Repositioning shared bikes under low-carbon policies

•A static bike repositioning problem under low-carbon policies is addressed.•Low-carbon policies include emission cap, carbon trading, carbon offset, and carbon tax.•An improved variable neighborhood search is developed.•The carbon trading policy promotes emission reduction and bike operator growth. Low-carbon policies implemented by the Chinese government have a significant impact on third-party logistics, particularly for bike-sharing operators. This study investigated the static bike repositioning problem under low-carbon policies. Repositioning shared bikes under low-carbon policies such as emission cap, carbon trading, carbon offset, and carbon tax requires strict emission limitations and complicated routing plans. Therefore, a mixed-integer linear programming (MILP) model was formulated for the integrated planning of vehicle routes and bike allocation, aiming to minimize the repositioning cost and total imbalance penalty. An improved variable neighborhood search (IVNS) is proposed to solve this problem. The algorithm includes a route generation strategy heuristic and an improved neighborhood search operator for optimizing the route design, and a greedy heuristic for tackling loading and unloading instructions along the route. Numerical experiments show that (i) the proposed IVNS algorithm outperforms the GUROBI solver and existing method in striking a balance between solution quality and computational time; and (ii) the carbon trading policy is more flexible, not only effectively reducing emissions but also encouraging the further development of the bike-sharing industry.