach to managing their day-to-day operations and provide insight on several central issues in the design of its systems. This work required the development of a number of new optimization models, characterization of their mathematical structure, and use of this insight in designing algorithms to solve them. Here, we focus on two particularly high-impact projects: an initiative to improve the allocation of docks to stations and the creation of an incentive scheme to crowdsource rebalancing. Both of these projects have been fully implemented to improve the performance of Motivate’s systems across the country; for example, the Bike Angels program in New York City yields a system-wide improvement comparable with that obtained through Motivate’s traditional rebalancing efforts at far less financial and environmental cost.

Methodology:

Estimating Unsatisfied Demand via User Dissatisfaction Functions: UDFs underlie almost all of our work with Motivate. These functions provide an inventory model that maps for each station and any planning horizon that station’s capacity (i.e., the maximum number of bikes that can be present at that station) and an initial number of bikes at that station at the start of the planning horizon to the expected number of stockouts over the course of the horizon....

We model users wishing to rent bikes through independent nonhomogeneous Poisson processes, one for each station. A user’s destination station is independently selected from an origin-dependent distribution, and biking times are independent (their distribution depends only on the origin/destination station pair)....

UDFs can thus be defined for each station and time interval in isolation; they map the initial number of bikes and empty docks at a station to the (expected) number of out-of-stock events over the course of the interval (O’Mahony 2015)....

To estimate the various parameters of, for example, the underlying Poisson processes or the transition matrix (of origin-dependent destination distributions), we use a combination of maximum likelihood and specialized decensoring techniques....

The nonlinear integer program for the system-wide optimization: Minimize UDFs.