Optimizing electric bus (EB) scheduling is crucial for advancing urban bus systems and reducing carbon emissions. In this study, we establish an EB scheduling model using a robust optimization paradigm to address the challenges associated with charging demand uncertainty during the operation period. To model the charging process of electric buses (EBs), we adopted a piecewise linear function to handle the nonlinear charging function. This approach improves the practicality of the model while ensuring basic realism. This study introduced a mixed-integer programming model to maximize the profit of the EB system, including the weighted delay time. The main constraints include the departure time window and the charging process. To account for the impact of multiple vehicle types on the scheduling of EBs, a distributed robust optimization model is established for the uncertainty of the EB operation. An instantiated analysis is conducted to schedule an EB line in a Chinese city. The results demonstrate that the distributed robust optimization model enhances the expected profit by approximately 27.27 %-54.24 % compared with the deterministic model. Additionally, the robust optimization model exhibits a steeper increase in expected profit as the uncertainty level increases. Furthermore, the mixed scheduling strategies with multiple vehicle types in the robust optimization model enhance the profit compared to the model relying solely on a single vehicle type. The results demonstrate the applicability and effectiveness of the proposed model for EB scheduling.
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