Interesting post, and it's very nice that the author decided to share all the scripts. Forecasting the demand is the first fundamental step to actually optimize the rebalancing operations that usually happen overnight. There is a lot of academic and applied research in this field.
I am glad you enjoyed the post. I have only recently started working with the bike data sets and it has been interesting. I will take a look at those articles. Thanks!
They should offer a cash reward that is less than their internal cost for a rebalancing operation. They should also implement congestion pricing. In Manhattan, I would love to be able to ride a citibike crosstown in mid town. Both stations are full in the middle of the day. If I take a bike out of the dock on the east side, I should get a credit, and I should pay money when I dock it at a busy station on the west side. It would be a wash for me, or I might pay a little. The upside is, those trips should be very easy for citibike to fullfill, it's not like riding out from an empty bike area to a crowded area.
In some cities they reward you for returning bikes to certain locations that have a borrow/return ratio imbalance. For example, they will add bonus minutes to your card so if you go over the standard single-trip time period (e.g. 30 minutes) you can use the extra minutes to avoid getting an extra charge.
Pittsburgh will be getting it's first bike sharing program this May, with 50 stations and I believe about 500 bikes.
If you've ever been to Pittsburgh you will immediately notice how hilly the city is in downtown and in neighboring Oakland. I look forward to the bike sharing program but I don't believe people will be very willing to bike uphill a significant distance without some reward like you are suggesting.
Prof. David Shmoys (Cornell University) is working on optimising the rebalancing operations of the of CitiBike NYC (press article http://www.news.cornell.edu/stories/2015/01/cornell-research...), Prof. Günther Raidl has been doing the same for a while for the CityBike Vienna (Austria) network (http://www.citylab.com/commute/2014/08/balancing-bike-share-...), and three researchers from Udine (Italy), and Vienna (Austria), including myself, have been working on the same problem on similar data sets (summary paper http://link.springer.com/article/10.1007/s10601-015-9182-1, or preprint http://www.tunnuz.net/documents/digaspero_rendl_urli_constra...).