The Bicycle Sharing System (BSS), a public service system operated by the government or a private company, provides the convenient use of a bicycle as a temporary method of transportation. More specifically, this system allows people to rent a bike from one location, use it for a short time period and then return it to either to the same or a different location for an inexpensive fee. With the development of IT technology in the 1990s, it became possible to balance the bicycle inventory among the various destinations. In fact, a critical aspect to maintaining a satisfactory BSS is effectively rebalancing bicycle inventory across the various stations. In this research, we focus on the static bicycle repositioning problem with a single vehicle which is abstracted from the operation issue in the bicycle sharing system. The mathematical model for the static bicycle reposition problem had been created and several variations had been analyzed. This research starts to solve the problem from a very restrictive and constrained model and relaxes the constraints step by step to approach the real world case scenario. Several realistic assumptions have been considered in our research, such as a limited working time horizon, multiple visit limitation for the same station, multiple trips used for the vehicle, etc. In this research, we use the variable neighborhood search heuristic algorithm as the basic structure to find the solution for the static bicycle reposition problem. The numeric results indicate that our algorithms can provide good quality result within short solving time. By solving such a problem well, in comparison to benchmark algorithms, this research provides a starting place for dynamic bicycle repositioning and multiple vehicle repositioning
