A robust satisficing multi-objective optimization approach for bike-sharing systems with heterogeneous user types

Diverse subscription policies have been employed to cater to the commuting needs of users in bike-sharing systems. Frequent riders choose to purchase subscriptions to reduce their commuting costs. Thus, operators should improve their service level to maintain the market share. In addition, a small proportion of non-subscribers (e.g, tourists) use the system occasionally but contribute to the operational profits. Thus, providers are willing to fulfill more non-subscriber demand to ensure high profitability. However, jointly optimizing these objectives for the heterogeneous users in bike-sharing systems is challenging, especially under demand uncertainty. To tackle these concerns, this study presents a robust satisficing framework focusing on both service level and profit under demand uncertainty, which frees the decision-makers from formulating the demand ambiguity. This study further defines a novel risk measure, which is formulated according to the $\varphi$-divergence probability distance. The proposed risk measure aims to minimize the violation risk of the service level and profit targets. To avoid overconservation of solutions, side information like weather and weekends is integrated into the model. A tailored local search algorithm is proposed to address large-scale problems, which is capable of integrating rebalancing routes and addressing decentralized demand dynamics. Extensive numerical experiments show that the proposed model achieves higher robustness, lower violation probability and degree, and higher average-case out-of-sample performance than other benchmarks. Managerial insights are also concluded for the operators.