Several bike sharing schemes have been deployed around the world over the last decade, with one launching in London over the summer of 2010. A common operational problem with such schemes is the availability of adequate bikes (enough to satisfy demand from users wishing to depart from an area) as well as empty spaces (in order to accommodate demand from users arriving to an area and wishing to part with their bikes). Arrival and departure patterns are found to vary significantly during the course of each day and the week. To meet both types of demand, bike scheme operators commonly deploy teams that work around the clock repositioning bikes among bike stations throughout the city. Using the London bike sharing scheme as a case study and utilising bike availability data collected from the Transport for London website, we seek to establish bike travel patterns. We then proceed with the development of a bike repositioning algorithm that meets both types of demand while seeking to minimise operational cost. The latter is determined by the amount of teams operating at any time, distance travelled and the amount of bikes that need to be moved across the city as part of this process.