A static free-floating bike repositioning problem with multiple heterogeneous vehicles, multiple depots, and multiple visits

In this paper, a bike repositioning problem with multiple depots, multiple visits, and multiple heterogeneous vehicles for the free-floating bike-sharing system (FFBSS) is studied. Two types of nodes (i.e., easily and hardly access nodes) with different penalties are defined to represent different convenience levels of getting bikes from the FFBSS. The objective of the repositioning is to minimize the weighted sum of the inconvenience level of getting bikes from the system and the total unmet demand and the total operational time. To solve this problem, an enhanced version of chemical reaction optimization (CRO) is developed. A loading and unloading quantity adjustment procedure with the consideration of the node characteristics, including the type of node and its current state (i.e., in a balanced, surplus, or deficit state) is proposed and incorporated into this version to improve its solution quality. A concept of the nearby-node set is also proposed to narrow the search space. Numerical results are presented and indicate that compared to the traditional CRO and CPLEX, the enhanced CRO improves solution quality and has potential to tackle the repositioning problem for larger, longer repositioning duration, and more vehicle instances. The results also demonstrate the effectiveness of the proposed adjustment procedure.