A mathematical model for re-balancing bike-sharing system bikes using public transportation fleet

The bike-sharing system has proved to be an efficient means of transportation for commuting short-distance trips within urban areas. It provides a cost-effective, flexible, and reliable solutions for commuters. However, managing these systems is complex due to the relocation strategies and operational costs associated with trucks usage which contribute to environmental issues and traffic congestion.Thereby, this paper adopts a planning-oriented approach to conceptualize Ride-a-Bike system named as “RB” comprising of existing Public Transport (PT) buses with bike carriers. This system not only mitigate the issues of bike relocation, but also effective in managing passenger travel requests and optimizing operator’s additional revenues. The system is formulated as a Mixed-Integer Linear Programming (MILP) model to maximize bike relocation operations and operator’s additional revenue, through operation of RB system. Thereby, a trade-off between relocation operations and operator’s additional revenue is introduced through the provision of incentives to RB system passengers. The efficiency of the optimization model is evaluated using the PT network of Genova, Italy considering different operational scenarios involving bike demand, bike surplus, passenger demand, and dwell time thresholds. The results demonstrate that the proposed system efficiently performs bike relocation tasks while simultaneously optimize operator’s additional revenues, all while adhering to dwell time thresholds. The sensitivity analysis of operational parameters highlights the important statistics in terms of their impacts over the optimal objective values. Thus, it provides detailed insights for stakeholders to make informed decisions regarding adjustments to dwell time to better accommodate bike relocation demands.