Service area design and allocation problem for electric bike sharing system under demand uncertainty

Currently, the electric bike sharing system (EBSS) has gained popularity due to its efficiency and eco-friendliness. However, limited battery capacity of electric bikes (EBs) complicates the system design. To address this, we propose a service area design and allocation model incorporating hybrid stations, aiming to maximize daily net profit. Two cases are explored to address demand uncertainty. First, an expected value model is established, where demand is described probabilistically. Second, demand uncertainty is addressed by modeling random variables as uncertain parameters within an uncertainty set. A two-stage robust optimization model is developed, which maximizes the net profit in the worst-case scenario. We design a row generation approach to solve adjustable two-stage robust programs. Numerical experiments with data from the Daha EBSS in Yangzhou, China, demonstrate the model applicability. Moreover, the proposed algorithm outperforms the existing scenario-based approach in terms of both solution quality and computational efficiency.