A target-based optimization model for bike-sharing systems: From the perspective of service efficiency and equity

The emergence of bike-sharing systems has considerably improved last- and first-mile transportation systems. To ensure attractiveness to end users, operators aim to design effective service-oriented operational strategies to meet the desired service targets for users. Most existing studies focus on the service efficiency of bike-sharing systems, while service equity is overlooked. In this study, we propose a target-based stochastic distributionally robust optimization (TSDRO) model that addresses both the efficiency and equity of the service level in docked bike-sharing systems under demand uncertainty. We first employ a dissatisfaction risk measure to jointly quantify the probability and magnitude of user dissatisfaction in a zone. Then, we apply a lexicographic-order approach to define the objective function to achieve equity of service among different zones. This lexicographic approach optimizes the worst-off individual and the second-worst zone in an iterative manner. To address demand ambiguity, we use a data-driven method to explore the relationship between the demand distribution and several exogenous factors, including weather and weekends, and then construct a scenario-based distributionally robust optimization model. Based on duality theory and linear decision approximation, this model can be reformulated as a tractable equivalent deterministic model, which can be solved via a bisection-search approach to optimality. Numerical experiments based on real operational data show that compared with the benchmark models, the TSDRO model achieves (i) better out-of-sample performance in terms of service efficiency and (ii) higher service equity among users in different zones. Moreover, setting a lower target level may generate a better solution.