An exact approach for the static docked bike rebalancing problem that minimizes the routing costs and unmet demand under various geographic considerations

Abstract

Bike sharing systems have the potential to significantly alleviate traffic congestion, reduce emissions and diminish reliance on parking facilities in city centers. One critical factor influencing the success of a bike sharing system is the effectiveness of rebalancing operations. These operations involve repositioning of the bikes at available stations through pickup and delivery activities performed by trucks, so that the anticipated user demand is satisfied. The Static Docked Bike Rebalancing Problem (SBRP) focuses on determining a cost-effective sequence of stations to be visited by trucks, along with the corresponding quantity of bikes to be picked up or delivered at each station. Deviating from past studies, we propose a new formulation for the SBRP problem which minimizes the cost of rebalancing operations, while factoring in the cost of unsatisfied user demand. The developed mathematical model is a mixed-integer nonlinear program, which is reformulated as a mixed-integer linear program. Lazy constraints and valid inequalities are introduced to improve performance and reduce computational times. A new set of problem instances is also generated based on benchmark problem instances from past studies. The applicability of the proposed methodology is also examined on a real case of the bike rebalancing problem, in the municipality of Penteli, a suburban area of Athens, Greece. The experimental findings demonstrate that the proposed model is capable of solving small scale instances to global optimality. Furthermore, the proposed heuristic manages to match the optimal solutions in very short computational times. To analyze the impact of the geographic distribution of station locations on the total cost of transportation of the rebalancing network, different computational experiments have been performed. The results obtained indicate that the stations’ geographic distribution has a significant impact on the total routing costs of the network.