The Financial Times has an essay about the challenges of allocating bikes across a system of subscribers to common pool bike supply. Go check out the story.

Planners, particularly walk and bike planners, are fond of dismissing mathematical and analytical problems in transport, I strongly suspect because a good number of planners are badly trained in math. While it’s 100 percent true, I think, that much of planning is about negotiating and deal making, in private-sector transport services, the way the world seems to be going, things actually have to run, and for many things to run, you have to solve a math puzzle.

So London’s Barclay Bike services has a bike allocation problem that mirrors (but not quite) the basic empty backhaul problem in transport that plagues everything from freight to airlines.

Nick Aldworth, who manages the bikes for Transport for London, explained to me that running London’s scheme is about coping with all the people who want to get from A to B, while encouraging as many as possible to go from B to A, and C to D. “We need people to understand there is a limit to what we can achieve in one direction,” he said. “We need that balance.”

There is a limit, but people don’t have to understand–they are paying for service. If this market works and Barclay can’t figure it out, somebody else will.

Here’s the visualization of bike movements around London:

Boris Bikes redux from Sociable Physics on Vimeo.

So we have a standard spatial allocation problem, where the routing is generally figured out by customers, The issue for Barclay is that it probably has three separate market segments for origins and destinations: 1) are regular commuters whose demand patterns can be predicted, within reason, using Bayesian methods–i.e., what these customers have done on most every weekday; 2) ‘package’ commuters, who have multiple modal options and package services based on the whims and characteristics of the day (raining, snowing, etc). and 3) tourists and other stochastic (but somewhat predictable) consumers who are likely in their behavior to act like group #2 (people who will take a bike from one location, leave it, and then call a cab or take a bus when tired, leaving the bike in a potentially low-demand deposit area).

Customers from group 1 are easy to serve; the second two less so because of the stochastic nature of their timings and destinations, but, again, probably have some aggregate spatial demand patterns you can loosely predict by the days of the week, the seasons, and the likely aggregation of activities. You know people are going to visit Westminister Abbey, for example, or the Tower.

Barclay has a lot of data that the government would never get to collect, as the video suggests. They should be able to do the allocation with a reasonable amoun