Balancing Bike Sharing Systems

Bike Sharing Systems became popular in recent years to extend the public transportation network of cities or regions. Most research in this area focuses on finding the optimal locations for bike sharing stations. Still various approaches on how to operate such a system efficiently exist. The usefulness of a bike sharing system strongly depends on the user convenience which is directly connected to the availability of bikes and parking slots when and where they are needed. To increase user convenience a fleet of vehicles (usually cars with a trailer) are used to move bikes between different stations to avoid empty or full stations. The goal of this thesis is to provide an algorithm to efficiently calculate transportation routes for balancing such a bike sharing system to improve user convenience. This problem can be seperated into two different scenarios. The static case focuses on rebalancing the system while there is no user activity or the user activity is negligible (e.g. during night time if users are only allowed to rent bikes during the day time). This thesis is considering the dynamic case, in which the system is still online during the rebalancing process. The proposed algorithm is divided into two parts: solution search and solution evaluation. The first part is implemented using two different variants of a Variable Neighborhood Search (VNS) with an embedded Variable Neighborhood Descent (VND). While the set of neighborhood structures for the VNS variants is equal they differ in the neighborhood structures used for the VND. The solution evaluation part incorporates a Linear Programming (LP) approach to calculate the optimal set of loading instructions for a solution found by the first part. In addition a greedy approach is constructed to calculate a set of loading instructions. Finally three variants (D: complete VND+LP; W: VND(with only two neighborhoods structures used)+LP; G: complete VND+Greedy) are tested on three different sets of test instances with 60, 90 and 120 stations to evaluate the performance of the algorithm. One initial conclusion is that nearly all the given computation time is used to calculate optimal loading instructions with LP. Comparing variant D and W gives the impression that D is performing better although no strong statistical evidence was found. Compared to variant D and W the solutions found by variant G are between 0.5% and 5% worse. On the other hand the greedy approach evaluates about twice as much solutions than the other two methods in the same amount of time. For real world applications the greedy approach may be the better one. Although it is not guaranteed to find the optimal solution it will find good solutions relatively fast.