Joint optimization of the inventory routing problem considering the recycling of broken bikes in the bike-sharing system

Bike-sharing system has become an indispensable element of sustainable urban transportation, effectively resolving the "last mile" transportation challenge for city dwellers. A major daily operational task in these systems is planning a fleet to rebalance the bikes over time, ensuring the optimal availability of bikes and docks to users. Recycling is also a daily work with the an increase in the number of broken bikes. However, rebalancing or recycling operation is always regarded as an independent tasks. They are separately studied in existing papers. Thus, this paper develops an operational strategy for recycling broken bikes during the rebalancing process, and studies the combination of the station inventory and vehicle routing problems. First, an inventory routing model is constructed with the aim of minimizing the total costs including procurement, expected user loss, inventory and transportation costs. Then, a two-stage iterative algorithm is developed with both exact and heuristic algorithms. We use real-world data from Capital Bikeshare to test our proposed model and approach, which shows the two-stage iterative algorithm is efficient and outperforms existing solutions in reducing total costs. Finally, the sensitivity analysis is performed on key parameters such as the vehicle’s capacity, unit penalty costs for customer dissatisfaction events, unit inventory holding costs and the observation period of rebalancing. It shows that enterprises can reduce the total cost by altering vehicle’s capacity, reducing the unit inventory holding costs or changing the observation period of rebalancing.