Optimization Model May Help Cities Improve Bike-Sharing Programs

An increasingly popular transportation option in cities has created a series of problems that are ripe for operations research, as Willem-Jan van Hoeve illustrates in a paper published March 2017 in the European Journal of Operational Research with coauthors Robert Hampshire, previously an assistant professor of operations research at Carnegie Mellon’s H. John Heinz III College, and a visiting student, Jasper Schuijbroek.

The trio studied bike-sharing systems and how to solve common cost drivers, such as balancing the number of bikes so an appropriate number of both bicycles and open docks are available to users. Rebalancing the bicycle inventory over time “is, next to pricing, perhaps the most important operations challenge,” said Van Hoeve, Carnegie Bosch Associate Professor of Operations Research, adding that it offered “a nice mix of stochastic and deterministic optimization.” 

Previous models didn’t work well because they were able to accommodate, at most, 50 bike stations over a limited time, even though larger cities can have more than a thousand stations.

Using data from Hubway, a bike-sharing system in Boston, and Capital Bikeshare in Washington, D.C., they created a database and captured usage patterns to predict what might be needed. They clustered groups of stations in order to reallocate bikes to create inventory between the upper and lower bounds of optimal levels during different times. The clusters also made the models small enough to scale.

The group developed a model that estimates the minimum and maximum number of bikes and parking spaces needed at each station to serve 95 percent of demand for a given time frame. For example, the most bicycles might be needed between 8 and 9 a.m. near railway stations, and the sought-after parking spots might be needed near restaurants at lunchtime.

Determining the appropriate number of parking spaces is a critical issue. If riders can’t drop off their bikes, they likely will have to pay for more time — a point of frustration for the service’s customers.